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Nuclear composition, size and atomic masses: NEET MCQs with answers

49 questions on this topic of Atoms and Nuclei (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. The nuclear radius of an isotope with mass number 125 is 6.0 fm. What is the approximate nuclear radius of an isotope with mass number 64?

  1. 4.0 fm
  2. 3.6 fm
  3. 5.2 fm
  4. 4.8 fm
Show answer and explanation

Answer: (D) 4.8 fm

Nuclear radius is proportional to A^(1/3). Therefore, R₁/R₂ = (A₁/A₂)^(1/3) = (125/64)^(1/3) = 5/4. Thus, R₂ = R₁ × (4/5) = 6.0 × 0.8 = 4.8 fm.

medium

2. Statement I: A free neutron is unstable and decays into a proton, an electron, and an antineutrino with a mean life of about 1000 s. Statement II: A free proton is unstable and spontaneously decays into a neutron, a positron, and a neutrino. Choose the correct option:

  1. Both Statement I and Statement II are correct.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. Both Statement I and Statement II are incorrect.
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect.

A free neutron is unstable outside the nucleus and undergoes β⁻ decay with a mean lifetime of about 1000 s. A free proton is stable because its mass is less than that of a neutron, so it cannot spontaneously decay into a heavier neutron outside the nucleus.

hard

3. The ratio of the electrostatic potential at the surface of two spherical nuclei with equal nuclear charge density but mass numbers A₁ and A₂ is:

  1. (A₁ / A₂)
  2. (A₁ / A₂)^(1/3)
  3. (A₁ / A₂)^(2/3)
  4. (A₁ / A₂)^(4/3)
Show answer and explanation

Answer: (C) (A₁ / A₂)^(2/3)

Charge density ρ_c is constant, so Z ∝ V ∝ R³. The potential at the surface is V = kQ/R ∝ Z/R ∝ R³ / R = R². Since R ∝ A^(1/3), we have V ∝ (A^(1/3))² = A^(2/3). Thus, V₁ / V₂ = (A₁ / A₂)^(2/3).

medium

4. Consider two nuclei X and Y. If the ratio of their radii is R_X : R_Y = 1 : 2, what is the ratio of their nuclear mass numbers A_X : A_Y?

  1. 1 : 4
  2. 1 : 8
  3. 1 : √2
  4. 1 : 16
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Answer: (B) 1 : 8

Since R = R₀ A^(1/3), we have A ∝ R³. Therefore, A_X / A_Y = (R_X / R_Y)³ = (1/2)³ = 1/8.

easy

5. The ratio of the nuclear radius of ¹²⁵Te to that of ²⁷Al is:

  1. 25 : 9
  2. 5 : 3
  3. 125 : 27
  4. √5 : √3
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Answer: (B) 5 : 3

Nuclear radius varies as R = R₀ A^(1/3). Therefore, R(¹²⁵Te) / R(²⁷Al) = (125 / 27)^(1/3) = 5 / 3.

hard

6. Assuming the nuclear radius formula R = R₀ A^(1/3) with R₀ = 1.2 fm, the electrostatic potential at the surface of a gold nucleus (₇₉Au¹⁹⁷) is approximately: (Take 1/(4πε₀) = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C, 197^(1/3) ≈ 5.82)

  1. 2.8 × 10⁶ V
  2. 1.6 × 10⁷ V
  3. 1.6 × 10⁵ V
  4. 8.5 × 10⁷ V
Show answer and explanation

Answer: (B) 1.6 × 10⁷ V

The radius R = R₀ A^(1/3) = 1.2 × 10⁻¹⁵ × 5.82 ≈ 6.98 × 10⁻¹⁵ m ≈ 7.0 × 10⁻¹⁵ m. The potential V = (1/(4πε₀)) × (Ze / R) = (9 × 10⁹ × 79 × 1.6 × 10⁻¹⁹) / (7.0 × 10⁻¹⁵) = 1.1376 × 10⁻⁷ / 7.0 × 10⁻¹⁵ ≈ 1.63 × 10⁷ V.

