NEET Physics Class 12 Chapter 3 Modern Physics MCQs

Chapter 3 Modern Physics Multiple Choice Questions Exercise -1 Section (A): photoelectric effect

Question 1. A metal surface is illuminated by a light of a given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one-fourth of its original value, then the maximum kinetic energy of the emitted photoelectrons would be:

1. Unchanged
2. 1/16Th of the original value
3. Twice the original value
4. Four times the original value

Answer: 1. Unchanged

Question 2. Mark the correct statement: in photoelectric effect –

1. Electrons are emitted from a metal surface when light falls on it.
2. The kinetic energy of photoelectrons is more for light of longer wavelength in comparison to that due to shorter wavelength.
3. Both of the above
4. None of the above

Answer: 4. None of the above

Question 3. If the threshold wavelength of light for the photoelectric effect from the sodium surface is 6800 aº then, the work function of sodium is

1. 1.8 ev
2. 2.9 ev
3. 1.1 ev
4. 4.7 ev

Answer: 1. 1.8 ev

Question 4. When the distance of a point light source from a photocell is r1, the photoelectric current is i1, if the distance becomes r₂, then the current is i₂, and the ratio (i₁:i₂) is equal to

1. R²₂ : r²₁
2. R² : r₁
3. R₁²: r²₂
4. R₁ : r₂

Answer: 1. R²₂ : r²₁

Question 5. The maximum energy of the electrons released in photocell is independent of

1. Frequency of incident light.
2. Intensity of incident light.
3. Nature of cathode surface.
4. None of these.

Answer: 2. Intensity of incident light.

Question 6. In the photoelectric effect, we assume the photon energy is proportional to its frequency and is completely absorbed by the electrons in the metal. Then the photoelectric current

1. Decreases when the frequency of the incident photon increases.
2. Increases when the frequency of the incident photon increases.
3. Does not depend on the photon frequency but only on the intensity of the incident beam.
4. Depends both on the intensity and frequency of the incident beam.

Answer: 3. Does not depend on the photon frequency but only on the intensity of the incident beam.

Question 7. When stopping potential is applied in an experiment on the photoelectric effect, no photocurrent is observed. This means that

1. The emission of photoelectrons is stopped
2. The photoelectrons are emitted but are reabsorbed by the emitter metal
3. The photoelectrons accumulated near the collector plate
4. The photoelectrons are dispersed from the sides of the apparatus.

Answer: 2. The photoelectrons are emitted but are reabsorbed by the emitter metal

Question 8. If the frequency of light in a photoelectric experiment is doubled then the stopping potential will

1. Be doubled
2. Be halved
3. Become more than double
4. Become less than double

Answer: 3. Become more than double

Question 9. The energy of a photon of frequency ν is e = hν and the momentum of a photon of wavelength λ is p = h/λ. From this statement, one may conclude that the wave velocity of light is equal to E 3 × 108 ms–1

1. 3×10-8 ms-1
2. \(\frac{E}{p}\)
3. Ep
4. \(\left(\frac{E}{p}\right)^2\)

Answer: 2. \(\frac{E}{p}\)

Question 10. Which one of the following graphs in the figure shows the variation of photoelectric current (I) with voltage between the electrodes in a photoelectric cell?

Answer: 1.

Question 11. The collector plate in an experiment on the photoelectric effect is kept vertically above the emitter plate. The light source is put on and a saturation photocurrent is recorded. An electric field is switched on which has a vertically downward direction.

1. The photocurrent will increase
2. The kinetic energy of the electrons will increase
3. The stopping potential will decrease
4. The threshold wavelength will increase

Answer: 2. The kinetic energy of the electrons will increase

Question 12. The frequency and intensity of a light source are both doubled. Consider the following statements.

The saturation photocurrent remains almost the same.

The maximum kinetic energy of the photoelectrons is doubled.

1. Both 1 and 2 are true
2. Is true but 2 is false
3. 1 is false but 2 is true
4. both 1 and 2 are false

Answer: 2. Is true but 2 is false

Question 13. A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential.

1. Will Increase
2. Will Decrease
3. Will Remain Constant
4. Will Either Increase Or Decrease

Answer: 3. Will Remain Constant

Question 14. A point source causes a photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

Answer:

Question 15. The photoelectrons emitted from a metal surface:

1. Are all at rest
2. Have the same kinetic energy
3. Have the same momentum
4. Have speeds varying from zero up to a certain maximum value

Answer: 4. Have speeds varying from zero up to a certain maximum value

Question 16. The stopping potential as a function of the frequency of incident radiation is plotted for two different photoelectric surfaces A and B. The graphs show the work function of A is

1. Greater than that of B
2. Smaller than that of B
3. Same as that of B
4. No comparison can be made from the given graphs.

Answer: 2. Smaller than that of B

Question 17. In an electron gun electrons are accelerated through a potential difference V. If e = charge of electron and m = mass of electron then maximum electron velocity will be

1. 2ev/m
2. \(\sqrt{2 \mathrm{eV} / \mathrm{m}}\)
3. \(\sqrt{2 \mathrm{~m} / \mathrm{eV}}\)

Answer: 2. \(\sqrt{2 \mathrm{eV} / \mathrm{m}}\)

Question 18. Light of wavelength 5000 Å falls on a sensitive plate with a photoelectric work function of 1.9 eV. The kinetic energy of the photoelectron emitted will be:

1. 0.58ev
2. 2.48ev
3. 1.24ev
4. 0.58ev1.16ev

Answer: 1. 0.58ev

Question 19. In the photo-emissive cell, with an exciting wavelength, the fastest electron has speed v. If the exciting wavelength is changed to 3 v1/4, the speed of the fastest emitted electron will be:

1. v (3/4)1/2
2. v (4/3)1/2
3. Less than v (4/3)1/2
4. Greater than v (4/3)

Answer: 4. Greater than v (4/3)

Question 20. When the intensity of incident light increases:

1. Photo – Current Increases
2. Photo – Current Decreases
3. Kinetic Energy Of Emitted Photoelectrons Increases
4. Kinetic Energy Of Emitted Photoelectrons Decreases

Answer: 1. Photo – Current Increases

Question 21. If the wavelength of the photo is 6000 Å, then its energy will be :

1. 0.66 eV
2. 1.66 eV
3. 2.66 eV
4. 3.5 eV

Answer: 3. 2.66 eV

Question 22. Work function a metal is 5.26 × 10–18 then its threshold wavelength will be:

1. 736.7 Å
2. 760.7 Å
3. 301 Å
4. 344.4 Å

Answer: 4. 344.4 Å

Question 23. A radio station transmits waves of wavelength 300 m. Radiation capacity of the transmitter is 10 KW. Find out the number of photons that are emitted per unit of time:

1. 1.5 × 1035
2. 1.5 × 1031
3. 1.5 × 1029
4. 1.5 × 103

Answer: 2. 1.5 × 1031

Question 24. Work function a metal is 5.26 × 10–18 then its threshold wavelength will be:

1. 736.7 Å
2. 760.7 Å
3. 301 Å
4. 344.4 Å

Answer: 2. 760.7 Å

Question 25. A radio station transmits waves of wavelength 300 m. The Radiation capacity of the transmitter is 10 KW. Find out the number of photons that are emitted per unit of time:

1. 1.5 × 1035
2. 1.5 × 1031
3. 1.5 × 1029
4. 1.5 × 103

Answer: 1. 1.5 × 1035

Question 26. The accelerating voltage of an electron gun is 50,000 volts. De-Broglie wavelength of the electron will be

1. 0.55 Å
2. 0.055 Å
3. 0.077 Å
4. 0.095 Å

Answer: 2. 0.055 Å

Question 27. photo-cell is illuminated by a source of light, which is placed at a distance d from the cell, If the sustained becomes d/2, then the number of electrons emitted per second will be:-

1. Remain same
2. Four times
3. Two times
4. One-fourth

Answer: 2. Four times

Question 28. Relation between wavelength of photon and electron of same energy is :

1. \(\lambda_{\text {ph }}>\lambda_e\)
2. \(\lambda_{\mathrm{ph}}<\lambda_{\mathrm{e}}\)
3. \(\lambda_{\mathrm{ph}}<\lambda_{\mathrm{e}}\)
4. \(\frac{\lambda_e}{\lambda_{\mathrm{ph}}}=\text { constant }\)

Answer: 1. \(\lambda_{\text {ph }}>\lambda_e\)

Question 29. The wavelength associated with an electron accelerated through a potential difference of 100 V is nearly

1. 100 Å
2. 123 Å
3. 1.23 Å
4. 0.123 Å

Answer: 4. 0.123 Å

Question 30. The work function of a photometal is 6.63 eV. The threshold wavelength is

1. 3920 Å
2. 1866 Å
3. 186.6 Å
4. 18666 Å

Answer: 2. 1866 Å

Question 31. The speed of an electron having a wavelength of 10–10 m is :

1. 4.24 × 106 m/s
2. 5.25 × 106 m/s
3. 6.25 × 106 m/s
4. 7.25 × 106 m/s

Answer: 4. 7.25 × 106 m/s

Question 32. Sodium and copper have work functions of 2.3 eV and 4.5 eV respectively. Then the ratio of threshold wavelengths is nearest to:

1. 1: 2
2. 4: 1
3. 2: 1
4. 1: 4

Answer: 3. 2: 1

Question 33. The de-Broglie wavelength :

1. Is proportional to the mass
2. Is proportional to the impulse
3. Inversely proportional to the impulse
4. Does not depend on impulse

Answer: 3. Inversely proportional to impulse

Question 34. The minimum wavelength of a photon is 5000 Å, its energy will be :

1. 2.5 eV
2. 50 eV
3. 5.48 eV
4. 7.48 eV

Answer: 1. 2.5 eV

Question 35. The wavelength associated with an electron accelerated through a potential difference of 100 V is of the order of:

1. 1.2Å
2. 10.5 Å
3. 100 Å
4. 1000 Å

Answer: 1. 1.2Å

Question 36. The slope of a graph drawn between threshold frequency and stopping potential is :

1. e
2. h
3. h/e
4. he

Answer: 3. h/e

Question 37. The photoelectric work function of a metal is 3.3 eV. The threshold frequency for this metal is approximately:

1. 3.3 × 1013 Hz
2. 8.0 × 1014 Hz
3. 1.65 × 1015 Hz
4. 9.9 × 1015 Hz

Answer: 2. 8.0 × 1014 Hz

Question 38. A particle of mass 11 × 10–12 kg is moving with a velocity of 6 × 10–7 m/s. Its de–Broglie wavelength is nearly:

1. 10–20 m
2. 10–16 m
3. 10–12 m
4. 10–8 m

Answer: 2. 10–16 m

Question 39. According to Einstein’s photoelectric equation, the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is

Answer: 3.

Question 40. A photosensitive metallic surface has a work function, h v0. If photons of energy 2h v0 fall on this surface, the electrons come, out with a maximum velocity of 4 × 106 m/s. when the photon energy is increased to 5hv 0, then the maximum velocity of photoelectrons will be

1. 2 × 107 m/s
2. 2 × 107 m/s
3. 8 × 105 m/s
4. 8 × 106 m/s

Answer: 4. 8 × 106 m/s

Question 41. When photons of energy hv fall on an aluminum plate (of work function E 0), photoelectrons of maximum kinetic energy K are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be

1. K + E0
2. 2K
3. K
4. K + hv

Answer: 4. K + hv

Question 42. The momentum of a photon of energy 1 MeV is kgm/s, will be:-

1. 0.33 × 106
2. 7 × 10–24
3. 10–22
4. 5 × 10–22

Answer: 4. 5 × 10–22

Question 43. A 5 W source emits monochromatic light of wavelength 5000 Å. When placed 0.5 m away, it liberates photoelectrons from a photosensitive metallic surface, When the source is moved to a distance of 1.0 m, the number of photoelectrons liberated will be reduced by a factor of :

1. 4
2. 8
3. 16
4. 2

Answer: 1.4

Question 44. The work function of the surface of a photosensitive material is 6.2 eV. The wavelength of the incident radiation for which the stopping potential is 5 V lies in the.

