Nuclei – Nucleus: NEET MCQs with Answers

14 free questions on Nuclei – Nucleus for NEET (UG), starting with previous-year NEET and AIPMT questions. Try each one, then tap Show answer for the answer and a short explanation.

Syllabus covered: Nucleus, Atomic Masses and Radioactivity: Composition and size of nucleus, atomic masses, Radioactive Decay Law, Half-life and Mean Life

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Question 1

Previous-year question
An α-particle consists of [NEET 2019]
  1. 2 protons and 2 neutrons only
  2. 2 electrons, 2 protons and 2 neutrons
  3. 2 electrons and 4 protons only
  4. 2 protons only
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Answer: (A) 2 protons and 2 neutrons only
Explanation: An α-particle is a doubly ionised helium nucleus ₂He⁴ – two protons and two neutrons, with no electrons. Its charge is +2e and its mass number is 4.

Question 2

Previous-year question
For a radioactive material the half-life is 10 minutes. If initially there are 600 nuclei, the time taken for the disintegration of 450 nuclei is [NEET 2018]
  1. 20 minutes
  2. 10 minutes
  3. 15 minutes
  4. 30 minutes
Show answer
Answer: (A) 20 minutes
Explanation: If 450 have decayed, 150 remain, i.e. N/N₀ = 150/600 = 1/4 = (1/2)². Two half-lives have elapsed, so t = 2 × 10 = 20 minutes.

Question 3

Previous-year question
Radioactive material A has decay constant 8λ and material B has decay constant λ. Initially they have the same number of nuclei. After what time will the ratio of the number of nuclei of A to that of B be 1/e? [NEET 2017]
  1. 1/7λ
  2. 1/8λ
  3. 1/9λ
  4. 1/λ
Show answer
Answer: (A) 1/7λ
Explanation: N_A/N_B = e⁻⁸λᵗ/e⁻λᵗ = e⁻⁷λᵗ. Setting this equal to 1/e gives 7λt = 1, i.e. t = 1/7λ.

Question 4

Previous-year question
A nucleus of uranium decays at rest into nuclei of thorium and helium. Then [AIPMT 2015]
  1. The helium nucleus has less momentum than the thorium nucleus
  2. The helium nucleus has more momentum than the thorium nucleus
  3. The helium nucleus has less kinetic energy than the thorium nucleus
  4. The helium nucleus has more kinetic energy than the thorium nucleus
Show answer
Answer: (D) The helium nucleus has more kinetic energy than the thorium nucleus
Explanation: Momentum conservation gives the two fragments equal and opposite momenta of the same magnitude. Since K = p²/2m and the helium nucleus is much lighter, it carries much more kinetic energy.

Question 5

Previous-year question
A radioisotope ‘X’ with half-life 1.4 × 10⁹ years decays to ‘Y’ which is stable. A rock sample from a cave was found to contain X and Y in the ratio 1 : 7. The age of the rock is [AIPMT 2014]
  1. 1.96 × 10⁹ years
  2. 3.92 × 10⁹ years
  3. 4.20 × 10⁹ years
  4. 8.40 × 10⁹ years
Show answer
Answer: (C) 4.20 × 10⁹ years
Explanation: X : Y = 1 : 7 means the surviving fraction is 1/8 = (1/2)³, i.e. three half-lives have elapsed. Age = 3 × 1.4 × 10⁹ = 4.2 × 10⁹ years.

Question 6

The density of nuclear matter is about 2.3 × 10¹⁷ kg/m³. If the entire mass of the Earth (6 × 10²⁴ kg) were packed into a sphere of this density, its radius would be closest to
  1. 180 m
  2. 1.8 km
  3. 18 m
  4. 18 km
Show answer
Answer: (A) 180 m
Explanation: The volume needed is V = M/ρ = (6 × 10²⁴)/(2.3 × 10¹⁷) ≈ 2.6 × 10⁷ m³. Using V = (4/3)πr³ gives r³ ≈ 6.2 × 10⁶ m³. Taking the cube root gives r ≈ 184 m, or about 180 m.

Question 7

When beryllium is bombarded with alpha particles, a penetrating neutral radiation is emitted that can knock protons out of light nuclei such as helium, carbon and nitrogen. Why did Chadwick reject the idea that this radiation consisted of photons?
  1. Conservation of energy and momentum would require photons of far more energy than the alpha-beryllium bombardment could supply
  2. The radiation was strongly deflected by a magnetic field, which photons never are
  3. Photons cannot pass through matter at all, whereas this radiation was penetrating
  4. Photons carry no momentum, so they could not knock out any particle
Show answer
Answer: (A) Conservation of energy and momentum would require photons of far more energy than the alpha-beryllium bombardment could supply
Explanation: The only neutral radiation known then was photons. Applying conservation of energy and momentum to the ejected protons showed that such photons would need much more energy than the bombardment could provide. The results were explained by assuming a neutral particle with mass nearly equal to that of the proton, which is the neutron.
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Question 8

A nucleus M emits a β⁻ particle to form N, and N then emits an α particle to form R. Compared with M, the nucleus R has
  1. 1 fewer proton and 3 fewer neutrons
  2. 1 more proton and 3 fewer neutrons
  3. 1 fewer proton and 4 fewer neutrons
  4. 2 fewer protons and 2 fewer neutrons
Show answer
Answer: (A) 1 fewer proton and 3 fewer neutrons
Explanation: In β⁻ decay one neutron turns into a proton, so the change is +1 proton and −1 neutron. In α decay the nucleus loses 2 protons and 2 neutrons. Adding the two steps gives −1 proton and −3 neutrons. The mass number falls by 4, as expected, and M and N are isobars.

