Question
- In a typical nuclear reaction, e.g.
although number of nucleons is conserved, yet energy is released. How? Explain.
- Show that nuclear density in a given nucleus is independent of mass number A.
although number of nucleons is conserved, yet energy is released. How? Explain.
✓
Answer
- In nuclear reaction
Cause of the energy released:
- Binding energy per nucleon of$^{3}_{2}\text{ He}$ becomes more than the (BE/A) of $^{2}_{1}\text{ H}.$
- Mass defect between the reactant and product nuclei.
$ = \big[2\text{m}(^{2}_{1}\text{H}) - \text{m}(^{3}_{2}\text{He}) + \text{m}(\text{n})\big]\text{C}^{2}$
- The radius of nucleus of mass number A is given by $R = R_0A^{1/3}$
Density of the matter in the nucleus
$\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{\text{A}{(u)}}{\frac{4}{3}\pi\text{R}_{0}^{3}\text{A}}$
$\rho = \frac{1}{\frac{4}{3}\pi\text{R}_{0}^{3}} = \frac{3}{4\pi\text{R}_{0}^{3}}$
The expression of the density is independent of mass number A.
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