NEET Physics Class 12 Chapter 4 Nuclear Physics MCQ’s

Chapter 4 Nuclear Physics Multiple Choice Questions Exercise 1 Section (A): Properties Of The Nucleus

Question 1. The mass number of a nucleus is

1. Always less than its atomic number
2. Always more than its atomic number
3. Equal to its atomic number
4. Sometimes more than and sometimes equal to its atomic number

Answer: 4. Sometimes more than and sometimes equal to its atomic number

Question 2. The stable nucleus that has a radius 1/3 that of os189 is –

1. ₃Li⁷
2. ₂He⁴
3. ₅B¹⁰
4. ₆C¹²

Answer: 1. ₃Li⁷

Question 3. For a uranium nucleus, how does its mass vary with volume?

1. m ∝ v
2. M ∝ 1/v
3. M ∝ \(\sqrt{V}\)
4. M ∝ v²

Answer: 1. m ∝ v

Question 4. The graph of ln (R/R₀) versus ln A (r = radius of a nucleus and a = its mass number) is

1. A straight line
2. A parabola
3. An ellipse
4. None of them

Answer: 1. A straight line

Question 5. 1 Amu is equivalent to:

1. 931 Mev
2. 0.51ev
3. 9.31 mev
4. 1.02 mev

Answer: 1. 931 Mev

Question 6. If the mass number for an element is m and the atomic number is z, then several neutrons will be :

1. M – z
2. Z –m
3. M + z
4. Z

Answer: 1. M – z

Question 7. Which of the following particles has a similar mass to an electron?

1. Proton
2. Neutron
3. Positron
4. Neutrino

Answer: 3. Positron

Question 8. Different atoms of the same element which have different masses but have the same chemical properties are called:

1. Isochoric
2. Isotope
3. Isobar
4. Isobaric

Answer: 2. Isotope

Question 9. The Mass-energy equation e = mc² was given by

1. Newton
2. Kepler
3. Einstein
4. Millikan

Answer: 3. Einstein

Question 10. The mass numbers of nuclei a and b are respectively 135 and 5. The ratio of their radii is:

1. 1: 27
2. 27 :1
3. 1 : 3
4. 3: 1

Answer: 2. 27 :1

Question 11. If the nucleus 125 13 52 ai has a nuclear radius of about 3.6 fm, then it would have its radius approximately as :

1. 6.0 FM
2. 9.6 FM
3. 12.0 FM
4. 4.8 FM

Answer: 1. 6.0 FM

Question 12. Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

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

Answer: 4. 1/3: 1

Question 13. A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2: 1. The ratio of their nuclear sizes will be:

1. 21/3 : 1
2. 1: 31/2
3. 31/2 : 1
4. 1: 21/3

Answer: 4. 1: 21/3

Question 14. If the radius of the 125 13 52 al the nucleus is estimated to be 3.6 fermis, then the radius of the nucleus is near:

1. 6 Fermi
2. 8 Fermi
3. 4 Fermi
4. 5 Fermi

Answer: 1. 6 Fermi

Question 15. The uncle of which one of the following pairs of nuclei are isotones:-

1. ₃₄Se⁷⁴, ₃₁Ga⁷¹
2. ₃₈Sr⁸⁴, ₃₈Sr⁸⁶
3. ₄₂Mo⁹²,₄₀Zr⁹²
4. ₂₀Ca⁴⁰,₁₆S³²

Answer: 1. ₃₄Se⁷⁴, ₃₁Ga⁷¹

Question 16. The range of a nuclear force is approximate –

1. 2 × 10^–10 M
2. 1.5 × 10^–20 m
3. 7.2 × 10^–4 m
4. 1.4 × 10^–15 m

Answer: 4. 1.4 × 10^–15 m

Question 17. The order of magnitude of the density of the uranium nucleus is, (m
p = 1.67 × 10–27 kg):

1. 1020 Kg m^–3
2. 1017 Kg m^–3
3. 1014 Kg m^–3
4. 1011 Kg m^–3

Answer: 2.1017 Kg m^–3

Question 18. Which has the highest penetrating power?

1. γ-Rays
2. β-Rays
3. α-Rays
4. Cathode rays

Answer: 1. γ-Rays

Question 19. The penetrating power is minimal for

1. α– Rays
2. β – Rays
3. ϒ – Rays
4. X – rays

Answer: 1. α– Rays

Chapter 4 Nuclear Physics Multiple Choice Questions Section (B): Mass Defect And Binding Energy

Question 1. Two protons are kept at a separation of 50Å. F n is the nuclear force and F e is the electrostatic force between them, then

1. F_n>>F_e
2. F_n=F_e
3. F_n<<F_e
4. F_nF_e

Answer: 3. F_n<<F_e

Question 2. Masses of nucleus, neutron, and protons are M, n m, and m p respectively. If the nucleus has been divided into neutrons and protons, then

1. M=(A-Z)m_n+Zm_p
2. M=ZM_n+(A-Z)m_p
3. M<A(A-X)m_n+Xm_p
4. M>(A-z)m_n+Zm_p

Answer: 2. M=ZM_n+(A-Z)m_p

Question 3. As the mass number A increases, the binding energy per nucleon in a nucleus

1. Increases
2. Decreases
3. Remains The Same
4. Varies In A Way That Depends On The Actual Value Of A.

Answer: 4. Varies In A Way That Depends On The Actual Value Of A.

Question 4. Which of the following is a wrong description of the binding energy of a nucleus?

1. It is the energy required to break a nucleus into its constituent nucleons.
2. It is the energy released when free nucleons combine to form a nucleus
3. It is the sum of the rest of the mass energies of its nucleons minus the rest of the mass energy of the nucleus
4. It is the sum of the kinetic energy of all the nucleons in the nucleus

Answer: 4. It is the sum of the kinetic energy of all the nucleons in the nucleus

Question 5. The energy of the reaction Li7 + p → 2 He4 is (the binding energy per nucleon in Li7 and He4 nuclei are 5.60 and 7.06 MeV respectively.)

1. 17.3 MeV
2. 1.73 MeV
3. 1.46 MeV
4. Depends On Binding Energy Of Proton

Answer: 1. 17.3 MeV

Question 6. Let Fpp, F on, and F nn denote the magnitudes of the nuclear force by a proton on a proton, by a proton on a neutron, and by a neutron on a neutron respectively. When the separation is 1 FM,

1. F_pp > F_pn = F _nn
2. F_pp= F_pn = F_nn
3. F_pp> F_pn > F_nn
4. F_pp< F_pn = F_nn

Answer: 2. F_pp= F_pn = F_nn

Question 7. The binding energies of two nuclei Pⁿ and Q²ⁿ and x and y joules. If 2x > y then the energy released in the reaction Pⁿ + Pⁿ → Q2ⁿ, will be

1. 2x + y
2. 2x – y
3. –(2x – y)
4. x + y

Answer: 3. –(2x – y)

Question 8. ₁H¹ + ₁H¹ + ₁H²→ X + ₁e⁰ + energy .The emitted particle is-

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

Answer: 3. α-particle

Question 9. In the following equation, particle X will be ₆C¹¹ → 5B¹¹ + β¹ + X

1. Neutron
2. Antineutrino
3. Neutrino
4. Proton

Answer: 3. Neutrino

Question 10. The mass of a proton is 1.0073 u and that of the neutron is 1.0087 u (u = atomic mass unit). The binding 24He energy of is (Given:- helium nucleus mass 4.0015 u)

1. 0.0305 J
2. 0.0305 erg
3. 28.4 MeV
4. 0.061 U

Answer: 3. 28.4 MeV

Question 11. The mass number of a nucleus is

1. Always Less Than Its Atomic Number
2. Always More Than Its Atomic Number
3. Sometimes Equal To Its Atomic Number
4. Sometimes Less Than And Sometimes More Than Its Atomic Number

Answer: 3. Sometimes Equal To Its Atomic Number

Question 12. For the stability of any nucleus

1. Binding Energy Per Nucleon Will Be More
2. Binding Energy Per Nucleon Will Be Less
3. Number Of Electrons Will Be More
4. None Of The Above

Answer: 1. Binding Energy Per Nucleon Will Be More

Question 13. IF Mo is the mass of an oxygen isotope 8O17, Mp and Mn are the masses of a proton and a neutron, respectively the nuclear binding energy of the isotope is

1. (M0 – 8Mp) C²
2. ( Mo – 8MP – 9Mn) C²
3. Moc²
4. (Mo – 17 Mn) C²

Answer: ( Mo – 8MP – 9Mn) C²

Question 14. If in a nuclear fusion process, the masses of the fusing nuclei are m 1 and m2 and the mass of the resultant nucleus is m 3, then

1. m₃ = |m₁ – m₂|
2. m₃ < (m₁ + m₂)
3. m₃ > (m₁ + m₂)
4. m₃ = m₁ + m₂)

Answer: 2. m₃ < (m₁ + m₂)

Question 15. M p denotes the mass of a proton and M n that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M (N, Z) of the nucleus is given (c is the velocity of light)

1. M(N, Z) = NM n + ZM p + B/c²
2. M(N, Z) = NM n + ZM p – B/c²
3. M(N, Z) = NM n + ZM p + B/c²
4. M(N, Z) = NM n + ZM p – B/c²