Question 9

A radioactive gas of half-life 3 h is injected into a sealed vessel at t = 0, giving an activity of 1600 Bq. At t = 6 h more of the same gas is injected, which suddenly raises the activity by 600 Bq. Which option correctly gives the shape of the ln A versus t plot and the activity at t = 9 h?
  1. Two parallel straight segments of equal negative slope, with an upward jump at 6 h; 500 Bq
  2. Two parallel straight segments of equal negative slope, with an upward jump at 6 h; 350 Bq
  3. A single straight line of negative slope; 200 Bq
  4. Two straight segments, the second steeper than the first, with an upward jump at 6 h; 500 Bq
Show answer
Answer: (A) Two parallel straight segments of equal negative slope, with an upward jump at 6 h; 500 Bq
Explanation: Since ln A = ln A₀ − λt, the plot is a straight line of slope −λ. At t = 6 h, two half-lives have passed and the activity is 400 Bq, which jumps to 1000 Bq on injection. The same isotope has the same λ, so the second segment is parallel to the first. One more half-life by t = 9 h gives 500 Bq.

Question 10

Consider the potential energy curve of a pair of nucleons, which has its minimum at a separation of about 0.8 fm. What is the nature of the nuclear force between the pair at separations of 0.4 fm, 1.5 fm and 10 fm respectively?
  1. Attractive, attractive, weakly attractive
  2. Repulsive, attractive, negligible
  3. Attractive, repulsive, negligible
  4. Repulsive, attractive, attractive and strong
Show answer
Answer: (B) Repulsive, attractive, negligible
Explanation: Force is the negative slope of the potential energy curve. Below about 0.8 fm the potential energy rises steeply as the nucleons approach, so the force is strongly repulsive. Just beyond the minimum the force is attractive. It falls rapidly to zero beyond a few femtometres because the nuclear force is short ranged.

Question 11

Two nuclei have mass numbers in the ratio 64 : 27. What are the ratios of their surface areas and of their densities, respectively?
  1. 16 : 9 and 64 : 27
  2. 4 : 3 and 64 : 27
  3. 16 : 9 and 1 : 1
  4. 4 : 3 and 1 : 1
Show answer
Answer: (C) 16 : 9 and 1 : 1
Explanation: Nuclear radius varies as A^(1/3), so the radii are in the ratio 4 : 3. Surface area varies as the square of the radius, which gives 16 : 9. Volume varies as A, just as mass does, so all nuclei have practically the same density and the ratio is 1 : 1.

Question 12

Two protons are held 50 Å apart. If Fₙ, Fₑ and F_g are the magnitudes of the nuclear, electrostatic and gravitational forces between them, which ordering is correct?
  1. Fₑ > Fₙ > F_g
  2. F_g > Fₑ > Fₙ
  3. Fₙ > Fₑ > F_g
  4. Fₑ > F_g > Fₙ
Show answer
Answer: (D) Fₑ > F_g > Fₙ
Explanation: A separation of 50 Å is 5 × 10⁶ fm, far beyond the few-femtometre range of the nuclear force, which has dropped to practically nothing. The electrostatic and gravitational forces are both long-range and fall only as 1/r². The electrostatic force between two protons is about 10³⁶ times the gravitational force at any separation.

Question 13

Assertion: The nucleons of a nucleus do not collapse towards a single point in spite of the very strong attractive nuclear force between them. Reason: The nuclear force between two nucleons becomes strongly repulsive when their separation falls below about 0.8 fm.
  1. Assertion is false, but Reason is true
  2. Both Assertion and Reason are true, and Reason correctly explains Assertion
  3. Assertion is true, but Reason is false
  4. Both Assertion and Reason are true, but Reason does not explain Assertion
Show answer
Answer: (B) Both Assertion and Reason are true, and Reason correctly explains Assertion
Explanation: The attraction holds nucleons together only down to a separation of about 0.8 fm. Below this the force turns strongly repulsive, which keeps nucleons from being pressed closer. This sets the nearly fixed spacing between nucleons, so the nucleus keeps a finite size and a nearly constant density.

Question 14

The potential energy of a pair of nucleons, plotted against their separation r, has a minimum at r₀ ≈ 0.8 fm, rises steeply for smaller r and approaches zero beyond a few femtometres. What does this curve imply about the nuclear force between them?
  1. The force is attractive at every separation and is largest as r approaches zero
  2. The force is zero at r₀, attractive for r > r₀ and repulsive for r < r₀
  3. The force is zero at r₀, repulsive for r > r₀ and attractive for r < r₀
  4. The force is largest and attractive at r₀, and repulsive for all r > r₀
Show answer
Answer: (B) The force is zero at r₀, attractive for r > r₀ and repulsive for r < r₀
Explanation: Force equals the negative slope of the potential energy curve, so it vanishes at the minimum. To the right of the minimum the potential energy rises with r, which gives a force pulling the nucleons together. To the left it rises steeply as r falls, which gives a strong force pushing them apart.

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