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Question

(a) In a typical nuclear reaction e.g
21H+21H32H+10n+3.27MeV,
although number of nucleons is conserved, yet energy is released, How? Explain.
(b) Show that nuclear density in a given nucleus is independent of mass number A.

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Solution

In a nuclear reaction, the aggregate of the masses of the target nucleus (21H) and the bombarding particle may be greater or less than the aggregate of the masses of the product nucleus (32He) and the outgoing particle (10n).
So, from the law of conservation of mass- energy some energy (3.27 Mev) is evolved or involved in a nuclear reaction.
This energy is called Q-value of the nuclear reaction.

Density of the nucleus =massofnucleusvolumeofnucleus

Mass of the nucleus =A amu =A×1.666×1027kg

Volume of the nucleus, V=43πR3=43π(R0A13)3

Where, R=R0A1/3 and V=43πR30A

Thus, density=A×1.66×1027(43πR30)A=1.66×1027(43πR30)

Which shows that the density is independent of mass number A.

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