Answer: 2. M(N, Z) = NM n + ZM p – B/c²

Question 16. In the reaction \({ }_1^2 \mathrm{H}+{ }_1^3 \mathrm{H} \rightarrow{ }_2^4 \mathrm{HE}+{ }_0^1 \mathrm{n} .\). If the binding energies of H, H and He are respectively a, b, and c (in MEV), then the energy (in MeV released in this reaction is)

1. a + b + c
2. c + a + b
3. c – (a + b)
4. a + b + c

Answer: 3. c – (a + b)

Question 17. The binding energy of deuteron is 2.2 MeV and that of He is 28 MeV. If two deuterons are fused to 4 form one 2 He then the energy released is:-

1. 25.8 MeV
2. 23.6 MeV
3. 19.2 MeV
4. 30.2 MeV

Answer: 2. 23.6 MeV

Question 18. If the binding energy per nucleon in and nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction \(\mathrm{p}+{ }_3^7 \mathrm{Li} \rightarrow 2{ }_2^4 \mathrm{He}\) energy of proton must be :

1. 39.2 MeV
2. 28.24 MeV
3. 17.28 MeV
4. 1.46 MeV

Answer: 3. 17.28 MeV

Question 19. If Mp is the mass of an oxygen isotope 8O17, M p and MN are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is:

1. (M_ο – 8MP)C²
2. (M_o – 8MP – 9MN)C²
3. M_oC²
4. (M_o – 17M N)C²

Answer: 2. M_oC²

Question 20. Binding energy per nucleon is of the order of –

1. 7.6 eV
2. 7.6 μeV
3. 7.6 MeV
4. 7.6 KeV

Answer: 3. 7.6 MeV

Question 21. A free neutron decays to a proton but a free proton does not decay to a neutron. This is because

1. A neutron Is A Composite Particle Made Of A Proton And An Electron Whereas Proton Is a Fundamental Particle
2. Neutron Is An Uncharged Particle Whereas Proton Is A Charged Particle
3. Neutron Has Larger Rest Mass Than The Proton
4. Weak Forces Can Operate In A Neutron But Not In A Proton.

Answer: 3. Neutron Has Larger Rest Mass Than The Proton

Question 22. M P and MN are masses of proton and neutron, respectively, at rest. If they combine to form a deuterium nucleus. The mass of the nucleus will be:

1. Less Than M_p
2. Less Than (M_p + M_n)
3. Less Than (M_p + 2m_n)
4. Greater Than (M_p + 2m_n)

Answer: 2. Less Than (M_p + M_n)

Question 23. The figure shows a plot of binding energy per nucleon (B.E/A) vs mass number (A) for nuclei. Four nuclei, P, Q, R, and S are indicated on the curve. The process that would release energy is

1. R → 2S
2. P → Q + S
3. P → 2R
4. Q → R + S

Answer: 3. P → 2R

Question 24. A positron of 1MeV collides with an electron of 1 MeV and gets annihilated and the reaction produces two-ray photons. If the effective mass of each photon is 0.0016 amu, then the energy of each ray photon is about-

1. 1.5 MeV
2. 3 MeV
3. 6 MeV
4. 2 MeV

Answer: 1. 1.5 MeV

Question 25. Masses of two isobars \({ }_{29}^{64} \mathrm{Cu} \text { and }{ }_{30}^{64} \mathrm{Zn}\) 63.9298 u and 63.9292 u respectively. It can be concluded from these data that:

1. Both the isobars are stable
2. 64Zn is radioactive, decaying to 64Cu through -decay
3. 64Cu is radioactive, decaying to 64Zn through -decay
4. 64Cu is radioactive, decaying to 64Zn through -decay

Answer: 4. 64Cu is radioactive, decaying to 64Zn through -decay

Question 26. The binding energy per nucleon vs. mass number curve for nuclei is shown in the figure. W, X, Y, and Z are four nuclei indicated on the curve. The process that would release energy is :

1. Y → 2Z
2. W → X + Z
3. W → 2Y
4. X → Y + Z

Answer: 3. W → 2Y

Chapter 4 Nuclear Physics Multiple Choice Questions Section (C): Radioactive Decay And Displacement Law

Question 1. An α-particle is bombarded on 14N. As a result, a 17O nucleus is formed and a particle is emitted. This article is a

1. Neutron
2. Proton
3. Electron
4. Positron

Answer: 2. Proton

Question 2. A free neutron decays into a proton, an electron, and:

1. A neutrino
2. An antineutrino
3. An α-article
4. A α-particle

Answer: 2. An antineutrino

Question 3. The specific activity (per gm) of radium is near –

1. 1 Bq
2. 1 Ci
3. 3.7 × 1010 Ci
4. 1 mCi

Answer: 2. 3.7 × 1010 Ci

Question 4. When a β¯ -particle is emitted from a nucleus, the neutron-proton ratio :

1. Is Decreased
2. Is Increased
3. Remains The Same
4. First Then (2)

Answer: 1. Is Decreased

Question 5. In one α and 2β-emissions:

1. Mass Number Reduces By 2
2. Mass Number Reduces By 6
3. Atomic Number Reduces By 2
4. Atomic Number Remains Unchanged

Answer: 4. Atomic Number Remains Unchanged

Question 6. Which ray contains (+Ve) charge particle :

1. α-rays
2. β-rays
3. γ-rays
4. X-rays

Answer: 1. α-rays

Question 7. Which of the following cannot be bombarded to disintegrate a nucleus –

1. α-ray
2. γ-ray
3. β-ray
4. Laser

Answer: 4. Laser

Question 8. Which of the following is a correct statement?

1. Beta Rays Are the Same As Cathode Rays.
2. Gamma Rays Are High Energy Neutrons.
3. Alpha Particles Are Singly-Ionized Helium Atoms.
4. Protons And Neutrons Have Exactly The Same Mass.

Answer: 1. Beta Rays Are Same As Cathode Rays.

Question 9. A deutron is bombarded on a ₇O¹⁶ nucleus then α-particle is emitted then the product nucleus is :

1. ₇N¹²
2. ₅B¹⁰
3. ₄Be⁹
4. ₇N¹⁴

Answer: 4. ₇N¹⁴

Question 10. An α– particle is bombarded on N¹⁴ As. a result, an O¹⁷ -nucleus is formed and a particle X is emitted. The particle X is

1. Neutron
2. Proton
3. Electron
4. Positron

Answer: 2. Proton

Question 11. In the reaction \({ }_{92} X^{234} \longrightarrow_{87} Y^{222}\) How many α-particles and β-particles are emitted?

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

Answer: 4. 3 and 1

Question 12. Which of the following radiations has the least wavelength?

1. γ-rays
2. β-rays
3. α-rays
4. X-rays

Answer: 1. γ-rays

Question 13. When U 238 nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is

1. \(\frac{4 u}{238}\)
2. \(-\frac{4 u}{234}\)
3. \(\frac{4 u}{234}\)
4. \(-\frac{4 \mathrm{u}}{238}\)

Answer: 3. \(\frac{4 u}{234}\)

Question 14. A nucleus with Z = 92 emits the following in a sequence : α, α, β–, β–, α, α, α, α; β–, β–, α. The Z of the resulting nucleus is:

1. 76
2. 78
3. 82
4. 74

Answer: 2. 78

Question 15. A nuclear reaction given by \(X^A \rightarrow_{z+1} Y^A+{ }_{-1} \mathrm{e}^0+\bar{v}\)

1. β-decay
2. γ-decay
3. fusion
4. fission

Answer: 1. β-decay

Question 16. In the radioactive decay process, the negatively charged emitted  – particles are

1. The Electrons Present Inside The Nucleus
2. The Electrons Produced Inside As A Result Of The Decay Of Neutrons Inside The Nucleus
3. The Electrons Produced As A Result Of Collisions Between Atoms
4. The Electrons Orbiting Around The Nucleus

Answer: 2. The Electrons Produced Inside As A Result Of The Decay Of Neutrons Inside The Nucleus

Question 17. Ub the disintegration series \(\underset{92}{238} \mathrm{U}{\alpha} X \xrightarrow{\beta^{-}} Y \underset{Z}{A}\) the values of Z and A respectively will be

1. 92,236
2. 88,230
3. 90,234
4. 31,234

Answer: 1. 92,236

Question 18. A nucleus represented by the symbol has:-

1. Z protons and A – Z neutrons
2. Z protons and A neutrons
3. A protons and Z – A neutrons
4. Z protons and A – Z PROTONS

Answer: 3. A protons and Z – A neutrons

Question 19. In the radioactive decay process, the negatively charged emitted -particles are:

1. The electrons present inside the nucleus
2. The electrons produced as a result of the decay of neutrons inside the nucleus
3. The electrons produced as a result of collisions between atoms
4. The electrons orbiting around the nucleus

Answer: 3. The electrons produced as a result of collisions between atoms

Question 20. A nuclear transformation is denoted by \(\mathrm{X}(\mathrm{n}, \alpha) \rightarrow{ }_3^7 \mathrm{Li}\). Which of the following is the nucleus of element X?