1. Ultraviolet region
2. Visible region
3. Infrared region
4. X-ray region

Answer: 1. Ultraviolet region

Question 45. Radiation of energy E falls normally on a perfecting reflecting surface. The momentum transferred to the surface is:

1. E/c
2. 2E/c
3. Ec
4. E/c2

Answer: 2. 2E/c

Question 46. According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal Vs the frequency, of the incident radiation gives a straight line whose slope:

1. Depends on the nature of the metal used
2. Depends on the intensity of the radiation
3. Depends both on the intensity of the radiation and the metal used
4. Is the same for all metals and independent of the intensity of the radiation

Answer: 4. Is the same for all metals and independent of the intensity of the radiation

Question 47. The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately:

1. 540 nm
2. 400 nm
3. 310 nm
4. 220 nm

Answer: 3. 310 nm

Question 48. If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor:

1. 1/2
2. 2
3. \(\frac{1}{\sqrt{2}}\)
4. \(\sqrt{2}\)

Answer: 3. \(\frac{1}{\sqrt{2}}\)

Question 49. The time that a photoelectron comes out after the photon strikes is approximately

1. 10–1 s
2. 10–4 s
3. 10–10 s
4. 10–16 s

Answer: 3. 10–10 s

Question 50. A photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is:

1. v/c
2. svc
3. h v/c2
4. h v/c

Answer: 4. h v/c

Question 51. The threshold frequency for a certain metal is 0. When light of frequency  = 20 is incident on it, the maximum velocity of photoelectrons is 4 x 106 m/s. If the frequency of incident radiation is increased to 5 o, then the maximum velocity of photo-electrons in m/s will be

1. (4/5) × 106
2. 2 × 106
3. 8 × 106
4. 2 × 107

Answer: 3. 8 × 106

Question 52. If the energy of a photon corresponding to a wavelength of 6000 Aº is 3.32 × 10 –19 joule, the photon energy (in joule) for a wavelength of 4000 Aº will be

1. 1.11 × 10–19
2. 2.22 × 10–19
3. 4.44 × 10–19
4. 4.98 × 10–19

Answer: 3. 4.44 × 10–19

Question 53. Light of frequency 1.5 times the threshold frequency is incident on photo-sensitive material. If the frequency is halved and intensity is doubled, the photo-current becomes

1. Quadrupled
2. Doubled
3. Halved
4. Zero

Answer: 4. Zero

Question 54. Which of the following figure, represents the variation of the particle momentum and associated de-Broglie wavelength

Answer: 4.

Question 55. The linear momenta of a proton and an electron are equal. Relative to an electron

1. The kinetic energy of the proton is more.
2. De-Broglie wavelength of the proton is more.
3. De-Broglie wavelength of the proton is less.
4. De-Broglie wavelength of proton and electron are equal.

Answer: 4. De-Broglie wavelength of proton and electron are equal.

Question 56. The maximum velocity of an electron emitted by light of wavelength incident on the surface of a metal of work function  is

1. \(\left[\frac{2(\mathrm{hc}+\lambda \phi)}{\mathrm{m} \lambda}\right]^{1 / 2}\)
2. \(\left[\frac{2(\mathrm{hc}+\lambda \phi)}{\mathrm{m} \lambda}\right]^{1 / 2}\)
3. \(\frac{2(\mathrm{hc}-\lambda \phi)}{\mathrm{m} \lambda}\)
4. \(\frac{2(\mathrm{hc}+\lambda \phi)}{\mathrm{m} \lambda}\)

Answer: 2. \(\left[\frac{2(\mathrm{hc}+\lambda \phi)}{\mathrm{m} \lambda}\right]^{1 / 2}\)

Question 57. The graph is plotted between the maximum kinetic energy of the electron with the frequency of incident photons in the Photoelectric effect. The slope of the curve will be

1. Charge of electron
2. The work function of metal
3. Planck’s constant
4. The ratio of the Planck constant and the charge of the electron

Answer: 3. Planck’s constant

Question 58. Light of frequency v is incident of photon v0. Then work function of the device will be

1. hv
2. hv0
3. h[v-v0]
4. h[v0-v]

Answer: 2. hv0

Question 59. Choose the correct equation

1. \(\frac{\mathrm{h} \lambda}{\mathrm{c}}=\mathrm{E}\)
2. \(\mathrm{h} \lambda=\frac{\mathrm{E}}{\mathrm{c}}\)
3. \(\frac{\mathrm{hc}}{\mathrm{E}}=\lambda\)
4. None of these

Answer: 3. \(\frac{\mathrm{hc}}{\mathrm{E}}=\lambda\)

Question 60. The energy of an electron with a de-Broglie wavelength of 10–10 meters, in [ev] is

1. 13.6
2. 12.27
3. 1.27
4. 150.6

Answer: 4. 150.6

Question 61. If particles are moving with the same velocity, then the maximum de-Broglie wavelength is for

1. Proton
2. α-particle
3. Neutron
4. β-particle

Answer: 4. β-particle

Question 62. The photoelectric effect can be explained by assuming that light

1. Is a form of transverse waves
2. Is a form of longitudinal waves
3. Can be polarised
4. Consists of quanta

Answer: 4. Consists of quanta

Question 63. A proton and photon both have the same energy of E = 100 K eV. The de Broglie wavelength of proton and photon be λ1 and λ2 then λ1/λ2 is proportional to –

1. E–1/2
2. E1/2
3. E–1
4. E

Answer: 2. E1/2

Question 64. The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is:

1. 1
2. 2
3. 3
4. 4

Answer: 1. 1

Question 65. For the photo-electric effect with incident photon wavelength λ, the stopping potential is V0. Identify the correct variation(s) of V0 with λ

Answer: 1.

Question 66. The work functions for metals A, B, and C are respectively 1.92 eV, 2.0 eV, and 5eV According to Einstein’s equation, the metals that will emit photoelectrons for radiation of wavelength 4100 Å is /are:-

1. None
2. An only
3. A and B only
4. All the three metals

Answer: 3. A and B only

Question 67. When a monochromatic source of light is at a distance of 0.2 m from a photoelectric cell, the cut-off voltage and the saturation current are respectively 0.6 V and 18 mA. If the same source is placed 0.6 m away from the cell, then:

1. The Stopping Potential Will Be 0.2 V
2. The Stopping Potential Will Be 1.8 V
3. The Saturation Current Will Be 6.0 Ma
4. The Saturation Current Will Be 2.0 Ma

Answer: 4. The Saturation Current Will Be 2.0 Ma

Question 68. A cesium photocell, with a steady potential difference of 60 volts across it, is illuminated by a small bright light placed 50 cm away. When the same light is placed one meter away, the photoelectrons emerge from the photocell: (assume that the potential difference applied is sufficient to produce saturation current)

1. Each Carry One-Quarter Of Their Previous Energy
2. Each Carry One-Quarter Of Their Previous Momentum
3. Are Half As Numerous
4. Are One Quarter As Numerous

Answer: 4. Are One Quarter As Numerous

Question 69. The work function for aluminium surface is 4.2 eV and that for sodium surface is 2.0 ev. The two metals were illuminated with appropriate radiations to cause photoemission. Then :

1. Both aluminum and sodium will have the same threshold frequency
2. The threshold frequency of aluminum will be more than that of sodium
3. The threshold frequency of aluminium will be less than that of sodium
4. The threshold wavelength of aluminum will be more than that of sodium

Answer: 2. The threshold frequency of aluminum will be more than that of sodium

Question 70. A photoelectric cell is illuminated by a point source of light 1 mm away. When the source is shifted to 2m then

1. Each Emitted Electron Carries One-Quarter Of The Initial Energy
2. Number Of Electrons Emitted Is Half The Initial Number
3. Each Emitted Electron Carries Half The Initial Energy
4. Number Of Electrons Emitted Is A Quarter Of The Initial Number

Answer: 2. Number Of Electrons Emitted Is Half The Initial Number

Question 71. Light of wavelength 4000 Å is incident on a metal plate whose work function is 2eV. What is the maximum kinetic energy of the emitted photoelectron?

1. 0.5 eV
2. 1.1 eV
3. 2.0 eV
4. 1.5 eV

Answer: 2. 1.1 eV

Question 72. The maximum wavelength of radiation that can produce the photoelectric effect in a certain metal is 200 nm. The maximum kinetic energy acquired by an electron due to radiation of wavelength 100 nm will be

1. 12.4 eV
2. 6.2 eV
3. Manganin
4. Aluminium

Answer: 2. 6.2 eV

Question 73. A photoelectric cell is illuminated by a point source of light 1 m away. When the source is shifted to 2 m then-

1. Each emitted electron carries one-quarter of the initial energy.
2. Number of electrons emitted is half the initial number.
3. Each emitted electron carries half the initial energy.
4. Number of electrons emitted is a quarter of the initial number.

Answer: 4. Number of electrons emitted is a quarter of the initial number.

Question 74. A photon of light enters a block of glass after traveling through a vacuum. The energy of the photon on entering the glass block

1. Increases because its associated wavelength decreases
2. Decreases because the speed of the radiation decreases
3. Stays the same because the speed of the radiation and the associated wavelength do not change
4. Stays the same because the frequency of the radiation does not change

Answer: 4. Stays the same because the frequency of the radiation does not change

Question 75. Two separate monochromatic light beams A and B of the same intensity (energy per unit area per unit time) are falling normally on a unit area of a metallic surface. Their wavelength is respectively. Assuming that all the incident light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam A to that from B is

1. \(\left(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}\right)\)
2. \(\left(\frac{\lambda_{\mathrm{B}}}{\lambda_{\mathrm{A}}}\right)\)
3. \(\left(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}\right)^2\)
4. \(\left(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}\right)^2\)

Answer: 1. \(\left(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}\right)\)

Question 76. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. The power of the pulse is 30mV and the speed of light is 3 × 10 ms–1. The final momentum of the object is:

1. 0.3 × 10–17 kg ms–1
2. 1.0 × 10–17 kg ms–1
3. 3.0 × 10–17 kg ms–1
4. 9.0 × 10–17 kg ms–1

Answer: 2. 1.0 × 10–17 kg ms–1

Question 77. When photons of energy hv fall on a photo-sensitive metallic surface (work function hv0) electrons are emitted from the metallic surface. This is known as the photoelectric effect. The electrons coming out of the surface have a K.E. It is possible to say that

1. All ejected electrons have the same K.E. equal to hv – hv0
2. The ejected electrons have a distribution of K.E., the most energetic ones having equal to hv – hv 0
3. The most energetic ejected electrons have K.E. equal to hv.
4. The K.E. of the ejected electrons is hv0

Answer: 2. The ejected electrons have a distribution of K.E., the most energetic ones having equal to hv – hv 0

Question 78. A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is 1 placed 2 m away, the number of electrons emitted by the photocathode would:

1. Decrease By A Factor Of 4
2. Increase By A Factor Of 4
3. Decrease By A Factor Of 2
4. Increase By A Factor Of 2

Answer: 1. Decrease By A Factor Of 4

Chapter 3 Modern Physics Multiple Choice Questions Section (B): De–Broglie Wave (Matterwaves)

Question 1. The ratio of de Broglie wavelengths of a proton and an alpha particle of the same energy is.

