Previous year questions: Nuclei

Board pattern for this chapter

The Nuclei chapter supplies graph-based questions on binding energy and the nuclear force, short calculations of mass defect and binding energy, and odd one-mark assertion items. All ten items below are rewritten from official CBSE papers between 2022 and 2025. Marks are printed in each heading, and the year tells you which paper to open.

Q1 (CBSE Board 2023, 3 marks)

Draw a graph of binding energy per nucleon against mass number for different nuclei, mention two features of the graph, and explain why lighter nuclei usually undergo fusion.

Answer: The graph rises steeply for light nuclei, stays nearly flat at about 8 MeV per nucleon for 30 < A < 170, peaks near 8.75 MeV at A = 56 and falls slowly for heavy nuclei to about 7.6 MeV at A = 238. Two features: the middle range is nearly independent of A, and the value drops at both the light and the heavy ends. Lighter nuclei fuse because the product of fusion lies higher on the curve, so the nucleons become more tightly bound and the mass difference is released as energy.

Q2 (CBSE Board 2023, 2 marks)

Draw a graph showing the variation of binding energy per nucleon with mass number A, and explain why the binding energy per nucleon for heavy nuclei with A greater than 170 decreases as A increases.

Answer: For heavy nuclei, the short-range nuclear force acts only between near neighbours, so the binding contribution per nucleon stops growing. At the same time the number of protons keeps rising, and the long-range Coulomb repulsion between them grows steadily. The repulsion subtracts more and more from the binding, so the curve bends down beyond A of about 170.

Q3 (CBSE Board 2023, 3 marks)

(a) Prove that the nuclear density is the same for all nuclei. (b) Sketch the potential energy of two nucleons against their separation and give two inferences.

Answer: (a) Volume is proportional to R cubed, and R goes as A to the power one-third, so volume is proportional to A. Mass is also proportional to A, so mass divided by volume is constant; numerically the density is of the order of 10 to the 17 kg per cubic metre. (b) The plot has a deep minimum near r0 = 0.8 fm, falls to about -100 MeV, and rises steeply for smaller separations. Two inferences: the force is attractive for separations greater than r0, and it is strongly repulsive when the nucleons are pushed closer than r0, which keeps nuclei from collapsing.

Q4 (CBSE Board 2023, 2 marks)

Draw the graph of binding energy per nucleon against mass number A for nuclei with 2 < A < 170, and use the graph to explain the release of energy in nuclear fission.

Answer: The graph rises to a peak near A = 56 and then flattens. A heavy nucleus has a lower binding energy per nucleon than the medium-mass fragments it produces on fission. Splitting therefore moves the nucleons up the curve into more tightly bound states, and the increase in binding energy appears as released energy.

Q5 (CBSE Board 2024, 3 marks)

(a) Write two characteristic properties of the nuclear force. (b) Draw a plot of the potential energy of a pair of nucleons against their separation and state two conclusions from it.

Answer: (a) At nuclear separations this force far exceeds the Coulomb repulsion, and its range is only a few femtometres, beyond which it fades to nothing. It is charge independent, acting on protons and neutrons alike. (b) The plot has a minimum at about 0.8 fm and about -100 MeV, and it turns strongly positive at smaller separations. Conclusions: the force is attractive beyond 0.8 fm and repulsive below it, and the repulsive core gives the nucleus a definite size.

Q6 (CBSE Board 2024, 2 marks)

The carbon isotope carbon-12 has a nuclear mass of 12.000000 u. Calculate the binding energy of its nucleus, given m proton = 1.007825 u and m neutron = 1.008665 u.

Answer: Carbon-12 has 6 protons and 6 neutrons. The parts mass 6 × 1.007825 + 6 × 1.008665 = 12.09894 u, so the mass defect is 0.09894 u. The binding energy is 0.09894 × 931.5, about 92.2 MeV, which is about 7.68 MeV per nucleon.

Q7 (CBSE Board 2024, 2 marks)

Differentiate between mass defect and binding energy per nucleon. Why is the binding energy per nucleon nearly constant in the range 30 < A < 170?

Answer: Mass defect is the difference between the sum of the masses of the separate protons and neutrons and the mass of the assembled nucleus; binding energy is that mass difference multiplied by c squared. Binding energy per nucleon is the binding energy divided by A, so it measures the tightness of binding per particle. It is nearly constant in 30 < A < 170 because the nuclear force is short-ranged: each interior nucleon interacts only with its near neighbours, so adding more nucleons does not raise the average binding per nucleon.

Q8 (CBSE Board 2025, 1 mark)

Assertion (A): During the formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus. Reason (R): For all nuclei, the value of binding energy per nucleon increases with mass number.

Answer: Assertion A is true, but Reason R is false. When nucleons come together, the lost mass appears as the binding energy, E b = ΔM c squared. The binding energy per nucleon does not increase with mass number throughout: it rises for light nuclei, stays nearly constant between A = 30 and 170, and falls for heavy nuclei.

Q9 (CBSE Additional PQ 2023-24, 3 marks)

A nucleus of mass number 250 at rest undergoes fission into two identical nuclei. Find the electrical potential energy of the two nuclei just after fission. Take R0 = 1.28 × 10 to the -15 m.

Answer: Each fragment has mass number 125, so its radius is R0 A to the power one-third = 1.28 × 10 to the -15 × (125) to the power one-third. Since 125 to the power one-third is 5, R = 6.4 × 10 to the -15 m. The centres are 2R apart, so the potential energy is (1/4πε0) (Z e)(Z e)/(2R), with Z = 50 for each fragment. Substituting gives about 9.0 × 10 to the 9 × (50 × 1.6 × 10 to the -19) squared/(1.28 × 10 to the -14), which is of the order of 4.5 × 10 to the -11 J, or about 280 MeV.

Q10 (CBSE Additional PQ 2022-23, 1 mark)

Assertion (A): The curve of binding energy per nucleon against mass number droops at high mass numbers (A greater than 170) as well as at low mass numbers (A less than 30). Reason (R): Nuclei with middle mass numbers (30 < A < 170) have higher binding energy per nucleon.

Answer: Both A and R are true, and R is the correct explanation of A. The middle-mass nuclei are the most tightly bound, which is why the curve is highest there and droops on both sides, and this shape is what makes both fission of heavy nuclei and fusion of light nuclei release energy.

What the board rewards

Graph questions need the shape and the numbers, so mark the peak near A = 56 at about 8.75 MeV and the value at A = 238 at about 7.6 MeV. Label the axes as binding energy per nucleon in MeV and mass number A, because unlabelled axes lose a mark even when the curve is right. Numerical answers need the particle count written explicitly before the masses, because the examiner looks for that step. Show the conversion with 931.5 MeV per u in the same line as the defect, so the units never drift. Assertion questions about the curve, the nuclear force and mass defect are usually answerable from the properties rather than from any calculation. In the numericals, the most common lost mark is a missed neutron: check that Z plus N equals A before substituting any mass. Read the reason separately from the assertion, because many of these items pair a true statement with a false reason.