JEE Physics Nuclei MCQs Set 26

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Multiple Choice Questions

Question 1: Radium ²²⁶Ra spontaneously decays to radon with the emission of α-particle and a γ ray. If the speed of the α particle upon emission from an initially stationary radium nucleus is 1.5 × 10⁷ m/s, what is the recoil speed of the resultant radon nucleus? Assume the momentum of γ ray is negligible compared to that of α particle.
(a) 2.0 × 10⁵ m/s
(b) 2.7 × 10⁵ m/s
(c) 3.5 × 10⁵ m/s
(d) 1.5 × 10⁷ m/s
Show Answer & Explanation

Answer: (b) 2.7 × 10⁵ m/s

Explanation:
1. Radon has mass number 222.
2. \( 4 \times 1.5 \times 10^{7} = 222 V \), so \( V = 2.7 \times 10^{5} m/s \).

Teacher's Note:
1. Recall the basic fact.

Question 2: A radioactive element forms its own isotope after three consecutive disintegrations. The particles emitted are
(a) 3 β-particles
(b) 2 β-particles and 1 α-particle
(c) 3 α-particle
(d) 2 α-particles and 1 β-particle
Show Answer & Explanation

Answer: (b) 2 β-particles and 1 α-particle

Explanation:
1. An isotope has the same \( Z \).
2. One α lowers \( Z \) by 2 and two β⁻ raise it by 2, so net \( Z \) is unchanged.

Teacher's Note:
1. Recall the basic fact.

Question 3: Half lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes. Initially the samples of A and B have equal numbers of nuclei. After 80 minutes the ratio of remaining numbers of A and B nuclei is
(a) 1 : 16
(b) 4 : 1
(c) 1 : 4
(d) 1 : 1
Show Answer & Explanation

Answer: (c) 1 : 4

Explanation:
1. A: \( 80/20 = 4 \) half-lives → 1/16.
2. \( B \): \( 80/40 = 2 \) half-lives → 1/4.
3. Ratio \( A \) : \( B = 1 \) : 4.

Teacher's Note:
1. Recall the basic fact.

Question 4: Match Column I with Column II.
Column IColumn II
(A) Nuclear fusion(1) E = mc²
(B) Nuclear fission(2) Generally possible for nuclei with low atomic number
(C) β-decay(3) Generally possible for nuclei with higher atomic number
(D) Mass-energy equivalence(4) Essentially proceeds by weak interaction

(a) A-3, B-2, C-4, D-1
(b) A-2, B-1, C-4, D-3
(c) A-1, B-3, C-4, D-2
(d) A-2, B-3, C-4, D-1
Show Answer & Explanation

Answer: (d) A-2, B-3, C-4, D-1

Explanation:
1. Fusion occurs for light nuclei.
2. Fission occurs for heavy nuclei.
3. β-decay proceeds by weak interaction.
4. Mass-energy equivalence is \( E \) = mc².

Teacher's Note:
1. Light nuclei fuse and heavy nuclei split.

Question 5: The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and 975 counts per minute at t = 5 minutes. The decay constant is approximately
(a) 0.922 per minute
(b) 0.691 per minute
(c) 0.461 per minute
(d) 0.230 per minute
Show Answer & Explanation

Answer: (c) 0.461 per minute

Explanation:
1. \( N/N_{0} = 1/10 = e^{-5\lambda} \).
2. \( \lambda = \ln10/5 = 2.303/5 = 0.461 \) per minute.

Teacher's Note:
1. Recall the basic fact.

Question 6: If 1 mg of U²³⁵ is completely annihilated, the energy liberated is
(a) 9 × 10¹⁰ J
(b) 9 × 10¹⁹ J
(c) 9 × 10¹⁸ J
(d) 9 × 10¹⁷ J
Show Answer & Explanation

Answer: (a) 9 × 10¹⁰ J

Explanation:
1. \( E \) = mc² = \( 10^{-6} \times (3 \times 10^{8})^{2} = 9 \times 10^{10} J \).

Teacher's Note:
1. Recall the basic fact.

Question 7: Actinium ²³¹Ac₈₉ emits in succession two β particles, four α-particles, one β and one α plus several γ rays. What is the resultant isotope?
(a) \( ^{221}\text{Au}_{79} \)
(b) \( ^{211}\text{Pb}_{82} \)
(c) \( ^{221}\text{Pb}_{82} \)
(d) \( ^{211}\text{Au}_{79} \)
Show Answer & Explanation

Answer: (b) \( ^{211}\text{Pb}_{82} \)

Explanation:
1. Total α-particles = \( 4 + 1 = 5 \), so \( A = 231 - 20 = 211 \).
2. Total \( \beta^{-} = 2 + 1 = 3 \), so \( Z = 89 + 3 - 10 = 82 \).
3. The nucleus is ²¹¹Pb₈₂.