1. 1
2. 2
3. 4
4. 0.25

Answer: 2. 2

Question 2. The ratio of de Broglie wavelengths of a proton and an alpha particle moving with the same velocity is

1. 1
2. 2
3. 4
4. 0.25

Answer: 3. 4

Question 3. The ratio of de Broglie wavelengths of a proton and a neutron moving with the same velocity is nearly

1. 1
2. √2
3. 1/√2
4. None of the above

Answer: 1. 1

Question 4. Two particles have identical charges. If they are accelerated through identical potential differences, then the ratio of their de Broglie wavelength would be

1. \(\lambda_1: \lambda_2=1: 1\)
2. \(\lambda_1: \lambda_2=m_2: m_1\)
3. \(\lambda_1: \lambda_2=\sqrt{m_2}: \sqrt{m_1}\)
4. \(\lambda_1: \lambda_2=\sqrt{m_1}: \sqrt{m_2}\)

Answer: 3. \(\lambda_1: \lambda_2=\sqrt{m_2}: \sqrt{m_1}\)

Question 5. If the velocity of a moving particle is reduced to half, then the percentage change in its wavelength will be

1. 100% decrease
2. 100% increase
3. 50% decrease
4. 50% increase

Answer: 2. 100% increase

Question 6. The momentum of the r-ray photon of energy 3 keV in kg-m/s will be

1. 1.6 × 10–19
2. 1.6 × 10–21
3. 1.6 × 10–24
4. 1.6 × 10–27

Answer: 3. 1.6 × 10–24

Question 7. Which one of the following statements is NOT true for de Broglie waves?

1. All atomic particles in motion have waves of a definite wavelength associated with them
2. The higher the momentum, the longer the wavelength
3. The faster the particle, the shorter the wavelength
4. For the same velocity, a heavier particle has a shorter wavelength

Answer: 2. The higher the momentum, the longer the wavelength

Question 8. In a TV tube, the electrons are accelerated by a potential difference of 10 kV. Then, their de Broglie wavelength is nearly

1. 1.2 Å
2. 0.12 Å
3. 12 Å
4. 0.01 Å

Answer: 2. 0.12 Å

Question 9. The de Broglie waves are associated with moving particles. This article may be

1. Electrons
2. He+, li2+ ions
3. Cricket ball
4. All of the above

Answer: 4. All of the above

Question 10. What voltage must be applied to an electron microscope to produce electrons λ = 1.0 Å

1. 190 volt
2. 180 volt
3. 160 volt
4. 150 volt

Answer: 4. 150 volt

Question 11. An α-particle moves along a circular path of radius 0.83 cm in a magnetic field of 0.25 Wb/m 2. The de Broglie wavelength associated with it will be

1. 10 Å
2. 1 Å
3. 0.1 Å
4. 0.01 Å

Answer: 4. 0.01 Å

Question 12. The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 metres per second is approximately – (Planck’s constant, h = 6.63 × 10–34 Js)

1. 10–33 metre
2. 10–31 metre
3. 10–16 metre
4. 10–25 metre

Answer: 1. 10–33 metre

Question 13. The de Broglie wavelength of an electron moving with a velocity of 1.5 × 108 ms–1 is equal to that of a photon. The ratio of the kinetic energy of the electron to that of the energy of a photon is:

1. 2
2. 4
3. 1/2
4. 1/4

Answer: 4. 1/4

Question 14. Let p and E denote the linear momentum and the energy of a photon. For another photon of a smaller wavelength (in the same medium)

1. Both P And E Increase
2. P Increases And E Decreases
3. P Decreases And E Increases
4. Both P And E Decreases

Answer: 1. Both P And E Increase

Chapter 3 Modern Physics Multiple Choice Questions Section(C): Bohr’S Atomic Model Of H-Atom And H-Like Species (Properties)

Question 1. The Lyman series of hydrogen spectrum lies in the region

1. Infrared
2. Visible
3. Ultraviolet
4. Of x – rays

Answer: 3. Ultraviolet

Question 2. Which one of the series of hydrogen spectrum is in the visible region

1. Lyman series
2. Balmer series
3. Paschen series
4. Bracket series

Answer: 2. Balmer series

Question 3. The Rutherford α-particle experiment shows that most of the α–particles pass through almost unscattered while some are scattered through large angles. What information does it give about the structure of the atom:

1. Atom is hollow
2. The whole mass of the atom is concentrated in a small centre called the nucleus
3. The nucleus is positively charged
4. All the above

Answer: 1. Atom is hollow

Question 4. The energy required to knock out the electron in the third orbit of a hydrogen atom is equal to

1. 13.6 eV
2. \(+\frac{13.6}{9} \mathrm{eV}\)
3. \(+\frac{13.6}{9} \mathrm{eV}\)
4. \(+\frac{13.6}{9} \mathrm{eV}\)

Answer: 3. \(+\frac{13.6}{9} \mathrm{eV}\)

Question 5. The ionization potential for the second He electron is

1. 13.6 eV
2. 27.2 eV
3. 54.4 eV
4. 100 eV

Answer: 3. 54.4 eV

Question 6. An electron makes a transition from orbit n 4 to orbit n = 2 of a hydrogen atom. The wave number of the emitted radiation (R = Rydberg’s constant) will be

1. \(\frac{16}{3 R}\)
2. \(\frac{2 R}{16}\)
3. \(\frac{3 R}{16}\)
4. \(\frac{4 \mathrm{R}}{16}\)

Answer: 3. \(\frac{3 R}{16}\)

Question 7. If a 0 is the Bohr radius, the radius of the n = 2 electronic orbit in triply ionized beryllium is –

1. 4a0
2. a0
3. a0/4
4. a0/16

Answer: 2. a0

Question 8. Which energy state of doubly ionized lithium (Li++) has the same energy as that of the ground state of hydrogen? Given Z for lithium = 3 :

1. n = 1
2. n = 2
3. n = 3
4. n = 4

Answer: 3. n = 3

Question 9. If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy state, its orbital speed reduces to half its initial value. If the radius of the electron orbit in the ground state is r, then the radius of the new orbit would be

1. 2r
2. 4r
3. 8r
4. 16r

Answer: 2. 4r

Question 10. The relation between λ₁: the wavelength of the series limit of the Lyman series, λ₂: the wavelength of the series limit of the Balmer series & λ₃: the wavelength of the first line of the Lyman series is:

1. λ₁ = λ₂ + λ₃
2. λ₃ = λ₁ + λ₂
3. λ₂ = λ₃ −λ₁
4. none of these

Answer: 4. none of these

Question 11. let v1 be the frequency of the series limited of the Lyman series, v2 be the frequency of the first line of the Lyman series, and v3 be the frequency of the series limited of the Balmer series.

1. ν₁ = ν₂ + ν₃
2. ν₂ = ν₁ + ν₃
3. \(v_3=\frac{1}{2}\left(v_1+v_3\right)\)
4. ν₁ = ν₂ = ν₃

Answer: 1. ν₁ = ν₂ + ν₃

Question 12. The innermost orbit of the hydrogen atom has a diameter of 1.06 Å. What is the diameter of the tenth orbit?

1. 5.3 Å
2. 10.6 Å
3. 53 Å
4. 106 Å

Answer: 4. 106 Å

Question 13. The energy difference between the first two levels of hydrogen atoms is 10.2 eV. What is the corresponding energy difference for a singly ionized helium atom?

1. 10.2 eV
2. 20.4 eV
3. 40.8 eV
4. 81.6 eV

Answer: 3. 40.8 eV

Question 14. An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom. The energy (In eV) required to remove both the electrons from a neutral helium atom is:

1. 38.2
2. 49.2
3. 51.8
4. 79.0

Answer: 4. 79.0

Question 15. In Bohr’s model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a0 is the radius of the ground state orbit, m is the mass and e is the charge on the electron, 0 is the vacuum permittivity, the speed of the electron is:

1. Zero
2. \(\frac{\mathrm{e}}{\sqrt{\varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)
3. \(\frac{\mathrm{e}}{\sqrt4\pi{\varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)

Answer: 3. \(\frac{\mathrm{e}}{\sqrt4\pi{\varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)

Question 16. The energy of an electron in the excited state of H-tom is –1.5 eV, then according to Bohr’s model, its angular momentum will be:

1. 3.15 × 10–34 J-sec
2. 2.15 × 10–34 J-sec
3. 5.01 × 10–30 J-sec
4. 3.15 × 10–33 J-sec

Answer: 1. 3.15 × 10–34 J-sec

Question 17. The wavelength of radiation emitted is λ0 when an electron jumps from the third to the second orbit of the hydrogen atom. For the electron jump from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be

1. \(\frac{16}{25} \lambda_0\)
2. \(\frac{20}{27} \lambda_0\)
3. \(\frac{27}{20} \lambda_0\)
4. \(\frac{25}{16} \lambda_0\)

Answer: 2. \(\frac{20}{27} \lambda_0\)

Question 18. In which of the following systems will be radius of the first orbit (n =1) be the minimum

1. Doubly Ionized Lithium
2. Singly Ionized Helium
3. Deuterium Atom
4. Hydrogen Atom

Answer: 3. Deuterium Atom

Question 19. The hydrogen atom is excited through a monochromatic radiation of wavelength 975 Å. In the emission spectrum, the number of possible lines are:

1. 2
2. 4
3. 5
4. 6

Answer: 4. 6

Question 20. According to Bohr’s model of the hydrogen atom, the relation between principal quantum number n and radius of stable orbit:

1. \(r \propto \frac{1}{n}\)
2. \(r \propto n\)
3. \(r \propto \frac{1}{n_2}\)
4. \(r \propto \frac{1}{n_2}\)

Answer: 4. \(r \propto \frac{1}{n_2}\)

Question 21. The minimum orbital angular momentum of the electron in a hydrogen atom is

1. h
2. h/2
3. h/2π
4. h/π

Answer: 3. h/2π

Question 22. The energy of a hydrogen-like atom in its ground state is – 54.4 eV. It may be

1. Hydrogen
2. Deuterium
3. Helium
4. Lithium

Answer: 3. Helium

Question 23. The wavelength of light emitted due to the transition of an electron from the second orbit to the first orbit in a hydrogen atom is

1. 6563 Å
2. 4102 Å
3. 4861 Å
4. 1215 Å

Answer: 4. 1215 Å

Question 24. The ratio of the specific charge of an α-particle to that of a proton is

1. 2: 1
2. 1: 1
3. 1: 2
4. 1: 3

Answer: 3. 1: 2

Question 25. If 13.6 eV energy is required to lionize the hydrogen atom, then the energy required to remove an electron from n = 2 is:

1. 10.2 eV
2. 0 eV
3. 3.4 eV
4. 6.8 eV

Answer: 3. 3.4 eV

Question 26. In the Bohr series of lines of the hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits is an atom of hydrogen?

1. 3 → 2
2. 5 → 2
3. 4 → 1
4. 2 → 5

Answer: 2. 5 →2

Question 27. When an electron in a hydrogen atom makes a transition from the first Bohr orbit to the second Bohr orbit, how much energy it absorbs?

