Question

The surface area $\left(X\right)$ of a nucleus varies with mass number $\left(A\right)$ as:

• A. $X\propto A^3$
• B. $X\propto A^2$
• C. $X\propto A^{\frac{1}{3}}$
• D. $X\propto A^{\frac{2}{3}}$

Answer 1

The correct option is D $X\propto A^{\frac{2}{3}}$

We know that,

$R\propto A^{\frac{1}{3}}$

The surface area $X$ of the nucleus is given by

$X=4\pi R^2$

$\Rightarrow X\propto R^2$

$\Rightarrow X\propto A^{\frac{2}{3}}$

Hence, option $\left(D\right)$ is correct.