easy

7. Which of the following statements regarding a neutron is INCORRECT according to NCERT?

  1. A neutron inside a stable nucleus is stable.
  2. A neutron possesses an intrinsic negative electric charge distributed uniformly inside it.
  3. The mean life of a free neutron is approximately 1000 s.
  4. An isolated free neutron decays spontaneously into a proton, an electron, and an antineutrino.
Show answer and explanation

Answer: (B) A neutron possesses an intrinsic negative electric charge distributed uniformly inside it.

A neutron is an electrically neutral particle with zero net charge. Inside a stable nucleus it is stable, but a free neutron is unstable and undergoes β-decay with a mean life of about 1000 s.

easy

8. Two spherical nuclei have mass numbers A₁ and A₂. The ratio of their nuclear mass densities ρ₁ / ρ₂ is:

  1. (A₁ / A₂)^(1/3)
  2. A₁ / A₂
  3. (A₂ / A₁)^(1/3)
  4. 1
Show answer and explanation

Answer: (D) 1

Nuclear mass is approximately proportional to A, and nuclear volume V = (4/3)πR³ ∝ A because R = R₀ A^(1/3). Therefore, nuclear density ρ = Mass / Volume ∝ A / A = constant, making the ratio ρ₁ / ρ₂ = 1 for all nuclei.

easy

9. Taking R₀ = 1.2 fm, the radius of a nucleus with mass number 216 is:

  1. 17.6 fm
  2. 7.2 fm
  3. 86.4 fm
  4. 259 fm
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Answer: (B) 7.2 fm

R = R₀A^(1/3) = 1.2 × 216^(1/3) = 1.2 × 6 = 7.2 fm.

easy

10. If the nuclear radius of a nucleus with mass number 8 is 2.4 fm, the nuclear radius of a nucleus with mass number 64 is:

  1. 9.6 fm
  2. 4.8 fm
  3. 3.6 fm
  4. 6.0 fm
Show answer and explanation

Answer: (B) 4.8 fm

Nuclear radius is given by R ∝ A^(1/3). Thus, R₂ / R₁ = (A₂ / A₁)^(1/3) = (64 / 8)^(1/3) = 8^(1/3) = 2. Therefore, R₂ = 2 × 2.4 fm = 4.8 fm.

medium

11. Which of the following pairs of nuclei are isodiaphers (nuclides having the same neutron excess, N - Z)?

  1. ²³Na₁₁ and ²⁴Mg₁₂
  2. ¹⁴C₆ and ¹⁴N₇
  3. ³H₁ and ³He₂
  4. ²³⁸U₉₂ and ²³⁴Th₉₀
Show answer and explanation

Answer: (D) ²³⁸U₉₂ and ²³⁴Th₉₀

For ²³⁸U₉₂, N = 238 - 92 = 146, so N - Z = 146 - 92 = 54. For ²³⁴Th₉₀, N = 234 - 90 = 144, so N - Z = 144 - 90 = 54. Since both have the same neutron excess (N - Z = 54), they are isodiaphers.

medium

12. Two spherical nuclei have mass numbers in the ratio 1 : 8. If they coalesce into a single spherical nucleus assuming nuclear volume is conserved, the ratio of the radius of the newly formed nucleus to that of the lighter initial nucleus is:

  1. 3 : 1
  2. 9^(1/3) : 1
  3. 2 : 1
  4. 9^(1/2) : 1
Show answer and explanation

Answer: (B) 9^(1/3) : 1

When nuclei coalesce, their mass numbers add: A_new = A₁ + A₂ = A₁ + 8A₁ = 9A₁. Since R ∝ A^(1/3), the ratio of the new radius to the lighter nucleus radius is (9A₁ / A₁)^(1/3) = 9^(1/3) : 1.

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