1. 3.4 eV
2. 10.2 eV
3. 13.6 eV
4. 1.51 eV

Answer: 2. 10.2 eV

Question 28. The radius of the first Bohr orbit is 0.5 Ã, then the radius of the fourth Bohr orbit will be :

1. 0.03 Å
2. 0.12 Å
3. 2.0 Å
4. 8.0 Å

Answer: 4. 8.0 Å

Question 29. The ionization energy of 10 times ionized sodium atom is

1. \(\frac{13.6}{11} \mathrm{eV}\)
2. \(\frac{13.6}{(11)^2} \mathrm{eV}\)
3. 13.6x(11)2ev
4. 13.6ev

Answer: 3. 13.6x(11)2ev

Question 30. An electron with a kinetic energy of 5 eV is incident on an H-atom in its ground state. The collision

1. Must Be Elastic
2. May Be Partially Elastic
3. May Be Completely Elastic
4. May Be Completely Inelastic

Answer: 1. Must Be Elastic

Question 31. An electron makes a transition from orbit n = 4 to orbit n = 2 of a hydrogen atom. The wave number of the emitted radiation (R = Rydberg’s constant) will be

1. 16/3R
2. 2R/16
3. 3R/16
4. 4R/16

Answer: 3. 3R/16

Question 32. The transition from state n = 4 to b = 3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation may be obtained in the transition

1. 2 → 1
2. 3 → 2
3. 4 → 2
4. 5 → 4

Answer: 4. 5 → 4

Question 33. Energy E of a hydrogen atom with principal quantum number n is given by E = The energy of a photon ejected when the electron jumps from n = 3 state to n = 2 states of hydrogen is passionate:

1. 0.85 eV
2. 3.4 eV
3. 1.9 eV
4. 1.5 eV

Answer: 3. 1.9 eV

Question 34. The total energy of an electron in the first excited state of a hydrogen atom is about – 3.4 V. Its kinetic energy in this state is –

1. –6.8 eV
2. 3.4 eV
3. 6.8 eV
4. –3.4 eV

Answer: 2. 3.4 eV

Question 35. The ionization potential of a hydrogen atom is 13.6eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr’s theory, the spectral lines emitted by hydrogen will be:-

1. Two
2. Three
3. Four
4. One

Answer: 2. Three

Question 36. In the phenomenon of electric discharge through gases at low pressure, the coloured glow in the tube appears as a result of

1. Excitation of electrons in the atoms
2. Collision between the atoms of the gas
3. Collisions between the charged particles emitted from the cathode and the atoms of the gas
4. Collision between different electrons of the atoms of the gas

Answer: 3. Collisions between the charged particles emitted from the cathode and the atoms of the gas

Question 37. The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

1. 3
2. 4
3. 1
4. 2

Answer: 1.

Question 38. An alpha nucleus of energy 2 mv2 bombards a heavy nuclear target of charge Ze. Then the distance of the closest approach for the alpha nucleus will be proportional to the following:

1. \(\frac{1}{\mathrm{Ze}}\)
2. v²
3. 1/m
4. 1/v4

Answer: 3. 1/m

Question 39. The threshold frequency for a metallic surface corresponds to an energy of 6.2 eV, and the stopping potential for a radiation incident on this surface is 5 V. The incident radiation lies in

1. X-ray region
2. Ultra-violet region
3. Infra-red region
4. Visible region

Answer: 2. Ultra-violet region

Question 40. Which of the following transitions in hydrogen atoms emit photons of the highest frequency?

1. n = 2 to n = 6
2. n = 6 to n = 2
3. n = 2 to n = 1
4. n = 1 to n = 2

Answer: 3. n = 2 to n = 1

Question 41. Suppose an electron is attracted towards the origin by a force r where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying the Bohr model to this system, the radius of the nth orbital of the electron is found to be ‘r n’ and the kinetic energy of the electron to be ‘Tn’. Then which of the following is true?

1. Tn independent of n, rn independent of n, Tn1
2. \(T_n \propto \frac{1}{n}, r_n \propto n\)
3. \(T_n \propto \frac{1}{n} n_1, r_n \propto n^2\)
4. \(T_n \propto \frac{1}{n}, r_n \propto n^2\)

Answer: 1. Tn independent of n, rn independent of n, Tn1

Question 42. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of the He + ion is:

1. 1/4
2. 1/2
3. 1
4. 2

Answer: 1. 1/4

Question 43. Energy levels A, B and C of a certain atom correspond to increasing values of energy i.e., E A < EB < EC. If 1, λ2 and λ3 are wave lengths of radiations corresponding to transitions C to B, to A and C to A respectively, which of the following relations is correct –

1. \(\lambda_3=\lambda_1+\lambda_3\)
2. \(\lambda_3=\lambda_2+\lambda_3=0\)
3. \(\lambda_3^2=\lambda_1^2+\lambda_2^2\)
4. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)

Answer: 4. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)

Question 44. If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of Li2+ is :

1. 30.6 eV
2. 13.6 eV
3. 13.6 eV
4. 122.4 eV

Answer: 1. 30.6 eV

Question 45. A hydrogen atom (ionisation potential 13.6 eV) transitions from the third excited state to the first excited state. The energy of the photon emitted in the process is

1. 1.89 eV
2. 2.55 eV
3. 12.09 eV
4. 1275 eV

Answer: 2. 2.55 eV

Question 46. Energy levels A, B and C of a certain atom correspond to increasing energy values, i.e. EA < EB < EC.

If λ1, λ2 and λ3 are the wavelengths of radiations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct?

1. \(\lambda_3=\lambda_1+\lambda_2\)
2. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)
3. \(\lambda_1+\lambda_2+\lambda_3=0\)
4. \(\lambda_3^2=\lambda_1^2+\lambda_2^2\)

Answer: 2. \(\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}\)

Question 47. In a mixture of H – He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He + ions (by collisions). Assume that the Bohr model of the atom is exactly valid. The quantum number n of the state finally populated in He+ ions is:

1. 2
2. 3
3. 4
4. 5

Answer: 3. 4

Question 48. The wavelength of the first spectral line in the Balmer series of hydrogen atoms is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly ionized helium atoms is:

1. 1215 Å
2. 1640 Å
3. 2430 Å
4. 4687 Å

Answer: 1. 1215 Å

Question 49. Which of the following statements is wrong

1. Infrared photon has more energy than photons of visible light.
2. Photographic plates are sensitive to ultraviolet rays.
3. Photographic plates can be made sensitive to infrared rays.
4. Infrared rays are invisible but can cast shadows like visible light rays.

Answer: 1. Infrared photon has more energy than photons of visible light.

Chapter 3 Modern Physics Multiple Choice Questions Section (D): Electronic Transition In The H/H-Like Atom

Question 1. Three photons coming from excited atomic-hydrogen samples are picked up. Their energies are 12.1eV, 10.2eV and 1.9eV. These photons must come from

1. A single atom
2. Two atoms
3. Three atom
4. Either two atoms or three atoms

Answer: 4. Either two atoms or three atoms

Question 2. In a hypothetical atom, if the transition from n = 4 to n = 3 produces visible light then the possible transition to obtain infrared radiation is:

1. n = 5 to n = 3
2. n = 4 to n = 2
3. n = 3 to n = 1
4. None Of These

Answer: 4. None Of These

Question 3. The ionization energy of the hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by electromagnetic radiation of energy 12.1 eV. How many spectral lines will be emitted by the hydrogen atoms?

1. One
2. Two
3. Three
4. Four

Answer: 3. Three

Question 4. The wavelength of the first line in the Balmer series in the hydrogen spectrum is λ. What is the wavelength of the second line :

1. \(\frac{20 \lambda}{27}\)
2. \(\frac{3 \lambda}{16}\)
3. \(\frac{5 \lambda}{36}\)
4. \(\frac{3 \lambda}{4}\)

Answer: 1. \(\frac{20 \lambda}{27}\)

Chapter 3 Modern Physics Multiple Choice Questions Section (E): X–Rays

Question 1. Why do we not use X-rays in the RADAR

1. They can damage the target
2. They are absorbed by the air
3. Their speed is low
4. They are not reflected by the target

Answer: 4. They are not reflected by the target

Question 2. Production of continuous X-rays is caused by

1. Transition of electrons from higher levels to lower levels in target atoms.
2. Retardiation of the incident electron when it enters the target atom.
3. Transition of electrons from lower levels to higher levels in target atoms.
4. Neutralizing the incident electron.

Answer: 2. Retardiation of the incident electron when it enters the target atom.

Question 3. The graph between the square root of the frequency of a specific line of characteristic spectrum of Xrays and the atomic number of the target will be

Question 4. The minimum wavelength min in the continuous spectrum of X-rays is

1. Proportional to the potential difference V between the cathode and anode.
2. Inversely proportional to the potential difference V between the cathode and anode.
3. Proportional to the square root of the potential difference V between the cathode and the anode.
4. Inversely proportional to the square root of the potential difference V between the cathode and the anode.

Answer: 2. Inversely proportional to the potential difference V between the cathode and anode.

Question 5. For the structural analysis of crystals, X-rays are used because

1. X-rays have wavelengths of the order of the inter-atomic spacing.
2. X-rays are highly penetrating radiations.
3. The wavelength of X-rays is of the order of nuclear size.
4. X-rays are coherent radiations.

Answer: 1. X-rays have wavelengths of the order of the inter-atomic spacing.

Question 6. A direct X-ray photograph of the intestines is not generally taken by radiologists because

1. Intestines would burst on exposure to X-rays.
2. The X-rays would not pass through the intestines.
3. The X-rays will pass through the intestines without causing a good shadow for any useful diagnosis.
4. A very small exposure to X-rays causes cancer in the intestines.

Answer: 3. The X-rays will pass through the intestines without causing a good shadow for any useful diagnosis.

Question 7. The characteristic X-ray radiation is emitted when

The bombarding electrons knock out electrons from the inner shell of the target atoms and one of the outer electrons falls into this vacancy.

1. The valance electrons are removed from the target atoms as a result of the collision.
2. The source of electrons emits a mono-energetic beam.
3. The electrons are accelerated to a fixed energy.

Answer: 1. The bombarding electrons knock out electrons from the inner shell of the target atoms and one of the outer electrons falls into this vacancy.

Question 8. X-rays are produced

1. During electric discharge at low pressure.
2. During nuclear explosions.
3. When cathode rays are reflected from the target.
4. When electrons from a higher energy state come back to a lower energy state.

Answer: 4. When electrons from a higher energy state come back to a lower energy state.

Question 9. If the current in the circuit for heating the filament is increased, the cutoff wavelength

1. Will increase
2. Will decrease
3. Will remain unchanged
4. Will change

Answer: 3. Will remain unchanged

Question 10. The characteristic X-ray spectrum is emitted due to the transition of

1. Valence electrons of the atom
2. Inner electrons of the atom
3. Nucleus of the atom
4. Both, the inner electrons and the nucleus of the atom

Answer: 2. Inner electrons of the atom

Question 11. The photoelectric work function for a metal surface is 4.125 eV. The cut-off wavelength for this surface is:

1. 4125 Å
2. 3000 Å
3. 6000 Å
4. 2062.5 Å

Answer: 2. 3000 Å

Question 12. If λmin is the minimum wavelength produced in an X-ray tube and kα is the wavelength of the line. As the operating tube voltage is increased.

1. (λk – λmin) increases
2. (λk – λmin) decreases
3. λkx increases
4. λka decreases

Answer: 1. (λk – λmin) increases

Question 13. X-rays obtained by Coolidge tube:

1. Are mono-chromatic
2. Have all wavelengths are below a maximum wavelength.
3. Have all wavelengths above a minimum wavelength.
4. Have all wavelengths be between a maximum and a minimum wavelength.

Answer: 3. Have all wavelengths are above a minimum wavelength.

Question 14. Penetration power of X-rays depends on 

1. Current flowing in filament
2. Nature of target
3. Applied potential difference
4. All of the above

Answer: 3. Applied potential difference

Question 15. The wavelength of an x-ray photon is 0.01 Å, and its momentum in Kg m/sec is

1. 6.6 x 10–22
2. 6.6 x 10–20
3. 6.6 x 10–46
4. 6.6 x 10–27

Answer: 1. 6.6 x 10–22

Question 16. For hard X-rays.

