Q158 / 160 · AP EAMCET 2022 (05 Jul Shift 1) · Physics

Choose the correct statement of the following

  • Correct answer
    A
    The nuclear density in general, is independent of mass number $A$.
  • B
    The radius of nucleus is directly proportional to the mass number $A$ of the nucleus.
  • C
    The binding energy of a nucleus is inversely proportional to its mass defect.
  • D
    Energy is observed when heavy nuclei undergo. transmutation into light nuclei.

Solution

We know that, the radius $(R)$ of nucleus is given as $R=R_0 A^{1 / 3}$ or $R \propto A^{1 / 3}$ Where, $\begin{aligned} R_0 & =\text { constant } \\ A & =\text { mass number }\end{aligned}$ $\therefore$ Nuclear density, $\rho=\frac{\text { mass }}{\text { volume }}=\frac{m A}{\frac{4}{3} \pi R^3}$ (here, $m$ is mass of each nucleon) $\rho=\frac{3 m}{4 \pi R_0^3}$ Hence, it is clear from above formula, nuclear density is independent of mass number $A$. The binding energy, $E=\Delta m c^2$ i. e $E \propto \Delta m$ Where, $\Delta m=$ mass defect Energy is released when heavy nuclei undergo transmutation into light nuclei.

Hence, the correct answer is option: 'A'.

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