1. \({ }_6^{12} \mathrm{C}\)
2. \({ }_5^{10} \mathrm{~B}\)
3. \({ }_5^9 \mathrm{~B}\)
4. \({ }_4^{11} \mathrm{Be}\)

Answer: 2. \({ }_5^{10} \mathrm{~B}\)

Question 21. When ₃Li⁷ nuclei are bombarded by protons, and the resultant nuclei are 4Be⁸, the emitted particles will be

1. Neutrons
2. Alpha Particles
3. Beta Particles
4. Gamma Photons

Answer: 4. Gamma Photons

Question 22. The ‘rad’ is the correct unit used to report the measurement of

1. The Rate Of Decay Of Radioactive Source
2. The Ability Of A Beam Of Gamma Ray Photons To Produce Ions In A Target
3. The Energy Delivered By Radiation To A Target.
4. The Biological Effect Of Radiation

Answer: 4. The Biological Effect Of Radiation

Question 23. In gamma-ray emission from a nucleus:

1. Both The Neutron Number And The Proton Number Change
2. There Is No Change In The Proton Number And The Neutron Number
3. Only The Neutron Number Changes
4. Only The Proton Number Changes

Answer: 2. There Is No Change In The Proton Number And The Neutron Number

Question 24. Bombardment of a neutron \({ }_0 \mathrm{n}^1+{ }_5 \mathrm{~B}^{10} \rightarrow{ }_2 \mathrm{He}^4+\mathrm{x}\) on boron, forms a nucleus x with emission of  particle Nuclear x is –

1. ₆C¹²
2. ₃Li⁶
3. ₃Li⁷
4. ₄Be⁹

Answer: 3. ₃Li⁷

Question 25. 22Ne nucleus, after absorbing energy, decays into two -particles and an unknown nucleus. The unknown nucleus is:

1. Nitrogen
2. Carbon&14
3. Boron&12
4. Oxygen

Answer: 2. Carbon&14

Question 26. Consider a sample of a pure beta-active material

1. All the beta particles emitted have the same energy
2. The beta particles originally exist inside the nucleus and are ejected at the time of beta decay
3. The antineutrino emitted in a beta decay has zero rest mass and hence zero momentum.
4. The active nucleus changes to one of its isobars after the beta decay

Answer: 4. The active nucleus changes to one of its isobars after the beta decay

Question 27. \(\mathrm{X}+\mathrm{n} \rightarrow \alpha+{ }_3 \mathrm{Li}^7\) then X will be :-

1. \({ }_5^{10} \mathrm{~B}\)
2. \({ }_5^9 \mathrm{~B}\)
3. \({ }_4^{11} \mathrm{~B}\)
4. \({ }_2^4 \mathrm{He}\)

Answer: 1. \({ }_5^{10} \mathrm{~B}\)

Question 28. M n and M p represent the mass of neutron and proton respectively An element having mass M has N neutron and Z-protons, then the correct relation will be:-

1. M < {N.mn + Z.Mp}
2. M > {N.mn + Z.M p}
3. M = {N.mn + Z.M p}
4. M = N {.mn + Mp}

Answer: 1. M < {N.mn + Z.Mp}

Question 29. In the nucleus of an atom, neutrons are in excess, then emitted particles are:

1. Neutron
2. Electron
3. Proton
4. Positron

Answer: 2. Electron

Question 30. A nuclei X with mass number A and charge number Z disintegrates into one α-particle and one β-particle. The resulting R has atomic mass and atomic number, equal to:

1. (A – Z) and (Z – 1)
2. (A – Z) and (Z – 2)
3. (A – and (A – 2)
4. (A – and (Z – 1)

Answer: 4. (A – and (Z – 1)

Question 31. In gamma-ray emission from a nucleus

1. Both The Neutron Number And The Proton Number Change
2. There Is No Change In The Proton Number And The Neutron Number
3. Only The Neutron Number Changes
4. Only The Proton Number Changes

Answer: 1. Both The Neutron Number And The Proton Number Change

Question 32. Which one of the following is a possible nuclear reaction?

1. \({ }_5^{10} \mathrm{~B}+{ }_2^4 \mathrm{He} \longrightarrow{ }_7^{13} \mathrm{~N}+{ }_1^1 \mathrm{H}\)
2. \({ }_{11}^{23} \mathrm{Na}+{ }_1^1 \mathrm{H} \longrightarrow{ }_{10}^{20} \mathrm{Ne}+{ }_2^4 \mathrm{He}\)
3. \({ }_{93}^{239} \mathrm{~Np} \longrightarrow{ }_{94}^{239} \mathrm{pu}+\mathrm{B}^{-}+\overline{\mathrm{v}}\)
4. \({ }_7^{11} \mathrm{~N}+{ }_1^1 \mathrm{H} \longrightarrow{ }_6^{12} \mathrm{C}+\mathrm{B}^{-}+\overline{\mathrm{v}}\)

Answer: 3. \({ }_{93}^{239} \mathrm{~Np} \longrightarrow{ }_{94}^{239} \mathrm{pu}+\mathrm{B}^{-}+\overline{\mathrm{v}}\)

Question 33. In an α-decay, the Kinetic energy of the Q particle is 48 MeV and the Q-value of the reaction is 50 MeV. The mass number of the mother nucleus is:- (Assume that the daughter nucleus is in the ground state)

1. 96
2. 100
3. 104
4. None of these

Answer: 2. 100

Question 34. Protons and singly ionized atoms of U²³⁵ & U²³⁸ are passed in turn (which means one after the other and not at the same time) through a velocity selector and then enter a uniform magnetic field. The protons describe semicircles of radius 10 mm. The separation between the ions of U235 and U238 after describing the semicircle is given by

1. 60mm
2. 30mm
3. 2350mm
4. 2380mm

Answer: 1. 60mm

Question 35. Which of the following processes represents a gamma decay?

1. \({ }^A X_Z+\gamma \longrightarrow{ }^A X_{Z-1}+a+b\)
2. \({ }^A X_Z+{ }^1 n_0 \longrightarrow A-3 X_{Z-2}+c\)
3. \({ }^A X_Z \longrightarrow{ }^A X_Z+f\)
4. \({ }^A X_Z \longrightarrow{ }^A X_Z+f\)

Answer: 3. \({ }^A X_Z \longrightarrow{ }^A X_Z+f\)

Question 36. A nucleus with mass number 220 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α-particle

1. 4.4 MeV
2. 5.4 MeV
3. 5.6 MeV
4. 6.5 MeV

Answer: 2. 5.4 MeV

Chapter 4 Nuclear Physics Multiple Choice Questions Section (D): Statistical Law Of Radioactive Decay

Question 1. In one average-life

1. Half The Active Nuclei Decay
2. Less Than Half The Active Nuclei Decay
3. More Than Half The Active Nuclei Decay
4. All The Nuclei Decay

Answer: 3. More Than Half The Active Nuclei Decay

Question 2. A freshly prepared radioactive source of half-life 2h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is –

1. 6 h
2. 12 h
3. 24 h
4. 128 h

Answer: 2. 12 h

Question 3. 10 grams of 57Co kept in an open container decays β–a particle with a half-life of 270 days. The weight of the material inside the container after 540 days will be very nearly –

1. 10 g
2. 7.5 g
3. 5 g
4. 2.5 g

Answer: 2. 7.5 g

Question 4. After a time equal to four half-lives, the amount of radioactive material remaining undecayed is –

1. 6.25 %
2. 12.50 %
3. 25.0 %
4. 50.0 %

Answer: 1. 6.25 %

Question 5. The decay constant of the parent nuclide in the Uranium series is. Then the decay constant of the stable end product of the series will be –

1. λ/238
2. λ/206
3. λ/208
4. zero

Answer: 4. zero

Question 6. The half-life of thorium (Th 23is 1.4 × 1010 years. Then the fraction of thorium atoms decaying per year is very nearly –

1. 1 × 10–11μ
2. 4.95 × 10–11
3. 0.69 × 10–11
4. 7.14 × 10–11

Answer: 1. 1 × 10–11

Question 7. The half-life of 215At is 100 μs. The time taken for the radioactivity of a sample of 215At to decay to 1/16th of its initial value is :

1. 400 μs
2. 6.3 μs
3. 40 μs
4. 300 μs

Answer: 4. 300 μs

Question 8. Two identical samples (same material and same amount) P and Q of a radioactive substance having mean life T are observed to have activities A P & AQ respectively at the time of observation. If P is older than Q, then the difference in their ages is:

1. \(\mathrm{T} \ell \mathrm{n}\left(\frac{\mathrm{A}_{\mathrm{P}}}{\mathrm{A}_{\mathrm{Q}}}\right)\)
2. \(T \ell n\left(\frac{A_Q}{A_P}\right)\)
3. \(\frac{1}{T} \ln \left(\frac{A_P}{A_Q}\right)\)
4. \(T\left(\frac{A_P}{A_Q}\right)\)

Answer: 1. \(\mathrm{T} \ell \mathrm{n}\left(\frac{\mathrm{A}_{\mathrm{P}}}{\mathrm{A}_{\mathrm{Q}}}\right)\)

Question 9. Two radioactive sources A and B initially contain an equal number of radioactive atoms. Source A has a half-life of 1 hour and source B has a half-life of 2 hours. At the end of 2 hours, the ratio of the rate of disintegration of A to that of B is:

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

Answer: 4. 1: 4

Question 10. If 10% of a radioactive material decays in 5 days then the amount of original material left after 15 days is about –

1. 65%
2. 73%
3. 70%
4. 63%

Answer: 2. 73%

Question 11. The half-life of radioactive Polonium (Po) is 138.6 days. For ten lakh Polonium atoms, the number of disintegrations in 24 hours is –

1. 2000
2. 3000
3. 4000
4. 5000

Answer: 4. 5000

Question 12. Half-lives of two radioactive substances A and B are respectively 20 min and 40 min. Initially, the samples of A and B have an equal number of nuclei. After 80 min the ratio of the remaining number of A and B nuclei is:

1. 1: 16
2. 4: 1
3. 1: 4
4. 1: 1

Answer: 1. 1: 16

Question 13. A nucleus n Xm emits one and two particles. The resulting nucleus is :

1. Nx^m–4
2. N –2 Y^{m – 4}
3. N – 4 Z ^{m – 4}
4. None Of These

Answer: 3. N – 4 Z ^{m – 4}

Question 14. The half-life of a radioactive element is 12.5 Hours and its quantity is 256 gm. After how much time its \quantity will remain 1 gm:-

1. 50 Hrs
2. 100 Hrs
3. 150 Hrs
4. 200 Hrs

Answer: 2. 100 Hrs

Question 15. If the half-life of a substance is 38 days and its quantity is 10.38 g. The quantity remaining after 19 days will be:

1. 0.151g
2. 7.0 g
3. 0.51g
4. 0.16 g

Answer: 1. 0.151g

Question 16. Remaining quantity (in %) of the radioactive element after 5 half-lives:

1. 4.125%
2. 3.125%
3. 31.1%
4. 42.125%

Answer: 2. 3.125%

Question 17. When neutrons are bvaomardexd on ⎯⎯→ 5B10 then +on1 X + 2He4, X is :

1. 3Li7
2. 3Li6
3. 5Be8
4. 2Li7

Answer: 1. 3Li7

Question 18. A sample of radioactive element containing 4 × 1016 active nuclei. The half-life of the element is 10 days, then the number of decayed nuclei after 30 days:-

1. 0.5 × 1016
2. 2 × 1016
3. 3.5 × 1016
4. 1 × 1016

Answer: 3. 3.5 × 1016

Question 19. A sample of radioactive element has a mass of 10 gm at an instant t = 0. The approximate mass of this element in the sample after two mean lives is:_

1. 1.35 gm
2. 2.50 gm
3. 3.70 gm
4. 6.30 gm

Answer: 1. 1.35 gm

Question 20. The decay constant of a radioactive substance is. The life and mean life of substance are respectively given by

1. \(\frac{1}{\lambda} \text { and } \frac{\log _e 2}{\lambda}\)
2. \(\frac{\log _e 2}{\lambda} \text { and } \frac{1}{\lambda}\)
3. \(\frac{\lambda}{\log _e 2} \text { and } \frac{1}{\lambda}\)
4. \(\frac{\lambda}{\log _e 2} \text { and } 2 \lambda\)

Answer: 2. \(\frac{\log _e 2}{\lambda} \text { and } \frac{1}{\lambda}\)

Question 21. The half-life of a certain radioactive substance is 12 days. The time taken for 8th of the sample to decay is

1. 36 days
2. 12 days
3. 4 days
4. 24 days

Answer: 1. 36 days

Question 22. If N 0 is the original mass of the substance of half-life period tl/2 = 5 years, then the amount of substance left after 15 years is:

1. N 0 / 8
2. N 0 / 16
3. N 0 / 2
4. N 0 / 4

Answer: 1. N 0 / 8

Question 23. The atomic bomb was first made by

1. Otto Hahn
2. Fermi
3. Oppenheimer
4. Taylor

Answer: 1. Otto has

Question 24. A radioactive element has a half-life of 3.6 days. At what time will it be left 1/32nd undecayed?

1. 4 days
2. 12 days
3. 18 days
4. 24 days

Answer: 3. 18 days

Question 25. If a sample of 16 g radioactive substance disintegrates to 1g in 120 days, then what will be the half-life of the sample?

1. 15 days
2. 7.5 days
3. 30 days
4. 60 days

Answer: 3. 30 days

Question 26. n α-particles per second are being emitted by N atoms of a radioactive element. The half-life of element will be

1. \(\left(\frac{\mathrm{n}}{\mathrm{N}}\right) \mathrm{s}\)
2. \(\left(\frac{N}{n}\right) s\)
3. \(\frac{0.693 \mathrm{~N}}{n} s\)
4. \(\frac{0.693 n}{N} s\)

Answer: 3. \(\frac{0.693 \mathrm{~N}}{n} s\)

Question 27. In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?

1. 37%
2. 50%
3. 63%
4. 69.3%

Answer: 3. 63%

Question 28. If the half-life of any sample of a radioactive substance is 4 days, then the fraction of the sample will remain undecayed after 2 days and will be

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

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

Question 29. A nucleus with Z = 92 emits the following in a sequence: α β–, β –, α α α β-; β–, β–, α, α+, β+, α: The Z of the resulting nucleus is

1. 76
2. 80
3. 82
4. 74

Answer: 2. 80

Question 30. If a radioactive substance decays \(\frac{1}{16} \text { th }\) of its original amount in 2 h, then the half-life of that substance is

1. 15 min
2. 30 min
3. 45 min
4. None Of These

Answer: 2. 30 min

Question 31. If N 0 is the original mass of the substance of half-life period T1/2 = 5 ye, then the amount of substance left after 15 yr is

1. N 0 /8
2. N 0/16
3. N 0/2
4. N 0/4

Answer: 1. N 0 /8

Question 32. The half-life of radium is about 1600 years. Of 100g of radium existing now, 25g will remain undocked after:-

1. 6400 years
2. 2400 years
3. 3200 years
4. 4800 years

Answer: 3. 3200 years

Question 33. In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is , then

1. R₁ = R₂ e–λ(t₁–t₂)
2. R₁ = R₂ eλ(t₁–t₂)
3. R₁ = R₂ (t₁ / t₂)
4. R₁ = R₂

Answer: 1.R₁ = R₂ e–λ(t₁–t₂)

Question 34. The atomic bomb was first made by

1. Otto Hahn
2. Fermi
3. Oppenheimer
4. Taylor

Answer: 1. Otto hahn

Question 35. Two radioactive materials X₁ and X₂ have decay constants 5λ and λ  respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be e after a time

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

Answer: 3. \(\frac{e}{\lambda}\)

Question 36. Starting with a sample of pure 66Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is:

1. 10 minute
2. 15 minute
3. 5 minute
4. 7 minute

Answer: 3. 5 minute

Question 37. The activity of the Po sample is 5 millicuries. Half-life of Po is 138 days, what amount of Po was initially taken? (Avogadro’s no. = 6.02×1026 Per k mole)

1. 3.18 × 1015 atoms
2. 3.18 × 1013 atoms
3. 3.18 × 1016 atoms
4. 3.18 × 1014 atoms

Answer: 1. 3.18 × 1015 atoms

Question 38. The half-life period of a radioactive element X is the same as the mean-life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

1. X and Y have the same decay rate initially
2. X and Y decay at the same rate always
3. Y will decay at a faster rate than X
4. X will decay at a faster rate than Y

Answer: 3. Y will decay at a faster rate than X

Question 39. A radioactive element ThA (₈₄Po²¹⁶) can undergo α and βis a type of disintegration with half-lives, T1 and T 2 respectively. Then the half-life of ThA is

1. T1 + T2
2. T1 T2
3. T1 – T2
4. \(\frac{\mathrm{T}_1 \mathrm{~T}_2}{\mathrm{~T}_1+\mathrm{T}_2}\)

Answer: 4. \(\frac{\mathrm{T}_1 \mathrm{~T}_2}{\mathrm{~T}_1+\mathrm{T}_2}\)

Question 40. The mean lives of radioactive substances are 1620 years and 405 years for -emission and -emission respectively. Then the time in which three-fourths of a sample will decay is –

1. 224 years
2. 324 years
3. 449 years
4. 810 years

Answer: 3. 449 years

Question 41. Two radioactive materials X 1 and X2 have decay constants 10 and  respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 to that of X2 will be 1/e after a time.

1. 1/(10)
2. 1/(11)
3. 11/(10)
4. 1/(9)

Answer: 4. 1/(10)

Question 42. A sample of radioactive material has mass m, decay constant, and molecular weight M. Avogadro constant = N The initial activity of the sample is

1. \(\frac{\lambda \mathrm{m}}{\mathrm{M}}\)
2. \(\frac{\lambda \mathrm{mN}_{\mathrm{A}}}{\mathrm{M}}\)
3. \(m N_A e^\lambda\)

Answer: 3. \(m N_A e^\lambda\)

Question 43. The activity of a radioactive element is 103 dis/sec. Its half-life is 1 sec. After 3 sec. its activity will be :

1. 1000 dis/sec
2. 250 dis/sec
3. 125 dis/sec
4. none of these

Answer: 3. 125 dis/sec

Question 44. A 280-day-old sample of a radioactive substance has the activity of 6000 DPS. In the next 140 days, activity falls to 3000 dps. The initial activity of the sample would have been

1. 9000
2. 24000
3. 12,000
4. 18,000

Answer: 2. 24000

Question 45. A radioactive sample at any instant has a disintegration rate of 5000 disintegrations per minute. After
5 min, the rate is 1250 disintegrations per min. then the decay constant (per – minute) is

1. 0.4 In 2
2. 0.2 In2
3. 0.1 In 2
4. 0.8 In2

Answer: 4. 0.8 In2

Question 46. A radioactive sample consists of two distinct species having an equal number of atoms initially. The mean lifetime of one species is and that of the other is 5. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot?