1. The wavelength is higher
2. The intensity is higher
3. The frequency is higher
4. The photon energy is lower

Answer: 3. The frequency is higher

Question 17. If X-rays are passed through a strong magnetic field, then X-rays

1. Will deviate maximum
2. Will deviate minimum
3. Pass undeviated
4. None of these

Answer: 3. Pass undeviated

Question 18. The minimum wavelength of X-rays produced in a Coolidge tube operated at a potential difference of 40 k V is

1. 0.31 Å
2. 3.1 Å
3. 31 Å
4. 311 Å

Answer: 1. 0.31 Å

Question 19. An X-ray photon has a wavelength of 0.01Å. Its momentum (in kg ms–1) is :

1. 6.66 × 10–22
2. 3.3 × 10–32
3. 6.6 × 10–22
4. 0

Answer: 3. 6.6 × 10–22

Question 20. The minimum wavelength of X-rays emitted by an X-ray tube is 0.4125 Å. The accelerating voltage is :

1. 30 kV
2. 50 kV
3. 80 kV
4. 60 kV

Answer: 1. 30 kV

Question 21. If the frequency of Kα, X-ray of the element of atomic number 31 is f, then the frequency of Kα, X-ray for atomic number 51 is

1. 25/9 f
2. 16/25 f
3. 9/25 f
4. zero

Answer: 1. 25/9 f

Question 22. The intensity of gamma radiation from a given source is. On passing through 36 mm of lead, it is reduced to 1/8. The thickness of lead, which will reduce the intensity to 1/2 will be:

1. 6 mm
2. 9 mm
3. 18 mm
4. 12 mm

Answer: 4. 12 mm

Question 23. Which of the following X-rays has maximum energy, if they are produced by the collision of electrons of energy 40 keV with the same target

1. 300 Å
2. 10 Å
3. 4 Å
4. 0.31 Å

Answer: 4. 0.31 Å

Question 24. Both X-rays and γ-rays are electromagnetic waves, which of the following statements is true for them

1. The energy of X-rays is more than that of γ-rays.
2. The wavelength of X-rays in general, is larger than that of γ-rays.
3. The frequency of X-rays is greater than that of γ-rays.
4. The velocity of X-rays is greater than that of γ-rays.

Answer: 2. Wavelength of X-rays in general, is larger than that of γ-rays.

Question 25. According to Moseley’s law, the ratio of the slopes of the graph between Z for Kβ and Kα is :

1. \(\sqrt{\frac{32}{27}}\)
2. \(\sqrt{\frac{27}{32}}\)
3. \(\sqrt{\frac{33}{22}}\)
4. \(\sqrt{\frac{22}{33}}\)

Answer: 1. \(\sqrt{\frac{32}{27}}\)

Question 26. If the frequency of Kα X-ray emitted from the element with atomic number 31 is f, then the frequency of Kα X-ray emitted from the element with atomic number 51 would be (assume that screening constant for Kα is 1):

1. \(\frac{5}{3} f\)
2. \(\frac{51}{31} f\)
3. \(\frac{9}{25} \mathrm{f}\)
4. \(\frac{25}{9} f\)

Answer: 4. \(\frac{25}{9} f\)

Question 27. Which one of the following statements is WRONG in the context of X-rays generated from an X-ray tube?

1. The wavelength of characteristic X-rays decreases when the atomic number of the target increases
2. The cut-off wavelength of the continuous X-rays depends on the atomic number of the target
3. The intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube
4. The cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube

Answer: 2. Cut-off wavelength of the continuous X-rays depends on the atomic number of the target

Question 28. 50% of the X-rays coming from a Coolidge tube can pass through a 0.1 mm thick aluminum foil. The potential difference between the target and the filament is increased. The thickness of aluminum foil, which will allow 50% of the X-ray to pass through, will be –

1. zero
2. < 0.1 mm
3. 0.1 mm
4. > 0.1 mm

Answer: 4. > 0.1 mm

Question 29. When ultraviolet rays incident on metal plate the photoelectric effect does not occur, it occurs by incidence of:-

1. Infrared rays
2. X – rays
3. Radio wave
4. Lightwave

Answer: 2. X – rays

Question 30. An X-ray photon of wavelength λ and frequency ν collides with an initially stationary electron (but free to move) and bounces off. If λ’ and ν’ are respectively the wavelength and frequency of the scattered photon, then:

1. λ’=λ;ν’=v
2. λ'<λ;ν’>v
3. λ’>λ;ν’>v
4. λ’>λ;ν'<v

Answer: 4. λ’>λ;ν'<v

Chapter 3 Modern Physics Multiple Choice Questions Exercise -2

Question 1. An image of the sun is formed by a lens of focal length 30 cm on the metal surface of a photo-electric cell and it produces a current I. The lens forming the image is then replaced by another lens of the same diameter but of focal length of 15 cm. The photoelectric current in this case will be : (In both cases the plate is kept at the focal plane and normal to the axis lens).

1. I/2
2. 2I
3. I/2
4. 4I

Answer: 3. I/2

Question 2. Two identical, photocathodes receive light of frequencies f1 and f2. If the velocities of the photoelectrons (of mass m) coming out are respectively ν₁ and ν₂, then:

1. \(v_1^2-v_2^2=\frac{2 h}{m}\left(f_1-f_2\right)\)
2. \(v_1-v_2=\left[\frac{2 h}{m}\left(f_1+f_2\right)\right]^{1 / 2}\)
3. \(v_1^2-v_2^2=\frac{2 h}{m}\left(f_1+f_2\right)\)
4. \(v_1-v_2=\left[\frac{2 h}{m}\left(f_1-f_2\right)\right]^{1 / 2}\)

Answer: 1. \(v_1^2-v_2^2=\frac{2 h}{m}\left(f_1-f_2\right)\)

Question 3. Monochromatic light of frequency 6.0 × 1014 Hz is produced by a laser. The power emitted is 2 × 10 –3 W. The number of photons emitted, on the average, by the source per second is:

1. 5 × 1015
2. 5 × 1016
3. 5 × 1017
4. 5 × 1014

Answer: 1. 5 × 1015

Question 4. A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 × 10 6 ms–1. The velocity of the particle is

1. 2.7 × 10–18 ms–1
2. 9 × 10–2 ms–1
3. 3 × 10–31 ms–1
4. 2.7 × 10–21 ms–1
5. (Mass of electron = 9.1 × 10–31 kg)

Answer: 1. 2.7 × 10–18 ms–1

Question 5. The anode voltage of a photocell is kept fixed. The wavelength of the light falling on the cathode is gradually changed. The plate current  of the photocell varies as follows:

Answer: 3.

Question 6. The graph is showing the photocurrent with the applied voltage of a photoelectric effect experiment. Then

1. A and B will have the same intensity and B & C have the same frequency
2. B and C have the same intensity and A & B have the same frequency
3. A and B will have the same frequency and B & C have the same intensity
4. A and C will have the same intensity and B & C have the same frequency

Answer: 1. A and B will have the same intensity and B & C have the same frequency

Question 7. If λ=10–10 m changes to λ’= 0.5 × 10–10 m, find the energy difference (λE) given to the particle :

1. \(\Delta \mathrm{E} \text { is equal to }\left(\frac{1}{4}\right)^{\mathrm{th}} \text { of initial energy }\)
2. \(\Delta E \text { is equal to }\left(\frac{1}{2}\right)^{\text {th }} \text { of initial energy }\)
3. ΔE is equal to twice of initial energy
4. ΔE is equal to the initial energy

Answer: 4. ΔE is equal to the initial energy

Question 8. The wavelength involved in the spectrum of deuterium is slightly different from that of the hydrogen spectrum, because:

1. Size Of The Two Nuclei Are Different
2. Nuclear Forces Are Different In The Two Cases
3. Masses Of The Two Nuclei Are Different
4. Attraction Between The Electron And The Nucleus Is Different In The Two Cases

Answer: 3. Masses Of The Two Nuclei Are Different

Question 9. The total energy of an electron in the ground state of a hydrogen atom is –13.6 eV. The kinetic energy of an electron in the first excited state is:

1. 3.4 eV
2. 6.8 eV
3. 13.6 eV
4. 1.7 eV

Answer: 1. 3.4 eV

Question 10. In the Davisson-Germer experiment when an electron strikes the Ni-crystal which of the following is produced-

1. X-rays
2. ϒ-rays
3. Electron
4. photon

Answer: 3. Electron

Question 11. The wavelengths of Kα x-rays of two metals ‘A’ and ‘B’ are \(\frac{4}{1875 R} \text { and } \frac{1}{675 R}\) respectively, where ‘R’ is rydberg constant. The number of elements lying between ‘A’ and ‘B’ according to their atomic numbers is

1. 3
2. 6
3. 5
4. 4

Answer: 4. 4

Question 12. If Bohr’s theory applies to 100Fm257, then the radius of this atom in Bohr’s unit is:

1. 4
2. 1/4
3. 100
4. 200

Answer: 2. 1/4

Question 13. An electron in an excited state of Li 2+ ions has an angular momentum of 3h/2π. The de-Broglie wavelength of the electron in this state is pa0 (where a0 is the Bohr radius). The value of p is

1. 2
2. 4
3. 6
4. 10

Answer: 1. 2

Question 14. If m is the mass of the electron, ν its velocity, r is the radius of a stationary circular orbit around a nucleus with 1 charge Ze, then from Bohr’s first postulate, the kinetic energy \(\mathrm{K}=\frac{1}{2} m v^2\) of the electron in C.G.S. System is equal to:

1. \(\frac{1}{2} \frac{\mathrm{Ze}^2}{\mathrm{r}}\)
2. \(\frac{1}{2} \frac{\mathrm{Ze}^2}{\mathrm{r}^2}\)
3. \(\frac{1}{2} \frac{\mathrm{Ze}}{\mathrm{r}}\)
4. \(\frac{1}{2} \frac{Z e}{r^2}\)

Answer: 1. \(\frac{1}{2} \frac{\mathrm{Ze}^2}{\mathrm{r}}\)

Question 15. The attractive potential between electron and nucleus is given by v = v0 \(v=v_0 \ell n \frac{r}{r_0}, v_0 \text { and } r_0\) are constants and ‘ r ‘ is the radius. The radius ‘ r ‘ of the nth Bohr’s orbit depends upon principal quantum number ‘n’ as:

1. r∝n2²
2. r∝n
3. \(r \propto \frac{1}{n}\)
4. \(r \propto \frac{1}{n^2}\)

Answer: 2. \(r \propto \frac{1}{n}\)

Question 16. 50% of the x-ray coming from a Coolidge tube can pass through 0.1 mm thick aluminium foil. If the potential difference between the target and the filament is increased, the fraction of the X-ray passing through the same foil will be

1. 0%
2. <50%
3. >50%
4. 50%

Answer: 3. >50%

Question 17. Figure shows the intensity-wavelength relations of X-rays coming from two different Coolidge tubes. The solid curve represents the relation for tube A in which the potential difference between the target and the filament is VA and the atomic number of the target material is ZA. These quantities are VB and Z B for the other tube. Then,

1. V_A > VB Z_A > Z_B
2. V_A > VB, Z_A > Z_B
3. V_A < VB Z_A > Z_B
4. V_A < VB Z_A < Z_B

Answer: 2. V_A > VB Z_A > Z_B

Question 18. Wavelengths of the Kx lines of the two elements are 250 and 179 pm respectively. The number of elements between these elements in the sequence will be

1. Zero
2. 3
3. 2
4. 1

Answer: 2. 2

Question 19. Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

1. \(\lambda_0=\frac{2 \mathrm{mc} \lambda^2}{\mathrm{~h}}\)
2. \(\lambda_0=\frac{2 h}{m c}\)
3. \(\lambda_0=\frac{2 \mathrm{~m}^2 \mathrm{c}^2 \lambda^3}{\mathrm{~h}^2}\)
4. \(\lambda_0=\lambda\)

Answer: 1. \(\lambda_0=\frac{2 \mathrm{mc} \lambda^2}{\mathrm{~h}}\)

Question 20. Which of the following wavelengths is not possible for an X-ray tube which is operated at 40 kV?