Teacher's Note:
1. Recall the basic fact.

Question 8: A radioactive nucleus of mass M emits a photon of frequency ν and the nucleus recoils. The recoil energy will be
(a) \( Mc^2-h\nu \)
(b) \( h^2\nu^2/2Mc^2 \)
(c) \( 0 \)
(d) \( h\nu \)
Show Answer & Explanation

Answer: (b) \( h^2\nu^2/2Mc^2 \)

Explanation:
1. Photon momentum \( p \) = hν/c equals the recoil momentum.
2. Recoil energy = \( p^{2}/2M \) = h²ν²/(2Mc²).

Teacher's Note:
1. Recall the basic fact.

Question 9: Consider the following statements. I. The relative abundance of different isotopes differs from element to element. II. Atomic species of the same element differing in mass are called isotopes. III. Hydrogen has two isotopes.
(a) I only
(b) II only
(c) I and II
(d) I, II and III
Show Answer & Explanation

Answer: (c) I and II

Explanation:
1. Hydrogen has three isotopes (protium, deuterium, tritium), so III is false.

Teacher's Note:
1. Recall the basic fact.

Question 10:
Assertion (A): Cobalt-60 is useful in cancer therapy.
Reason (R): Cobalt-60 is source of γ-radiations capable of killing cancerous cells.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The γ-rays from Co-60 destroy cancer cells, which explains its use.

Teacher's Note:
1. Compare the two statements.

Question 11: The rate of disintegration at a given instant, is directly proportional to the number of atoms present at that instant. This is the statement of
(a) law of radioactive decay
(b) half life
(c) law of radioactive transformation
(d) group displacement law
Show Answer & Explanation

Answer: (a) law of radioactive decay

Explanation:
1. −dN/dt = \( \lambdaN \) is the law of radioactive decay.

Teacher's Note:
1. Recall the basic fact.

Question 12: If the total binding energies of ²₁H, ⁴₂He, ⁵⁶₂₆Fe and ²³⁵₉₂U nuclei are 2.22, 28.3, 492 and 1786 MeV respectively, identify the most stable nucleus of the following.
(a) ⁵⁶₂₆Fe
(b) ²₁H
(c) ²³⁵₉₂U
(d) ⁴₂He
Show Answer & Explanation

Answer: (a) ⁵⁶₂₆Fe

Explanation:
1. Binding energy per nucleon: \( H 1.11 \), He 7.08, Fe \( 8.79, U 7.60 \) MeV.
2. Fe has the highest and is the most stable.

Teacher's Note:
1. Recall the basic fact.

Question 13: At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of mixture is
(a) \( -N_1N_2e^{-(\lambda_1+\lambda_2)t} \)
(b) \( -\left(\frac{N_1}{N_2}\right)e^{-(\lambda_1+\lambda_2)t} \)
(c) \( -(N_1\lambda_1e^{-\lambda_1t}+N_2\lambda_2e^{-\lambda_2t}) \)
(d) \( -N_1\lambda_1N_2\lambda_2e^{(-\lambda_1+\lambda_2)t} \)
Show Answer & Explanation

Answer: (c) \( -(N_1\lambda_1e^{-\lambda_1t}+N_2\lambda_2e^{-\lambda_2t}) \)

Explanation:
1. Each species decays independently: dN/dt = \( -\lambda_{1}N_{1}e^{-\lambda_{1}t} - \lambda_{2}N_{2}e^{-\lambda_{2}t} \).

Teacher's Note:
1. Recall the basic fact.

Question 14: Mp denotes the mass of a proton and Mn 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 by (c is the velocity of light)
(a) \( M(N,Z)=NM_n+ZM_p+B/c^2 \)
(b) \( M(N,Z)=NM_n+ZM_p-Bc^2 \)
(c) \( M(N,Z)=NM_n+ZM_p+Bc^2 \)
(d) \( M(N,Z)=NM_n+ZM_p-B/c^2 \)
Show Answer & Explanation

Answer: (d) \( M(N,Z)=NM_n+ZM_p-B/c^2 \)

Explanation:
1. Nuclear mass = sum of nucleon masses − mass defect, and mass defect = \( B/c^{2} \).

Teacher's Note:
1. Recall the basic fact.

Question 15: The masses of neutron and proton are 1.0087 a.m.u. and 1.0073 a.m.u. respectively. If the neutrons and protons combine to form a helium nucleus (alpha particles) of mass 4.0015 a.m.u the binding energy of the helium nucleus will be (1 a.m.u. = 931 MeV)
(a) 28.4 MeV
(b) 20.8 MeV
(c) 27.3 MeV
(d) 14.2 MeV
Show Answer & Explanation

Answer: (a) 28.4 MeV

Explanation:
1. \( \Deltam = 2(1.0087) + 2(1.0073) - 4.0015 = 0.0305 u \).
2. \( B = 0.0305 \times 931 = 28.4 \) MeV.