Question 47. A 280-day-old sample of a radioactive substance has an activity of 6000 DPS. In the next 140 days, activity falls to 3000 dps. The initial activity of the sample would have been

1. 9000
2. 24000
3. 12,000
4. 18,000

Answer: 1. 9000

Question 48. A radioactive sample at any instant has a disintegration rate of 5000 disintegrations per minute. After 5 min, the rate is 1250 disintegrations per minute. then the decay constant (per – minute) is

1. 0.4 In 2
2. 0.2 In2
3. 0.1 In 2
4. 0.8 In2

Answer: 1. 0.4 In 2

Question 49. Radioactivity is –

1. Irreversible Process
2. Spontaneous Disintegration Process
3. Not Effected By Temperature Or Pressure
4. Process Obeying All Of The Above

Answer: 4. Process Obeying All Of The Above

Chapter 4 Nuclear Physics Multiple Choice Questions Section (E): Nuclear Fission And Fusion

Question 1. If the mass of the fissionable material is less than the critical mass, then

1. Fission And Chain Reactions Both Are Impossible
2. Fission Is Possible But Chain Reaction Is Impossible
3. Fission Is Impossible But Chain Reaction Is Possible
4. Fission And Chain Reaction Are Possible.

Answer: 2. Fission Is Possible But Chain Reaction Is Impossible

Question 2. Which of the following materials is used for controlling the fission

1. Heavy Water
2. Graphite
3. Cadmium
4. Beryllium Oxide

Answer: 3. Cadmium

Question 3. The atomic reactor is based on

1. Controlled Chain Reaction
2. Uncontrolled Chain Reaction
3. Nuclear Fission
4. Nuclear Fusion

Answer: 1. Controlled Chain Reaction

Question 4. Thermal neutron means

1. Neutron Being Heated
2. The Energy Of These Neutrons Is Equal To The Energy Of Neutrons in a heated atom
3. These neutrons have the Energy Of A Neutron In A Nucleus At a normal temperature
4. Such Neutrons Gather Energy Released In The Fission Process

Answer: 3. These neutrons have the Energy Of A Neutron In A Nucleus At a normal temperature

Question 5. \({ }_{92} U^{235}\) nucleus ab sorbs a slow neutron and undergoes fission into 54X139 and 38Sr94 nuclei.The other particles produced in this fission process are

1. 1β and 1α
2. 2β and 1 neutron
3. 2 Neutrons
4. 3 Neutrons

Answer: 4. 3 Neutrons

Question 6. Two lithium 6Li nuclei in a lithium vapor at room temperature do not combine to form a carbon 12C nucleus because

1. A Lithium Nucleus Is More Tightly Bound Than A Carbon Nucleus
2. The Carbon Nucleus Is An Unstable Particle
3. It Is Not Energetically Favourable
4. Coulomb Repulsion Does Not Allow The Nuclei To Come Very Close

Answer: 4. Coulomb Repulsion Does Not Allow The Nuclei To Come Very Close

Question 7. Choose the true statement.

1. The energy released per unit mass is more in fission than in fusion
2. The energy released per atom is more in fusion than in fission.
3. The energy released per unit mass is more in fusion and that per atom is more in fission.
4. Both fission and fusion produce the same amount of energy per atom as well as per unit mass.

Answer: The energy released per unit mass is more in fusion and that per atom is more in fission

Question 8. A fusion reaction is possible at high temperatures because –

1. Atoms Are Ionised At High Temperature
2. Molecules Break-Up At High Temperature
3. Nuclei Break-Up At High Temperature
4. Kinetic Energy Is High Enough To Overcome Repulsion Between Nuclei.

Answer: 4. Kinetic Energy Is High Enough To Overcome Repulsion Between Nuclei.

Question 9. In a uranium reactor whose thermal power is P = 100 MW, if the average number of neutrons liberated in each nuclear splitting is 2.5. Each splitting is assumed to release an energy E = 200 MeV. The number of neutrons generated per unit of time is –

1. 4 × 1018 s–1
2. 8 × 1023 s–1
3. 8 × 1019 s–1
4. 16 × 1018 s–1

Answer: 4. 16 × 1018 s–1

Question 10. Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice given below.

1. Fusion Of Two Nuclei With Mass Numbers Lying In The Range Of 1 < A < 50 Will Release Energy
2. Fusion Of Two Nuclei With Mass Numbers Lying In The Range Of 51 < A < 100 Will Release Energy
3. Fission Of A Nucleus Lying In The Mass Range Of 100 < A < 200 Will Release Energy When Broken Into Two Equal Fragments
4. Both and (2)

Answer: 3. Fission Of A Nucleus Lying In The Mass Range Of 100 < A < 200 Will Release Energy When Broken Into Two Equal Fragments

Question 11. A fission reaction is given by \({ }_{92}^{236} \mathrm{U} \rightarrow{ }_{54}^{140} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+\mathrm{x}+\mathrm{y}\) where x and y are two particle considering \({ }_{92}^{236} U\) to be at rest, the kinetic energies of the products are denoted by KXe, KSr, Kx (2MeV) and ky (2mev), respectively. let the binding energies per nucleon of ,\({ }_{92}^{236} \mathrm{U},{ }_{54}^{140} \mathrm{Xe}\) and \({ }_{38}^{94} \mathrm{Sr}\) MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s)
is(are)

1. \(x=n, y=n, K_{s r}=129 \mathrm{MeV}, K_{\mathrm{xe}}=86 \mathrm{MeV}\)
2. \(x=p, y=e-, K_{s t}=129 \mathrm{MeV}, \mathrm{K}_{\mathrm{xe}}=86 \mathrm{MeV}\)
3. \(x=p, y=n, K_{s r}=129 \mathrm{MeV}, K_{x_e}=86 \mathrm{MeV}\)
4. \(x=n, y=n, K_{s r}=86 \mathrm{MeV}, K_{x e}=129 \mathrm{MeV}\)

Answer: 1. \(x=n, y=n, K_{s r}=129 \mathrm{MeV}, K_{\mathrm{xe}}=86 \mathrm{MeV}\)

Question 12. In a fission reaction \({ }_{92}^{236} \mathrm{U} \longrightarrow{ }^{117} \mathrm{X}+{ }^{117} \mathrm{Y}+n+n\) the average binding energy per nucleon of X and Y is 8.5 MeV whereas that of 236U is 7.6 MeV. The
total energy liberated will be about \({ }_{92}^{236} \mathrm{U} \longrightarrow{ }^{117} \mathrm{X}+{ }^{117} \mathrm{Y}+n+n\)

1. 200ev
2. 2 me v
3. 200 me v
4. 20000 meV

Answer: 3. 200 me v

Question 13. Energy is released in nuclear fission due to

1. Few mass is converted into energy
2. The total binding energy of fragments is more than the B. E. of the parental element
3. The total B.E. of fragments is less than the B.E. of parental element
4. The total B.E. of fragments is equal to the B.E. of the parental elements is

Answer: 2. Total B.E. of fragments is less than the B.E. of parental element

Question 14. Boron rods in nuclear reactors are used as a:

1. Moderator
2. Control Rods
3. Coolant
4. Protective Shield

Answer: 2. Control Rods

Question 15. 200 Me V energy is obtained by fission of 1 nuclei of 92U 235, to obtain 1 kW energy number of fission per second will be:

1. 3.215 × 1013
2. 3.215 × 1014
3. 3.215 × 1015
4. 3.215 × 1016

Answer: 1. 3.215 × 1013

Question 16. The best moderator for neutrons is –

1. Beryllium Oxide
2. Pure Water
3. Heavy Water
4. Graphite

Answer: 3. Heavy Water

Question 17. Which of the following are suitable for the fusion process:-

1. Light nuclei
2. heavy nuclei
3. Element must be lying in the middle of the periodic table
4. Middle elements, which are lying on the binding energy curve

Answer: 1. Light nuclei

Question 18. Solar energy is mainly caused due to:-

1. Burning of hydrogen in the oxygen
2. Fusion of uranium present in the sun
3. Fusion of protons during the synthesis of heavier elements
4. Gravitational contraction

Answer: 3. Fusion of protons during synthesis of heavier elements

Question 19. Which one of the following acts as a neutron absorber in a nuclear reactor?