1. 0.25 Å
2. 0.5 Å
3. 0.52 Å
4. 1A

Answer: 1. 0.25 Å

Question 21. For soft X-rays, the attenuation constant for aluminum is 1.73 per cm. Then the percentage of X-rays that will pass through an aluminium sheet of thickness 1.156 cm will be

1. 13.5%
2. 6.8%
3. 20.4%
4. 27.0%

Answer: 1. 13.5%

Question 22. An x-ray tube, when operated at 50 kV tube voltage, records an anode current of 20 mA. If the efficiency of the tube for the production of X-rays is 1% then the heat produced per second in calories is nearly

1. 249
2. 238
3. 10
4. 2.38

Answer: 4. 2.38

Question 23. Which of the following are the characteristics required for the target to produce X-rays

1. Atomic number Low High Low High
2. Melting point High High Low Low

Answer: 2. Melting point High High Low Low

Question 24. In a discharge tube when a 200-volt potential difference is applied 6.25 1018 electrons move from cathode to anode and 3.125  1018 singly charged positive ions move from anode to cathode in one second. Then the power of the tube is:

1. 100 watt
2. 200 watt
3. 300 watt
4. 400 watt

Answer: 3. 300 watt

Question 25. The wavelength of Kα X-ray of an element having atomic number z = 11 isλ. The wavelength of Kα

1. 11
2. 44
3. 6
4. 4

Answer: 3. 6

Question 26. The angle volute of the photocell is kept fixed. The wavelength of the light falling on the cathode is gradually changed. The maximum kinetic energy (K.E.) of the photoelectrons emitted varies with as

Answer: 4.

Question 27. A photon of wavelength (less than threshold wavelength0) is incident on a metal surface of work function W 0. The de Broglie wavelength of the ejected electron of mass ‘m’ is

1. \(h\left[2 m\left(\frac{h c}{\lambda}-W_0\right)\right]\)
2. \(\frac{h}{2 m\left(\frac{h c}{\lambda}-W_0\right)}\)
3. \(\frac{h}{\sqrt{2 m\left(\frac{h c}{\lambda}-W_0\right)}}\)
4. \(\frac{1}{h \sqrt{2 m\left(\frac{h c}{\lambda}-W_0\right)}}\)

Answer: 3. \(\frac{h}{\sqrt{2 m\left(\frac{h c}{\lambda}-W_0\right)}}\)

Chapter 3 Modern Physics Multiple Choice Questions Exercise 3 Part -1: Neet / Aipmt Question (Previous Years)

Question 1. Monochromatic light of wavelength 667 nm is produced by a helium-neon laser. The power emitted is 9 mW. The number of photons arriving per second on average at a target irradiated by this beam is

1. 9 × 1017
2. 3 × 1016
3. 9 × 1015
4. 9 × 1019

Answer: 2. 3 × 1016

Question 2. The figure shows a plot of photocurrent versus anode potential for a photo-sensitive surface for three different radiations. Which one of the following is a correct statement?

1. Curves a and b represent incident radiations of different frequencies and different intensities
2. Curves a and b represent incident radiations of the same frequencies but of different intensities
3. Curves b and c represent incident radiations of different frequencies and different intensities
4. Curves b and c represent incident radiations of the same frequencies having the same intensity

Answer: 2. Curves a and b represent incident radiations of the same frequencies but of different intensities

Question 3. The number of photoelectrons emitted for light of a frequency ν is proportional to (higher than the threshold frequency ν0)

1. ν – ν0
2. Threshold Frequency (ν0)
3. Intensity Of Light
4. Frequency Of Light (ν)

Answer: 4. Frequency Of Light (ν)

Question 4. The ionization energy of the electron in the hydrogen atom in its ground state is 13.6 eV. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum wavelength of emitted radiation corresponds to the transition between

1. n = 3 to n = 2 states
2. n = 3 to n = 1 states
3. n = 2 to n = 1 states
4. n = 4 to n = 3 states

Answer: 4. n = 4 to n = 3 states

Question 5. The energy of a hydrogen atom in the ground state is –13.6 eV. The energy of a He+ ion in the first excited state will be

1. – 13.6 eV
2. – 27.2 eV
3. – 54.4 eV
4. – 6.8 eV

Answer: 1. – 13.6 eV

Question 6. A source S 1 is producing 1015 photons per second of wavelength 5000Å. Another source S 2 is producing 1.02 × 1015 photons per second of wavelength 5100 Å. Then (power of S2)/(power of S1) is equal to

1. 1.00
2. 1.02
3. 1.04
4. 0.98

Answer: 1. 1.00

Question 7. The potential difference that must be applied to stop the fastest photoelectrons emitted by a nickel surface, having work function 5.01 eV, when ultraviolet light of 200 nm falls on it, must be

1. 2.4 V
2. –1.2 V
3. – 2.4 V
4. 1.2 V

Answer: 2. –1.2 V

Question 8. When monochromatic radiation of intensity I falls on a metal surface, the number of photoelectrons and their maximum kinetic energy are N and T respectively. If the intensity of radiation is 2I, the number of emitted electrons and their maximum kinetic energy is respectively

1. N and 2T
2. 2N and T
3. 2N and 2T
4. N and T

Answer: 2. 2N and T

Question 9. The electron in the hydrogen atom jumps from its excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV, 13.62 eV the stopping potential is estimated to be (the energy of the electron in n th state \(E_n=-\frac{13.6}{n^2} e V\)

1. 5.1 V
2. 12.1 V
3. 17.2 V
4. 7V

Answer: 4. 7v

Question 10. The threshold frequency for a photosensitive metal is 3.3 × 10 14 Hz. If the light of frequency 8.2 × 1014 Hz is incident on this metal, the cut-off voltage for the photoelectric emission is near:

1. 2V
2. 3V
3. 5V
4. 1V

Answer: 1. 2V

Question 11. An electron in the hydrogen atom jumps from the excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having a work function 2.75 eV. If the stopping potential of the photoelectron is 10 V, the value of n is:

1. 3
2. 4
3. 5
4. 2

Answer: 2. 4

Question 12. Out of the following which one is not a possible energy for a photon to be emitted by a hydrogen atom according to Bohr’s atomic model?

1. 1.9 eV
2. 11.1 eV
3. 13.6 eV
4. 0.65 eV

Answer: 2. 11.1 eV

Question 13. Photoelectric emission occurs only when the incident light has more than a certain minimum:

1. Power
2. Wavelength
3. Intensity
4. Frequency

Answer: 4. Frequency

Question 14. The wavelength of the first line of the Lyman series for hydrogen atoms is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number Z of a hydrogen-like ion is:

1. 3
2. 4
3. 1
4. 2

Answer: 4. 2

Question 15. In the Davisson and Germer experiment, the velocity of electrons emitted from the electron gun can be increased by:

1. Increasing The Potential Difference Between The Anode And Filament
2. Increasing The Filament Current
3. Decreasing The Filament Current
4. Decreasing The Potential Difference Between The Anode And Filament

Answer: 1. Increasing The Potential Difference Between The Anode And Filament

Question 16. The decreasing order of wavelength of infrared, microwave, ultraviolet, and gamma rays is:

1. Microwave, Infrared, Ultraviolet, Gamma Rays
2. Gamma Rays, Ultraviolet, Infrared, Microwaves
3. Microwaves, Gamma Rays, Infrared, Ultraviolet
4. Infrared, Microwave, Ultraviolet, Gamma Rays

Answer: 1. Gamma Rays, Ultraviolet, Infrared, Microwaves

Question 17. Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively illuminate a metallic surface whose work function is 0.5 eV successively. The ratio of maximum speeds emitted electrons will be:

1. 1: 4
2. 1: 2
3. 1: 1
4. 1: 5

Answer: 2. 1: 2

Question 18. Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100kV then the de–Broglie wavelength associated with the electrons would:

1. Increases By 2 Times
2. Decrease By 2 Times
3. Decrease By 4 Times
4. Increases By 4 Times

Answer: 2. Decrease By 2 Times

Question 19. In the photoelectric emission process from a metal of work function 1.8 eV, the kinetic energy of most energetic electrons is 0.5 eV. The corresponding stopping potential is:

1. 1.8 V
2. 1.2 V
3. 0.5 V
4. 2.3 V

Answer: 3. 0.5 V

Question 20. The electron in a hydrogen atom first jumps from the third excited state to the second excited state and then from the second excited to the first excited state. The ratio of the wavelength 1: 2 emitted in the two cases is

1. 7/5
2. 27/20
3. 27/5
4. 20/7

Answer: 4. 20/7

Question 21. A 200 W sodium street lamp emits yellow light of wavelength 0.6 m. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is.

1. 1.5 × 1020
2. 6 × 1018
3. 62 × 1020
4. 3×1019

Answer: 1. 1.5 × 1020

Question 22. An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

1. \(\frac{24 \mathrm{hR}}{25 \mathrm{~m}}\)
2. \(\frac{25 \mathrm{hR}}{24 \mathrm{~m}}\)
3. \(\frac{25 \mathrm{~m}}{24 \mathrm{hR}}\)
4. \(\frac{25 \mathrm{~m}}{24 \mathrm{hR}}\)

Answer: 1. \(\frac{24 \mathrm{hR}}{25 \mathrm{~m}}\)

Question 23. Monochromatic radiation emitted when an electron on a hydrogen atom jumps from first excited to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the materials is :

1. 4 × 1015 Hz
2. 5 × 1015 Hz
3. 1.6 × 1015 Hz
4. 2.5 × 1015 Hz

Answer: 3. 1.6 × 1015 Hz

Question 24. An α-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 Wb/m2. The de Broglie wavelength associated with the particle will be:

1. 1 Å
2. 0.1 Å
3. 10 Å
4. 0.01 Å

Answer: 4. 0.01 Å

Question 25. If the momentum of the electron is changed by P, then the de Broglie wavelength associated with it changes by 0.5%. The initial momentum of the electron will be :

1. 200p
2. 400p
3. \(\frac{P}{200}\)
4. 100p

Answer: 1. 200p

Question 26. Two radiations of photon energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is:

1. 1: 4
2. 1: 2
3. 1: 1
4. 1: 5

Answer: 2. 1: 2

Question 27. The transition from the state n = 3 to n = 1 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

1. 2 → 1
2. 3 → 2
3. 4 → 2
4. 4 → 3

Answer: 4. 4 → 3

Question 28. For photoelectric emission from certain metals, the cutoff frequency is . If radiation of frequency 2 impinges on the metal plate the maximum possible velocity of the emitted electron will be (m is the electron mass):

1. \(\sqrt{\mathrm{h} v / \mathrm{m}}\)
2. \(\sqrt{\mathrm{h} v / \mathrm{m}}\)
3. \(2 \sqrt{h v / m}\)
4. \(2 \sqrt{h v / m}\)

Answer: 2. \(\sqrt{\mathrm{h} v / \mathrm{m}}\)

Question 29. The wavelength λe of an electron and λP of a photon of the same energy E are related by:

1. \(\lambda_{\mathrm{p}} \propto \lambda_{\mathrm{e}}\)
2. \(\lambda_{\mathrm{P}} \propto \sqrt{\lambda_e}\)
3. \(2 \sqrt{h v / m}\)
4. \(\sqrt{\mathrm{h} /(2 \mathrm{~m})}\)

Answer: 4. \(\sqrt{\mathrm{h} /(2 \mathrm{~m})}\)

Question 30. The ratio of longest wavelengths corresponding to the Lyman and Blamer series in the hydrogen spectrum is:

1. \(\frac{3}{23}\)
2. \(\frac{7}{29}\)
3. \(\frac{9}{31}\)
4. \(\frac{9}{31}\)

Answer: 4. \(\frac{9}{31}\)

Question 31. When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increases from emitted 0.5 eV to 0.8eV. The work function of the metal is:

1. 0.65 eV
2. 1.0 eV
3. 1.3 eV
4. 1.5 eV

Answer: 2. 1.0 eV

Question 32. A hydrogen atom in the ground state is excited by a monochromatic radiation of λ = 975 Å. The number of spectral lines in the resulting spectrum emitted will be:

1. 3
2. 2
3. 6
4. 10

Answer: 3. 6

Question 33. Which of the following figures represents the variation of particle momentum and the associated de Broglie wavelength?

Answer: 1.