Teacher's Note:
1. Recall the basic fact.

Question 16:
Assertion (A): Density of all the nuclei is same.
Reason (R): Radius of nucleus is directly proportional to the cube root of mass number.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. \( R ∝ A^{1}/3 \)), so volume \( ∝ A \) and density = mass/volume is independent of \( A \).

Teacher's Note:
1. Volume proportional to mass gives constant density.

Question 17: Half lives for α and β emission of a radioactive material are 16 years and 48 years respectively. When material decays giving α and β emission simultaneously, time in which 3/4th material decays is
(a) 29 years
(b) 24 years
(c) 64 years
(d) 12 years
Show Answer & Explanation

Answer: (b) 24 years

Explanation:
1. \( \lambda = \ln2(1/16 + 1/48) = \ln2/12 \), so the effective half-life is 12 years.
2. 3/4 decayed means 2 half-lives = 24 years.

Teacher's Note:
1. Recall the basic fact.

Question 18: In a given reaction ZAᴬ → Z₊₁Yᴬ → Z₋₁Kᴬ⁻⁴ → Z₋₁Kᴬ⁻⁴, radioactive radiations are emitted in the sequence of
(a) α, β, γ
(b) γ, α, β
(c) β, α, γ
(d) γ, β, α
Show Answer & Explanation

Answer: (c) β, α, γ

Explanation:
1. \( Z \to Z+1 \) with the same \( A \) is β⁻.
2. Then \( A - 4 \) and \( Z - 2 \) is α.
3. No change in \( A \) and \( Z \) is γ.

Teacher's Note:
1. Recall the basic fact.

Question 19: Fusion reaction occurs at temperatures of the order of
(a) 10³ K
(b) 10⁷ K
(c) 10 K
(d) 10⁴ K
Show Answer & Explanation

Answer: (b) 10⁷ K

Explanation:
1. Nuclei must overcome Coulomb repulsion, which needs about \( 10^{7} K \).

Teacher's Note:
1. Recall the basic fact.

Question 20: A radioactive substance has half life of four months. Three fourth of the substance will decay in
(a) three months
(b) four months
(c) eight months
(d) twelve months
Show Answer & Explanation

Answer: (c) eight months

Explanation:
1. 3/4 decayed leaves 1/4, which takes 2 half-lives = 8 months.

Teacher's Note:
1. Recall the basic fact.

Question 21: The fossil bone has a ¹⁴C : ¹²C ratio, which is 1/16 of that in a living animal bone. If the half-life of ¹⁴C is 5730 years, then the age of the fossil bone is
(a) 11460 years
(b) 17190 years
(c) 22920 years
(d) 45840 years
Show Answer & Explanation

Answer: (c) 22920 years

Explanation:
1. \( 1/16 = 2^{-4} \) means 4 half-lives: \( 4 \times 5730 = 22920 \) years.

Teacher's Note:
1. Recall the basic fact.

Question 22: γ-rays are deflected by
(a) an electric field but not by a magnetic field
(b) a magnetic field but not by an electric field
(c) both electric and magnetic field
(d) neither by electric field nor by magnetic field
Show Answer & Explanation

Answer: (d) neither by electric field nor by magnetic field

Explanation:
1. γ-rays are uncharged photons, so neither field deflects them.

Teacher's Note:
1. Recall the basic fact.

Question 23: The 'rad' is the correct unit used to report the measurement of
(a) the ability of a beam of gamma ray photons to produce ions in a target
(b) the energy delivered by radiation to a target
(c) the biological effect of radiation
(d) the rate of decay of a radioactive source
Show Answer & Explanation

Answer: (b) the energy delivered by radiation to a target

Explanation:
1. The rad measures the absorbed dose, the energy delivered to the target.

Teacher's Note:
1. Recall the basic fact.

Question 24: The mass of a ⁷₃Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of ⁷₃Li nucleus is nearly
(a) 46 MeV
(b) 5.6 MeV
(c) 3.9 MeV
(d) 23 MeV
Show Answer & Explanation

Answer: (b) 5.6 MeV

Explanation:
1. \( B = 0.042 \times 931.5 = 39.1 \) MeV.
2. \( B/A = 39.1/7 = 5.6 \) MeV.

Teacher's Note:
1. Recall the basic fact.

Question 25: Radioactivity is
(a) irreversible process
(b) self disintegration process
(c) spontaneous
(d) all of the above
Show Answer & Explanation

Answer: (d) all of the above

Explanation:
1. Radioactivity is a spontaneous, self disintegration process that cannot be reversed.

Teacher's Note:
1. Recall the basic fact.

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