1. Cd-rod
2. Heavy water (D2O)
3. Graphite
4. Distilled water (H2O)

Answer: 1. Cd-rod

Question 20. The functions of mediators in nuclear reactors are:

1. Decrease The Speed Of Neutrons
2. Increase The Speed Of Neutrons
3. Decrease The Speed Of Electrons
4. Decrease The Speed Of Electrons

Answer: 1. Decrease The Speed Of Neutrons

Question 21. A chain reaction in the fission of uranium is possible, because:

1. Two Intermediate Sized Nuclear Fragments Are Formed
2. Three Neutrons Are Given Out In Each Fission
3. Fragments In Fission Are Radioactive
4. Large Amount Of Energy Is Released

Answer: 2. Three Neutrons Are Given Out In Each Fission

Question 22. Nuclear fusion is common to the pair:

1. Thermonuclear Rector, Uranium-Based Nuclear Reactor
2. Energy Production In Sun, Uranium-Based Nuclear Reactor
3. Energy Production Of Heavy Nuclei Hydrogen Bomb
4. Disintegration Of Heavy Nuclei Hydrogen Bomb

Answer: 3. Energy Production Of Heavy Nuclei Hydrogen Bomb

Question 23. IN any fission process the ratio \(\frac{\text { mass of fission products }}{\text { maas of parent nucleus }}\)

1. Greater than 1
2. Depends on the mass of the parent nucleus
3. Less than 1
4. Less than 1

Answer: 3. Less than 1

Question 24. Fission of nuclei is possible because the binding energy in nucleons in them-

1. Decreases with mass number at low mass numbers
2. Increases with mass number at low mass numbers
3. Decreases with mass number at high mass numbers
4. Increases with mass number at high mass numbers

Answer: 3. Decreases with mass number at high mass numbers

Question 25. In the nuclear fusion reaction, \({ }_1^2 \mathrm{H}+{ }_1^3 \mathrm{H} \longrightarrow{ }_2^4 \mathrm{He}+\mathrm{n}\) given that the repulsive potential energy between the two nuclei is ~ 7.7 × 10 –14 J, the temperature at which the gases must be heated to initiate the reaction is nearly (Boltzmann’s constant k = 1.38 × 10 –23 J/K):

1. 107K
2. 105K
3. 103K
4. 109K

Answer: 4. 109K

Question 26. The operation of a nuclear reactor is said to be critical if the multiplication factor (k) has a value

1. 1
2. 1.5
3. 2.1
4. 2.5

Answer: 1. 1

Question 27. This question contains Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.  Statement-1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and Statement 2: For heavy nuclei, the binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.

1. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
2. Statment-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
3. Statement-1 is true, Statement-2 is false
4. Statement-1 is false, Statement-2 is true

Answer: 3. Statement-1 is true, Statement-2 is false

Chapter 4 Nuclear Physics Multiple Choice Questions Exercise 2

Question 1. The dynamic mass of an electron having rest mass m0 and moving with speed 0.8 c is

1. 0.6 m₀
2. 0.8 m₀
3. 3 m₀
4. 1.25 m₀

Answer: 3. 3 m₀

Question 2. An alpha nucleus of energy 2 mv2 bombards a heavy closet approach for the alpha nuclieus will be proportional to

1. v²
2. 1/M
3. 1/ v⁴
4. 1 / ze

Answer: 2. 1/M

Question 3. An α-particle of energy 5 MeV is scattered through 180º by a fixed uranium nucleus. The distance of the closest approach is of the order of:

1. 1 Å
2. 10–10 cm
3. 10-12 cm
4. 10–15 cm

Answer: 3. 10-12 cm

Question 4. Helium nuclei combine to form an oxygen nucleus. The energy released in the reaction is if mO = 15.9994 amu and mHe = 4.0026 amu

1. 10.24 MeV
2. 0 MeV
3. 5.24 MeV
4. 4 MeV

Answer: 1. 10.24 MeV

Question 5. A nucleus z X has mass represented by M(A, Z). If M p and M n denote the mass of proton and neutron respectively and BE the binding energy (in MeV), then:

1. \(B E=\left[M(A, Z)-Z M_p-(A-Z) M_n\right] c^2\)
2. \(B E=\left[Z M_p+(A-Z) M_n-M(A, Z)\right] c^2\)
3. \(B E=\left[Z M_p+A M_n-M(A, Z)\right] c^2\)
4. \(B E=M(A, Z)-Z M_p-(A-Z) M_n\)

Answer: 2. \(B E=\left[Z M_p+(A-Z) M_n-M(A, Z)\right] c^2\)

Question 6. If M (A, Z), M p and M n A denote the masses of the nucleus Z X, proton, and neutron respectively in units of u (1 u = 931.5 MeV/cand BE represents its binding energy in MeV, then

1. M (A, Z) = ZM p + (A – Z) Mn – BE/c²
2. M (A, Z) = ZM p + (A – Z) Mn – BE
3. M (A, Z) = ZM p + (A – Z) Mn – BE
4. M (A, Z) = ZM p + (A – Z) Mn + BE/c2

Answer: 1. M (A, Z) = ZM p + (A – Z) Mn – BE/c²

Question 7. The binding energy per nucleon of the deuteron and helium nuclei is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is:

1. 13.9 MeV
2. 26.9 MeV
3. 23.6 MeV
4. 19.2 MeV

Answer: 3. 23.6 MeV

Question 8. ₆C¹¹ undergoes a decay by emitted β+ then writes its complete equation. Given the mass value of m(5C1= 11.011434 u, m(5B1= 11.009305 u. m e = 0.000548 u and 1 u = 931.5 MeV/c² Calculate the Q-value of reaction.

1. 0.962 Mev
2. 09.62Mev
3. 096.2MeV
4. 962.0MeV

Answer: 1. 0.962 Mev

Question 9. The atomic weight of boron is 10.81 and it has two isotopes 5B10 and 5B11 in nature would be:

1. 19: 81
2. 10: 11
3. 15: 16
4. 81: 19

Answer: 1. 19: 81

Question 10. A nucleus of mass number 332 after many disintegrations α and β radiations, decays into another nucleus whose mass number is 220 and atomic number is 86. The numbers of α and β radiations will be:

1. 4, 0
2. 3, 6
3. 3, 2
4. 2, 1

Answer: 3. 3, 2

Question 11. A radioactive sample at any instant has a disintegration rate of 5000 disintegrations per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is :

1. 0.4 ln 2
2. 0.2 ln 2
3. 0.1 ln 2
4. 0.8 ln 2

Answer: 1. 0.4 ln 2

Question 12. At time t = 0, some radioactive gas is injected into a sealed vessel. At time T, some more of the same gas is injected into the same vessel. Which one of the following graphs best represents the variation of the logarithm of activity A of the gas with time t?

Answer: 2.

Question 13. N atoms of a radioactive element emit n alpha particles per second at an instant. Then the half-life of the element is

1. \(\frac{\mathrm{n}}{\mathrm{N}} \mathrm{sec} \text {. }\)
2. \(1.44 \frac{\mathrm{n}}{\mathrm{N}} \mathrm{sec} .\)
3. \(0.69 \frac{\mathrm{n}}{\mathrm{N}} \text { sec. }\)
4. \(0.69 \frac{N}{n} \text { sec. }\)

Answer: 4. \(0.69 \frac{N}{n} \text { sec. }\)

Question 14. Two isotopes P and Q of atomic weight 10 and 20, respectively are mixed in equal amounts by weight. After 20 days their weight ratio is found to be 1: 4. Isotope P has a half-life of 10 days. The half-life of isotope Q is

1. Zero
2. 5 days
3. 20 days
4. Infinite

Answer: 4. Infinite

Question 15. The half-life of a radioactive substance is 4 days. Its 100 g is kept for 16 days. After this period, the amount of substance that remained was:

1. 25 g
2. 15 g
3. 10 g
4. 6.25 g

Answer: 4. 6.25 g

Question 16. Two radioactive substances A and B have decay constants 5 and respectively. At = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be \(\left(\frac{1}{e}\right)^2\) after a time interval:

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

Answer: 4. \(\frac{1}{2 \lambda}\)

Question 17. The half-life period of a radio-active element X is the same as the mean lifetime of another radio-active element Y. Initially they have the same number of atoms. Then:

1. X will decay faster than Y
2. Y will decay faster than X
3. X and Y have the same decay rate initially
4. X and Y decay at the same rate always

Answer: 2. Y will decay faster than X

Question 18. How much uranium is required per day in a nuclear reactor of power capacity of 1 MW

1. 15 mg
2. 1.05 gm
3. 105 gm
4. 10.5 kg

Answer: 2. 1.05 gm

Question 19. Complete the equation for the following fission process \({ }_{92} \mathrm{U}^{235}+{ }_0 \mathrm{n}^1 \longrightarrow{ }_{38} \mathrm{Sr}^{90}+\ldots \ldots.\)

1. \({ }_{54} X^{143}+3{ }_0 n\)
2. \({ }_{54} X e^{145}\)
3. \({ }_{57} \mathrm{Xe}^{142}\)
4. \({ }_{54} \mathrm{Xe}^{142}+{ }_0 \mathrm{n}^1\)

Answer: 1. \({ }_{54} X^{143}+3{ }_0 n\)

Chapter 4 Nuclear Physics Multiple Choice Questions Part – 1: Neet / Aipmt Question (Previous Years)

Question 1. In the nuclear decay given below \({ }_Z^A X \longrightarrow{ }_{Z+1}^A Y \longrightarrow{ }_{Z-1}^{A-4} B^{\circ} \longrightarrow{ }_{Z-1}^{A-4} B \text {, }\)  the particles emitted in the sequence are

1. β,α, ϒ
2. ϒ,β,α
3. β,γ,α
4. α,β,γ

Answer: 1. β,α, ϒ

Question 2. The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an

1. Isobar Of Parent
2. Isomar Of Parent
3. Isotone Of Parent
4. Isotope Of Parent

Answer: 4. Isotope Of Parent

Question 3. A radioactive nucleus X converts into to stable nucleus Y. Half-life of X is 50 yr. Calculate the age of the radioactive sample when the radio of X and Y is 1:15.