Question 34. A certain metallic surface is illuminated with monochromatic light of wavelength. The stopping potential for photo-electric current for this light is 3V0. If the same surface is illuminated with light of wavelength 2 the stopping potential is V0, and the threshold wavelength for this surface for photo-electric effect is :

1. 4
2. \(\frac{\lambda}{4}\)
3. \(\frac{\lambda}{6}\)
4. 6

Answer: 1. 4

Question 35. A radiation of energy ‘E’ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C = Velocity of light):

1. \(\frac{2 E}{C}\)
2. \(\frac{2 E}{C^2}\)
3. \(\frac{2 E}{C^2}\)
4. \(\frac{2 E}{C^2}\)

Answer: 1. \(\frac{2 E}{C}\)

Question 36. When a metallic surface is illuminated with radiation of wavelength E the stopping potential is V. If the V same surface is illuminated with radiation of wavelength 2λ, the stopping potential is 4. The threshold wavelength for the metallic surface is:

1. 3
2. 4
3. 5
4. \(\frac{5}{2} \lambda\)

Answer: 1. 3

Question 37. Given the value of the Rydberg constant is 107 m–1, the wave number of the last line of the Balmer series in the hydrogen spectrum will be:

1. 2.5×107 m–1
2. 0.025 ×104 m–1
3. 0.5 ×107 m–1
4. 0.25×107 m–1

Answer: 4. 0.25×107 m–1

Question 38. An electron of mass m and a photon have the same energy E. The ratio of de-Broglie wavelengths associated with them is:

1. \(\frac{1}{c}\left(\frac{2 m}{E}\right)^{\frac{1}{2}}\)
2. \(\frac{1}{c}\left(\frac{E}{2 m}\right)^{\frac{1}{2}}\)
3. \(\left(\frac{E}{2 m}\right)^{\frac{1}{2}}\)
4. \(\lambda_0=\frac{2 m^2 c^2 \lambda^3}{h^2}\)

Answer: 2. \(\frac{1}{c}\left(\frac{E}{2 m}\right)^{\frac{1}{2}}\)

Question 39. Electrons of mass m with de-Broglie wavelength λ fall on the target in an X-ray tube. The cutoff wavelength (λ0) of the emitted X-ray is:

1. \(\lambda_0=\lambda\)
2. \(\lambda_0=\frac{2 m c \lambda^2}{h}\)
3. \(\lambda_0=\frac{2 h}{m c}\)
4. \(\lambda_0=\frac{2 m^2 c^2 \lambda^3}{h^2}\)

Answer: 2. \(\lambda_0=\frac{2 m c \lambda^2}{h}\)

Question 40. Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is:

1. –3 V
2. +3 V
3. +4 V
4. –1 V

Answer: 1. –3 V

Question 41. If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be:

1. \(\frac{20}{13} \lambda\)
2. \(\frac{16}{25} \lambda\)
3. \(\frac{9}{16} \lambda\)
4. \(\frac{20}{7} \lambda\)

Answer: 4. \(\frac{20}{7} \lambda\)

Question 42. The photoelectric threshold wavelength of silver is 3250 × 10 –10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10–10 m is : (Given h = 4.14 × 10–15 eVs and c = 3 × 108 ms–1)

1. 6 × 105 ms–1
2. 0.6 × 106 ms–1
3. 61 × 103 ms–1
4. 0.3 × 106 ms–1 43.

Answer: 1. 6 × 105 ms–1

Question 43. The ratio of wavelengths of the last line of the Balmer series and the last line of Lyman series is

1. 2
2. 1
3. 4
4. 0.5

Answer: 3. 4

Question 44. The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is:

1. \(\frac{h}{\sqrt{\mathrm{mkT}}}\)
2. \(\frac{h}{\sqrt{3 \mathrm{mkT}}}\)
3. \(\frac{2 \mathrm{~h}}{\sqrt{3 \mathrm{mkT}}}\)
4. \(\frac{2 h}{\sqrt{\mathrm{mkT}}}\)

Answer: 2. \(\frac{h}{\sqrt{3 \mathrm{mkT}}}\)

Question 45. The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is:

1. 1: 1
2. 1: – 2
3. 2: –1
4. 1: –1

Answer: 4. 1: –1

Question 46. When the light of frequency 2v0 (where v0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to 5v0, the maximum velocity of electrons emitted from the same plate is v2. The ratio of v1 to v2 is:

1. 1 : 2
2. 2: 1
3. 4: 1
4. 1: 4

Answer: 1. 1: 2

Question 47. An electron of mass m with an initial velocity = V0 (V0 > 0) enters an electric field = – E0 (E0 = constant > 0) at t = 0. If 0 is its de-Broglie wavelength at time t is:

1. \(\frac{\lambda_0}{\left(1+\frac{e E_0}{m V_0} t\right)}\)
2. \(\lambda_0\left(1+\frac{\mathrm{eE}_0}{\mathrm{mV}_0} \mathrm{t}\right)\)

Answer: 1. \(\frac{\lambda_0}{\left(1+\frac{e E_0}{m V_0} t\right)}\)

Question 48. The total energy of an electron in an atom in an orbit is – 3.4 eV. Its kinetic and potential energies are, respectively:

1. 3.4 eV, 3.4 eV
2. –3.4 eV, –3.4 eV
3. –3.4 eV, –6.8 eV
4. 3.4 eV, –6.8 eV

Answer: 4. 3.4 eV, –6.8 eV

Question 49. ∝-particle consists of:

1. 2 protons only
2. 2 protons and 2 neutrons only
3. 2 electrons, 2 protons and 2 neutrons
4. 2 electrons and 4 protons only

Answer: 2. 2 protons and 2 neutrons only

Question 50. An electron is accelerated through a potential difference of 10,000V. Its de Broglie wavelength is, (nearly) : (me = 9×10–31 kg)

1. 12.2 nm
2. 12.2 × 10–13 m
3. 12.2 × 10–12 m
4. 12.2 × 10–14 m

Answer: 3. 12.2 × 10–12 m

Question 51. The radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals 0.51Å and its ground state energy equals –13.6 eV. If the electron in the hydrogen atom is replaced by a muon (u–) [charge same as electron and mass 207 me], the first Bohr radius and ground state energy will be

1. 0.53 × 10–13 m, – 3.6 eV
2. 25.6 × 10–13 m, – 2.8 eV
3. 2.56 × 10–13 m, – 2.8 keV
4. 2.56 × 10–13 m, – 13.6 eV

Answer: 3. 2.56 × 10–13 m, – 2.8 keV

Question 52. The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photon emission from the substance is (approximately)

1. 3100 nm
2. 966 nm
3. 31 nm
4. 310 nm

Answer: 4. 310 nm

Question 53. A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelength and λp λα are in the ratio:

1. 2 :1
2. 2 : 1
3. 1 : 1
4. 4 : 1

Answer: 1. 102 × 10–3 nm

Question 54. The de Broglie wavelength of an electron moving with kinetic energy of 144 eV is nearly

1. 102 × 10–3 nm
2. 102 × 10–4 nm
3. 102 × 10–5 nm
4. 102 × 10–2 nm

Answer: 1. 102 × 10–3 nm

Question 55. The wave nature of electrons was experimentally verified by,

1. de Broglie
2. Hertz
3. Einstein
4. Davisson and Germer

Answer: 4. Davisson and Germer

Question 56. An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength 1.227 10 −2 mm of the electron is the potential difference is

1. 104v
2. 10v
3. 102v
4. 103v

Answer: 1. 104v

Question 57. Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and the intensity is doubled?

1. Zero
2. Doubled
3. Four times
4. One-fourth

Answer: 1. Zero

Question 58. Light with an average flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence having a surface area of 20 cm2. The energy received by the surface during 1 minute

1. 48x103J
2. 10x103J
3. 12x103J
4. 24x103J

Answer: 4. 24x103J

Question 59. An electromagnetic wave of wavelength ‘ λ’ is incident on a photosensitive surface of negligible work λd function. If m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength ‘ λd’ then

• \(\lambda_{\mathrm{d}}=\left(\frac{2 \mathrm{mc}}{\mathrm{h}}\right) \lambda^2\)
• \(\lambda=\left(\frac{2 \mathrm{mc}}{\mathrm{h}}\right) \lambda_{\mathrm{d}}^2\)
• \(\lambda=\left(\frac{2 \mathrm{~h}}{\mathrm{mc}}\right) \lambda_{\mathrm{d}}^2\)
• \(\lambda=\left(\frac{2 \mathrm{~h}}{\mathrm{mc}}\right) \lambda_{\mathrm{d}}^2\)

Answer: 2. \(\lambda=\left(\frac{2 \mathrm{mc}}{\mathrm{h}}\right) \lambda_{\mathrm{d}}^2\)

Question 60. The number of photons per second on average emitted by the source of monochromatic light of h Js 3.3 10-3 = h6.6 10−34 −3 wavelength 600 nm, when it delivers the power of watt be

1. 1017
2. 1016
3. 1015
4. 1018

Answer: 2. 1016

Chapter 3 Modern Physics Multiple Choice Questions Part – 2: Jee (Main) / Aieee Problems (Previous Years)

Question 1. The transition from the state n =4 to n =3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

1. 3 → 2
2. 4 → 2
3. 5 → 4
4. 2 → 1

Answer: 3. 5 → 4

Question 2. The surface of a metal is illuminated with a light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is : (hc = 1240 eV.nm)

1. 1.41 eV
2. 1.51 eV
3. 1.68 eV
4. 3.09 eV

Answer: 1. 1.41 eV

Question 3. Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax. When the ultraviolet light is replaced by X-rays, both V 0 and Kmax increase.

Statement 2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

1. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
2. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1
3. Statement-1 is false, Statement-2 is true.
4. Statement-1 is true, Statement-2 is false.

Answer: 4. Statement-1 is true, Statement-2 is false.

Question 4. If a source of power 4 kW produces 1020 photons/second, the radiation belongs to a part of the spectrum called:

1. X-rays
2. ultraviolet rays
3. microwaves
4. γ-rays

Answer: 1. X-rays

Question 5. The energy required for the electron excitation in Li ++ from the first to the third Bohr orbit is:

1. 12.1 eV
2. 36.3 eV
3. 108.8 eV
4. 122.4 eV

Answer: 3. 108.8 eV

Question 6. This question has Statement –1 and Statement –2. Of the four choices given after the statements, choose the one that best describes the two statements: Statement –1: A metallic surface is irradiated by a monochromatic light of frequency  (the threshold frequency). The maximum kinetic energy and the stopping potential are Kmax and V0 respectively. If the frequency incident on the surface is doubled, both the K max and V 0 are also doubled.

Statement –2:

1. The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.
2. Statement –1 is true, statement –2 is false.
3. Statement –1 is true, Statement –2 is true, Statement –2 is the correct explanation of
   Statement –1
4. Statement –1 is true, Statement –2 is true, Statement –2 is not the correct explanation of Statement–1
5. Statement–1 is false, Statement –2 is true

Answer: 4. Statement–1 is false, Statement –2 is true

Question 7. After absorbing a slowly moving neutron of Mass m N (momentum ≈ 0) a nucleus of mass M breaks into two nuclei of masses m 1 and 5m1 (6 m1 = M + mN ) respectively. If the de Broglie wavelength of the nucleus with mass m 1 is λ, the de Broglie wavelength of the nucleus will be:

1. 5λ
2. λ/5
3. λ
4. 25λ

Answer: 3.

Question 8. The hydrogen atom is excited from ground state to another state with a principal quantum number equal to

1. 2
2. 3
3. 5
4. 6

Answer: 4. 6

Question 4. Then the number of spectral lines in the emission spectra will be:

1. 2
2. 3
3. 5
4. 6

Answer: 4. 6

Question 9. The anode voltage of a photocell is kept fixed. The wavelength of the light falling on the cathode is gradually changed. The plate current of the photocell varies as follows: 

Answer: 4.

