Physics · Atoms and nuclei · chapter 13 of 14

Class 12 Physics Chapter 13: Nuclei case study question with answers

One case-based question of the kind the board asks: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

Ananya, a student in Kochi, plots the binding energy per nucleon E_bn of stable nuclei against mass number A from a table of data. Her graph is shown, with a few points marked and their E_bn values in MeV in brackets. P and Q are nuclei of mass numbers 90 and 180. She wants to compare the energy available from fusing very light nuclei with that from splitting heavy ones, reading the values from her graph.

Part 1 · 1 mark

The curve is nearly flat between A = 30 and A = 170 because the nuclear force

(a) is much stronger than the gravitational force(b) is short-ranged, so an interior nucleon is bound only by its near neighbours(c) does not depend on electric charge(d) becomes repulsive below 0.8 fm

Show answer

Answer: (b) is short-ranged, so an interior nucleon is bound only by its near neighbours

Saturation: with a short-ranged force, an interior nucleon's binding does not grow with the size of the nucleus, and most nucleons are interior. Charge independence, strength and the repulsive core are true properties but do not explain the flat region.

Part 2 · 1 mark

Using the marked values, the energy released per nucleon of fuel when two ²H nuclei fuse into ⁴He is about how many times that released per nucleon when nucleus Q splits into two nuclei like P?

(a) 1.0(b) 0.19(c) 8.6(d) 12

Show answer

Answer: (c) 8.6

Fusion: 4 × 7.1 − 2 × (2 × 1.1) = 24.0 MeV from 4 nucleons, 6.0 MeV per nucleon. Fission: 180 × (8.7 − 8.0) = 126 MeV from 180 nucleons, 0.70 MeV per nucleon. Ratio 6.0/0.70 ≈ 8.6. 0.19 compares the energies per reaction (24/126), not per nucleon.

Part 3 · 2 marks

Explain, using the graph, why neither the fission nor the fusion of nuclei near ⁵⁶Fe can release energy.

Answer and marking scheme

⁵⁶Fe sits at the peak of the curve, E_bn ≈ 8.75 MeV. Splitting it gives lighter nuclei with lower E_bn, and fusing two such nuclei gives a heavier one with lower E_bn. Either way the nucleons end up less tightly bound, the products have more mass than the reactants, the Q-value is negative, and energy has to be supplied.

⁵⁶Fe at the peak: the products of either process have lower E_bn (1)
less binding means more mass: negative Q-value, energy must be supplied (1)

Explain, using the graph, why stars can build up elements by fusion as a source of energy only up to mass numbers near 56.

Answer and marking scheme

Fusing two nuclei releases energy only when the product has a higher E_bn than the reactants. E_bn rises with A up to the peak near A = 56 (⁵⁶Fe, 8.75 MeV) and falls beyond it, so fusion beyond the peak would absorb energy rather than release it; elements more massive than those near the peak cannot be made this way.

fusion releases energy only if E_bn rises (1)
E_bn falls beyond A ≈ 56, so fusion there absorbs energy (1)

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