1. 200 yr
2. 350 yr
3. 150 yr
4. 250 yr

Answer: 1. 200 yr

Question 4. The mass of a 3Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding 73Li energy per nucleon of a nucleus is nearly

1. 46 MeV
2. 5.6 MeV
3. 3.9 MeV
4. 23 MeV

Answer: 2. 5.6 MeV

Question 5. The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

1. \(\log _e \frac{2}{5}[latex]
2. [latex]\frac{5}{\log _e 2}\)
3. 5 log₁₀2
4. 5 log_e2

Answer: 4. 5 log₁₀2

Question 6. 2 An alpha nucleus of energy 2 bombards a heavy nuclear target of charge Ze. Then the distance of the closest approach for the alpha nucleus will be proportional to

1. \(\frac{1}{\mathrm{Ze}}\)
2. u²
3. \(\frac{1}{\mathrm{~m}}\)
4. \(\frac{1}{u^4}\)

Answer: 3. \(\frac{1}{\mathrm{~m}}\)

Question 7. The decay constant of a radioisotope is λ. If A₁ and A2 are its activities at times t₁ and t₂ respectively, the number of nuclei that have decayed during the time (t₂ – t

1. A₁t₁ – A₂t₂
2. A₁ – A₂
3. (A₁ – A₂)/λ
4. λ(A₁ – A₂)

Answer: 3. (A₁ – A₂)/λ

Question 8. The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

1. 23.6 MeV
2. 2.2 MeV
3. 28.0 MeV
4. 30.2 MeV

Answer: 1. 23.6 MeV

Question 9. Two radioactive nuclei P and Q, in a given sample decay into a stable nucleolus R. At time t = 0, many P species are 4 N₀ and that of Q are N₀. The half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially, there are no nuclei of R present in the sample. When the number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be –

1. 9N₀
2. 3N₀
3. 2 5N₀
4. 22N₀

Answer: 2. 3N₀

Question 10. The half life of a radioactive isotope ‘X’ is 50 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio of 1: 15 in a sample of a given rock. The age of the rock was estimated to be:

1. 150 years
2. 200 years
3. 250 years
4. 100 years

Answer: 2. 200 years

Question 11. The power obtained in a reactor using U 235 disintegration is 1000 kW. The mass decay of U 235 per hour is:

1. 10 microgram
2. 20 microgram
3. 40 microgram
4. 1 microgram

Answer: 3. 40 microgram

Question 12. A radioactive nucleus of mass M emits a photon of frequency  and the nucleus recoils. The recoil energy will be:

1. Mc² – hν
2. h²v² / 2Mc²
3. zero
4. hν

Answer: 2. h²v² / 2Mc²

Question 13. A nucleus \({ }_n^m x\) emits one –particle and two – particles. The resulting nucleus is :

1. \({ }_{n-4}^{m-6} Z\)
2. \(\mathrm{m}_{\mathrm{m}}-6\)
3. \({ }_n^{m-4} X\)
4. \({ }_{n-2}^{m-4} Y\)

Answer: 3. \({ }_n^{m-4} X\)

Question 14. Fusion reaction takes place at high temperatures because:

1. Nuclei Break Up At High Temperature
2. Atoms Get Ionised At High Temperature
3. Kinetic Energy Is High Enough To Overcome The Coulomb Repulsion Between Nuclei
4. Molecules Break Up At High Temperature

Answer: 3. Kinetic Energy Is High Enough To Overcome The Coulomb Repulsion Between Nuclei

Question 15. If the nuclear radius of 27 Al is 3.6 Fermi, the approximate nuclear radius of 64 Cu in Fermi is:

1. 2.4
2. 1.2
3. 4.8
4. 3.6

Answer: 3. 4.8

Question 16. A mixture consists of two radioactive materials A₁ and A₂ with half-lives of 20s and 10 s respectively. Initially, the mixture has 40 g of A1 and 160 g of A₂. The amount of the two in the mixture will become equal after:

1. 60 s
2. 80 s
3. 20 s
4. 40 s

Answer: 4. 40 s

Question 17. The half life of a radioactive nucleus is 50 days. The time interval (t₂ – between the time t₂ when 3 of 1 it has decayed and the time t1 when 3 of it had decayed is:

1. 30 days
2. 50 days
3. 60 days
4. 15 days

Answer: 2. 50 days

Question 18. A certain mass of Hydrogen is changed to Helium by the process of fusion. The Mass defect in the fusion reaction is 0.02866 u. The energy liberated per u is : (given 1u = 931 MeV)

1. 26.7 MeV
2. 6.675 MeV
3. 13.35MeV
4. 2.67 MeV

Answer: 2. 6.675 MeV

Question 19. The half life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1: 7 in a sample of a given rock. The age of the rock is estimated to be:

1. 60 years
2. 80 years
3. 100 years
4. 40 years

Answer: 1. 60 years

Question 20. The Binding energy per nucleon of\({ }_3^7 \mathrm{Li} \text { and }{ }_2^4 \mathrm{He}\)  and nucleon are 5.60 MeV and 7.06 MeV, respectively. In 7 1 4 4 the nuclear reaction \({ }_3^7 \mathrm{Li}+{ }_1^1 \mathrm{H} \rightarrow{ }_2^4 \mathrm{He}+{ }_2^4 \mathrm{He}+\mathrm{Q}\), the value of energy Q released is

1. 19.6MeV
2. –2.4 MeV
3. 8.4 MeV
4. 17.3 MeV

Answer: 4. 17.3 MeV

Question 21. A radioisotope ‘X’ with a half-life of 1.4 × 109 years decays to ‘Y’ which is stable. A sample of the rock from a cave was found to contain ‘X’ and ‘Y’ in the ratio 1: 7. The age of the rock is

1. 1.96 × 109 years
2. 3.92 × 109 years
3. 4.20 × 109 years
4. 8.40 × 109 years

Answer: 3. 4.20 × 109 years

Question 22. If radius of the \({ }_{12}^{27} \mathrm{Al}\) Al Te nucleus is taken to be \(\mathrm{R}_{\mathrm{Al}^{\prime}}\) the the radius of \({ }_{53}^{125} \mathrm{Te}\) nucleus is nearly:

1. \(\frac{5}{3} R_{A l}\)
2. \(\frac{3}{5} R_{A I}\)
3. \(\left(\frac{13}{53}\right)^{1 / 3} \mathrm{R}_{\mathrm{Al}}\)
4. \(\left(\frac{53}{13}\right)^{1 / 3} R_{\mathrm{Al}}\)

Answer: 1. \(\frac{5}{3} R_{A l}\)

Question 23. The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is :

1. 60
2. 15
3. 30
4. 45

Answer: 1. 60

Question 24. Radioactive material ‘A’ has a decay constant of ‘8 ’ and material ‘B’ has a decay constant of ‘λ’. Initially, they have same number of nuclei. After what time, the ratio of many nuclei of material ‘B’ to that ‘A’ will be \(\frac{1}{\mathrm{e}}\)?

1. \(\frac{1}{\lambda}\)
2. \(\frac{1}{7 \lambda}\)
3. \(\frac{1}{8 \lambda}\)
4. \(\frac{1}{9 \lambda}\)

Answer: 2. \(\frac{1}{7 \lambda}\)

Question 25. For a radioactive material, the half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:

1. 20
2. 15
3. 30
4. 10

Answer: 1. 20

Question 26. The rate of radioactive disintegration at an instant for a radioactive sample of half life 2.2 × 109 s is 1010 s–1. The number of radioactive atoms in that sample at that instant is

1. 3.17×1020
2. 3.17×1017
3. 3.17×1018
4. 3.17×1019

Answer: 4. 3.17×1019

Question 27. 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, –6.8 eV
3. 3.4 eV, –6.8 eV
4. 3.4 eV, 3.4 eV

Answer: 3. 3.4 eV, –6.8 eV

Question 28. The radius of the first permitted Bohr orbit for the electron, in a hydrogen atom equals 0.51 Å and its− ground state energy equals –13.6 eV. If the electron in the hydrogen atom is replaced by muon [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 eV
4. 2.56 × 10–13 m, –13.6 eV

Answer: 3. 2.56 × 10–13 m, –2.8 eV

Question 29. The total energy of an electron in the nth stationary orbit of the hydrogen atom can be obtained by

1. \(E_n=\frac{13.6}{n^2} e V\)
2. \(E_n=-\frac{13.6}{n^2} e V\)
3. \(\mathrm{E}_{\mathrm{n}}=-\frac{1.36}{\mathrm{n}^2} \mathrm{eV}\)
4. En=-13.6xn2ev

Answer: 2. \(E_n=-\frac{13.6}{n^2} e V\)

Question 30. For which one of the following. Bohr model is not valid?