Question 10. The radiation corresponding to the 3 → 2 transition of the hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 10 –4 T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to:

1. 1.8 eV
2. 1.1 eV
3. 0.8 eV
4. 1.6 eV

Answer: 2. 1.1 eV

Question 11. Hydrogen (1H¹), Deuterium (1H³), singly ionized Helium (2He4)+, and doubly ionized lithium (3Li6)++ all have one electron around the nucleus. Consider an elelctron transition from n = 2 to n = 1. If the wavelengths of emitted radiation are λ1, λ2, λ3, and λ4 respectively then approximately which one of the following is correct?

1. 4λ1 = 2λ2 = 2λ3 = λ4
2. λ1 = 2λ2 = 2λ3 = λ4
3. λ1 =λ2 = 4λ3 = λ4
4. λ1 = 2λ2 = 3λ3 = 4λ4

Answer: 3. λ1 =λ2 = 4λ3 = λ4

Question 12. As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion

1. Its Kinetic Energy Increases But Potential Energy And Total Energy Decrease
2. Kinetic Energy, Potential Energy, And Total Energy Decrease
3. Kinetic Energy Decreases, Potential Energy Increases But Total Energy Remains the Same
4. Kinetic Energy And Total Energy Decrease But Potential Energy Increases

Answer: 1. Its Kinetic Energy Increases But Potential Energy And Total Energy Decrease

Question 13. Match List-1 Fundamental Experiment) with List-2 (its conclusion) and select the correct option from the choices given below the list :

1. (A) – (1) (B) – (4) (C) – (3)
2. (A) – (2) (B)-(4) (C) – (3)
3. (A) – (2) (B) (1) (C) -(3)
4. (A) – (4) (B) – (3) (C) – (2)

Answer: 3. (A) – (4) (B) – (3) (C) – (2)

Question 14. Radiation of wavelength λis incident on a photocell. The fastest emitted electron has speed υ. If the 3 wavelength is changed to \(\frac{3 \lambda}{4}\), the speed of the fastest emitted electron will be:

1. \(<v\left(\frac{4}{3}\right)^{\frac{1}{2}}\)
2. \(=v\left(\frac{4}{3}\right)^{\frac{1}{2}}\)
3. \(=v\left(\frac{4}{3}\right)^{\frac{1}{2}}\)
4. \(>v\left(\frac{4}{3}\right)^{\frac{1}{2}}\)

Answer: 4. \(>v\left(\frac{4}{3}\right)^{\frac{1}{2}}\)

Question 15. An electron beam is acceleration by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If λmin is the smallest possible wavelength of Xray in the spectrum, the variation of log λmin with log V is correctly represented in:

Answer: 2.

Question 16. A particle A of mass m and initial velocity υ collides with a particle B of mass 2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λA to λB after the collision is:

1. \(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{2}\)
2. \(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{3}\)
3. \(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=2\)
4. \(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{2}{3}\)

Answer: 3. \(\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=2\)

Question 18. If the series limit frequency of the Lyman series is vL, then the series limit frequency of the Pfund series is:

1. vL/16
2. vL/25
3. 25vL
4. 16vL

Answer: 2. vL/25

Question 19. An electron from various excited states of a hydrogen atom emits radiation to come to the ground state. Let λn, and λg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let λn be the wavelength of the emitted photon in transition from the nth state to the ground state. For large n, (A, B are constants)

1. \(\hat{n}_{\mathrm{n}}^2 \approx \mathrm{A}+\mathrm{B} \lambda_{\mathrm{n}}^2\)
2. \(\Lambda_n^2 \approx \lambda\)
3. \(\lambda_n \approx A+\frac{B}{\lambda_n^2}\)
4. \(\wedge_n \approx A+B \lambda_n\)

Answer: 3. \(\lambda_n \approx A+\frac{B}{\lambda_n^2}\)

Question 20. The surface of certain metal is first illuminated with light of wavelength λ1 = 350 nm and then, by the light of wavelength λ2 = 540 nm. It is found that the maximum speed of the photoelectrons in the two cases differs by a factor of 2. The work function of the metal (in eV) is close to:

1. 2.5
2. 5.6
3. 1.4
4. 1.8

Answer: 4. 1.8

Question 21. The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin(3.14 × 107)ct + sin (6.28 × 107)ct]. If this light falls on a sliver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photoelectrons? (c = 3 × 108 ms–1, h = 6.6 × 10–34 J-s)

1. 6.82 eV
2. 12.5 eV
3. 7.72 eV
4. 8.52 eV

Answer: 3. 7.72 eV

Question 22. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. The resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to:

1. 500 keV
2. 25 keV
3. 1 keV
4. 100 keV

Answer: 2. 25 keV

Question 23. A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be : (hc = 12500 eV- Å)

1. 16 a0
2. 25 a0
3. 9a0
4. 4a0

Answer: 1. 16 a0

Question 24. If the de-Broglie wavelength of an electron is equal to 10–3 times the wavelength of a photon of frequency 6 × 1014 Hz, then the speed of the electron is equal to : (Speed of light = 3 × 108 m/s, Planck’s constant = 6.63 × 10–34J. s Mass of electron = 9.1 × 10-31 kg)

1. 1.7 × 106 m/s
2. 1.45 × 106 m/s
3. 1.8 × 106 m/s
4. 1.1 × 106 m/s

Answer: 2. 1.45 × 106 m/s

Question 25. In a hydrogen-like atom, when an electron jumps from the M – M-shell to the L – L-shell, the wavelength of emitted radiation is. If an electron jumps from the N-shell to the L-shell, the wavelength of emitted radiation will be:

1. \(\frac{16}{25} \lambda\)
2. \(\frac{25}{16} \lambda\)
3. \(\frac{20}{27} \lambda\)
4. \(\frac{20}{27} \lambda\)

Answer: 3. \(\frac{20}{27} \lambda\)

Question 26. In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to : ( e hc = 1240 nm–V)

1. 2.0 V
2. 0.5 V
3. 1.0 V
4. 1.5 V

Answer: 3. 1.0 V

Question 27. 2 A particle of mass m moves in a circular orbit in a central potential field U(r) = 2. If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as:

1. \(r_n \propto \sqrt{n}, E_n \propto \frac{1}{n}\)
2. \(r_n \propto \sqrt{n}, E_n \propto n\)
3. \(r_n \propto n^2, E_n \propto \frac{1}{n^2}\)
4. \(r_n \propto \mathrm{n}, \mathrm{E}_{\mathrm{n}} \propto \mathrm{n}\)

Answer: 2. \(r_n \propto \sqrt{n}, E_n \propto n\)

Question 28. A particle A of mass ‘m’ and charge ‘q’ is accelerated by a potential difference of 50 V. Another particle B of mass 4m and charge q is accelerated by a potential difference of 2500 V. The ratio of de–Broglie A wavelengths \(\mathrm{} \frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}\) is close to

1. 14.14
2. 10.00
3. 0.07
4. 4.47

Answer: 1. 14.14

Question 29. An alpha-particle of mass m suffers 1 -1-dimensional elastic collision with a nucleus at rest of unknown mass. it’s scattered directly backward losing, 64% of its initial kinetic energy. The mass of the nucleus is:

1. 3.5 m
2. 1.5 m
3. 4 m
4. 2 m

Answer: 3. 4 m

Question 30. When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photocurrent is \(-\frac{V_0}{2}\) When the surface is illuminated by monochromatic light of frequency \(\frac{v}{2},\) the stopping potential is –V0. The threshold frequency for photoelectric emission is:

1. \(\frac{4}{3} v\)
2. 2v
3. \(\frac{3 v}{2}\)
4. \(\frac{5 v}{3}\)

Answer: 3. \(\frac{3 v}{2}\)

Question 31. In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapor and emerges with an energy of 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to:

1. 1700 nm
2. 220 nm
3. 2020 nm
4. 250 nm

Answer: 4. 250 nm

Chapter 3 Modern Physics Multiple Choice Questions Self Practice Paper

Question 1. Yellow light of 557 nm wavelength is incident on a cesium surface. It is found that no photoelectrons flow in the circuit when the cathode-anode voltage drops below 0.25V. Then the threshold wavelength for the photoelectric effect from cesium is

1. 577 nm
2. 653 nm
3. 734 nm
4. 191 nm

Answer: 2. 653 nm

Question 2. The helium atom emits a photon of wavelength 0.1 A. The recoil energy of the atom due to the emission of photons will be

1. 2.04 eV
2. 4.91 eV
3. 1.67 eV
4. 9.10 eV

Answer: 1. 2.04 eV

Question 3. Electrons with an energy of 80 keV are incident on the tungsten target of an X−ray tube. K shell electrons of tungsten have −72.5keV energy. X−rays emitted by the tube contain only

1. A continuous x−ray spectrum (bremsstrahlung) with a minimum wavelength of ~ 0.155å.
2. A continuous X-ray spectrum (bremsstrahlung) with all wavelengths.
3. The characteristic x−ray spectrum of tungsten.
4. A continuous x−ray spectrum (bremsstrahlung) with a minimum wavelength of ~ 0.155å and the characteristic x−ray spectrum of tungsten.

Answer: 4. A continuous X-ray spectrum (bremsstrahlung) with a minimum wavelength of ~ 0.155å and the characteristic X-ray spectrum of tungsten.

Question 4. Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has a wavelength (given in terms of the Rydberg constant R for the hydrogen atom) equal to

1. 9/(5R)
2. 36/(5R)
3. 18/(5R)
4. 4/R

Answer: 3. 18/(5R)

Question 5. For the case discussed above, the wavelength of light emitted in the visible region by He + ions after collisions with H atoms is

1. 6.5 × 10–7 m
2. 5.6 × 10–7 m
3. 4.8 × 10–7 m
4. 4.0 × 10–7 m

Answer: 3. 4.8 × 10–7 m

Question 6. Photoelectric effect experiments are performed using three different metal plates p, q, and r having work functions p = 2.0 eV, vq = 2.5 eV, and vr = 3.0 eV respectively. A light beam containing wavelengths of 550 nm, 450 nm, and 350 nm with equal intensities illuminates each of the plates. The correct -V graph for the experiment is [Take hc = 1240 eV nm

Answer: 1.

Question 7. If λCu is the wavelength of the Kα X-ray line of copper (atomic number 29) and λMo is the wavelength of the Kα X-ray line of molybdenum (atomic number 42), then the ratio λCu/λMo is close to

1. 1.99
2. 2.14
3. 0.50
4. 0.48

Answer: 2. 2.14

Question 8. A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u 1 and u 2, respectively. If the ratio u 1: u2 = 2: 1 and hc = 1240 eV nm, the work function of the metal is nearly

1. 3.7 eV
2. 3.2 eV
3. 2.8 eV
4. 2.5 eV

Answer: 1. 3.7 eV

Question 9. Consider a hydrogen atom with its electron in the nth orbital. Electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm)

1. 1
2. 2
3. 3
4. 4

Answer: 2. 2

Question 10. The orbital angular momentum for an electron revolving in an orbit is given by. This momentum for an s-electron will be given by –

1. \(+\frac{1}{2} \cdot \frac{h}{2 \pi}\)
2. Zero
3. \(\frac{\mathrm{h}}{2 \pi}\)
4. \(\sqrt{2} \cdot \frac{h}{2 \pi}\)

Answer: 2. Zero

Question 11. In Bohr’s model of the hydrogen atom, the centripetal force is provided by the Coulomb attraction between the proton and the electron. If a0 is the radius of the ground state orbit, m is the mass e is the charge of an electron and e0 is the vacuum permittivity, the speed of the electron is:

1. zero
2. \(\frac{\mathrm{e}}{\sqrt{\varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)
3. \(\frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)
4. \(\frac{\sqrt{4 \pi \varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}{\mathrm{e}}\)

Answer: 3. \(\frac{\mathrm{e}}{\sqrt{4 \pi \varepsilon_0 \mathrm{a}_0 \mathrm{~m}}}\)