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AP EAPCET 05-Jul-2022 Shift 1 Paper

Section: Physics

Question : 118 of 160

Marks: +1, -0

Choose the correct statement of the following

The nuclear density in general, is independent of mass number A.
The radius of a nucleus is directly proportional to the mass number ,A of the nucleus.
The binding energy of a nucleus is inversely proportional to its mass defect .
Energy is absorbed 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}

R \propto A^{1/3}

Where,

R_0=\text{constant}

A=\text{mass number}

\therefore

Nuclear density,

\rho=\frac{\text{mass}}{\text{volume}}=\frac{mA}{\frac{4}{3}\pi R^3}

(here,

m

is mass of each nucleon)

\Rightarrow \;\; \rho=\frac{mA}{\frac{4}{3}\pi (R_0 A^{1/3})^3}=\frac{mA}{\frac{4}{3}\pi R_0^3 A}

\rho=\frac{3m}{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.

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