1. Singly Ionized Neon Atom (Ne+)
2. Hydrogen Atom
3. Singly Ionized Helium Atom (He+)
4. Deuteron Atom

Answer: 1. Singly Ionized Neon Atom (Ne+)

Question 31. What happens to the mass number and atomic number of an element when it emits -radiation?

1. The mass number decreases by four and the atomic number decreases by two.
2. Mass number and atomic number remain unchanged.
3. The mass number remains unchanged while the atomic number decreases by one.
4. Mass number increases by four and atomic number increases by two.

Answer: 2. Mass number and atomic number remain unchanged.

Question 32. The half life of a radioactive sample undergoing -decay is 1.4 × 1017s. If the number of nuclei in the sample is 2.0 × 1021, the activity of the sample is nearly:

1. 104 Bq
2. 105 Bq
3. 106 Bq
4. 103 B

Answer: 1. 104 Bq

Question 33. When a uranium isotope \({ }_{92}^{235} U\) is bombarded with a neutron it generate \({ }_{36}^{89} \mathrm{Kr}\) three neutrons and

1. \({ }_{36}^{103} \mathrm{Kr}[latex]
2. [latex]{ }_{56}^{144} B a\)
3. \({ }_{40}^{91} \mathrm{Zr}\)
4. \({ }_{36}^{101} \mathrm{Kr}\)

Answer: 2. \({ }_{56}^{144} B a\)

Question 34. The energy equivalent of 0.5 g of a substance is

1. 0.5x1013J
2. 4.5x1016J
3. 4.5x1013J
4. 1.5x1013J

Answer: 3. 4.5x1013J

Question 35. A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragmentsis 8.5 MeV. The total gain in the Binding Energy in the process is

1. 9.4MeV
2. 804Mev
3. 216MeV
4. 0.9MeV

Answer: 3. 216MeV

Question 36. A 9. Radioactive nucleus \({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X}\) undergoes spontaneous decay in the sequence \({ }_{\mathrm{z}}^{\mathrm{A}} \mathrm{X} \rightarrow_{\mathrm{z}-1} \mathrm{~B} \rightarrow_{\mathrm{Z}-3} \mathrm{C} \rightarrow_{\mathrm{z}-2} \mathrm{D}\) where Z is the atomic number of element X. The possible decay particles
in the sequence are:

1. \(\alpha, \beta^{+}, \beta^{-}\)
2. \(\beta^{+}, \alpha, \beta^{-}\)
3. \(\beta^{-}, \alpha, \beta^{+}\)
4. \(\alpha, \beta^{-}, \beta^{+}\)

Answer: 2. \(\beta^{+}, \alpha, \beta^{-}\)

Question 37. The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be

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

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

Chapter 4 Nuclear Physics Multiple Choice Questions Part – 2: Jee (Main) / Aieee Problems (Previous Years)

Question 1. The above is a plot of binding energy per nucleon Eb, against the nuclear mass M; A, B, C, D, and E, correspond to different nuclei. Consider four reactions:

1. A + B → C + e
2. C → A + B +e
3. D + E → F + e and
4. F → D + E + e,

Answer: 4. F → D + E + e,

Question 2. The half life of a radioactive substance is 20 minutes. The approximate time interval (t2 – between the time t2 when \(\frac{2}{3}\) of it has decayed and time t1 when \(\frac{1}{3}\) of it had decayed is:

1. 7 min
2. 14 min
3. 20 min
4. 28 min

Answer: 3. 20 min

Question 3. Statement – 1: A nucleus having energy E1 decays by b– emission to a daughter nucleus having energy E 2, but the b– rays are emitted with a continuous energy spectrum having endpoint energy E1 – E2. Statement – 2: To conserve energy and momentum in B-decay at least three particles must take part in the transformation.

1. Statement 1 is correct but statement 2 is not correct.
2. Statement-1 and statement-2 both are correct and statement-2 is the correct explanation of statement-1.
3. Statement-1 is correct, statement-2 is correct and statement-2 is not the correct explanation of statement-1.
4. Statement-1 is incorrect, and statement-2 is correct.

Answer: 2. Statement-1 and statement-2 both are correct and statement-2 is the correct explanation of statement-1.

Question 4. Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (mass of neutron = 1.6725 × 10–27 kg, Mass of proton = 1.6725 × 10–27 kg, mass of electron = 9 × 10–31 kg)

1. 0.73 MeV
2. 7.10 MeV
3. 6.30 MeV
4. 5.4 MeV

Answer: 1. 0.73 MeV

Question 5. In a hydrogen-like atom, electrons make a transition from an energy level with quantum number n to another with a quantum number (n–1). If n>>1, the frequency of radiation emitted is proportional to :

1. \(\frac{1}{n}\)
2. \(\frac{1}{n^2}\)
3. \(\frac{1}{n 3 / 2}\)

Answer: 4. \(\frac{1}{n 3 / 2}\)

Question 6. Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively, initially the samples have equal numbers of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

1. 4:1
2. 1:4
3. 5:4
4. 1:16

Answer: 3. 5:4

Question 7. A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by

1. \(t=\frac{T}{\log (1.3)}\)
2. \(\mathrm{t}=\frac{\mathrm{T}}{2} \frac{\log 2}{\log 1.3}\)
3. \(\mathrm{t}=\mathrm{T} \frac{\log 1.3}{\log 2}\)
4. t=T log (1.3)

Answer: 3. \(\mathrm{t}=\mathrm{T} \frac{\log 1.3}{\log 2}\)

Question 8. A sample of radioactive material A, which has an activity of 10 mCi(1 Ci = 3.7 × 10 10 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively:

1. 10 days and 40 days
2. 20 days and 5 days
3. 5 days and 10 days
4. 20 days and 10 days

Answer: 1. 10 days and 40 days

Question 9. At a given instant, say t = 0, two radioactive substances A and B have equal activities. The ratio \(\frac{R_B}{R_A}\) of Their Activities after time itself decays with time \(t \text { as } e^{-3 t}\) If the half-life of A is n2, the half-life of B is :

1. \(\frac{\ell n 2}{4}\)
2. 2ln2
3. 4ln2
4. \(\frac{\ell \mathrm{n} 2}{2}\)

Answer: 2. 2ln2

Question 10. Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0, it was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to:

1. 150
2. 400
3. 360
4. 2000

Answer: 2. 400

Question 11. Consider the nuclear fission \(\mathrm{Ne}^{20} \rightarrow 2 \mathrm{He}^4+\mathrm{C}^{12}\)  Given that the binding energy/nucleon of Ne²⁰, He⁴, and C¹² are, respectively, 8.03 MeV, 7.07 MeV, and 7.86 MeV, identify the correct statement:

1. Energy Of 11.9 Mev Has To Be Supplied
2. 8.3 Mev Energy Will Be Released
3. Energy Of 12.4 Mev Will Be Supplied
4. Energy Of 3.6 Mev Will Be Released

Answer: 3. Energy Of 12.4 Mev Will Be Supplied

Question 12. In a radioactive decay chain, the initial nucleus is \({ }_{90}^{232} \mathrm{Th}.\) At the end there are 6 β-particles and 4 βparticles that are emitted. If the end nucleus is

1. A=202;X=8
2. A=208;Z=80
3. A=200;Z=81
4. A=208; Z=82

Answer: 4. A=208; Z=82

Chapter 4 Nuclear Physics Multiple Choice Questions Self Practice Paper

Question 1. Binding Energy per nucleon of a fixed nucleus XA is 6 MeV. It absorbs a neutron moving with KE = 2 MeV, and converts into Y at the ground state, emitting a photon of energy 1 MeV. The Binding Energy per nucleon of Y (in MeV) is

1. \(\frac{(6 A+1)}{(A+1)}\)
2. \(\frac{(6 A-1)}{(A+1)}\)
3. 7
4. \(\frac{7}{6}\)

Answer: 2. \(\frac{(6 A-1)}{(A+1)}\)

Question 2. The half life of a radioactive substance ‘A’ is 4 days. The probability that a nucleus will decay in two-half

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

Answer: 3. \(\frac{1}{4}\)

Question 3. To determine the half life of a radioactive element, a student plots a graph of \(\ln \left|\frac{d N(t)}{d t}\right|\) versus t. Here \(\frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}}\) is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is:

1. 8
2. 6
3. 7
4. 9

Answer: 1. 8

Question 4. The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10–25 kg. The mass (in mg) of the radioactive sample is

1. 8
2. 3
3. 5
4. 1

Answer: 4. 1

Question 5. An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for the safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

1. 64
2. 90
3. 108
4. 12

Answer: 3. 108

Question 6. The energy spectrum of b -particles (number N(E) as a function of -energy E) emitted from a radioactive source is:

Answer: 4.

Question 7. The ‘rad’ is the correct unit used to report the measurement of

1. The Rate Of Decay Of Radioactive Source
2. The Ability Of A Beam Of Gamma Ray Photons To Produce Ions In A Target
3. The Energy Delivered By Radiation To A Target.
4. The Biological Effect Of Radiation

Answer: 4. The Biological Effect Of Radiation