Question

Find the ratio of radii of two nuclei with mass number $8$ and $64$. Also find the ratio of their densities.

• A. $1:3,1:1$
• B. $3:2,1:1$
• C. $1:2,1:1$
• D. $1:2,1:8$

Answer 1

The correct option is C $1:2,1:1$

The expression for the radius of the nucleus is given by,

$R=R_0{\left(A\right)}^{\frac{1}{3}}$

$\Rightarrow \frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{\frac{1}{3}}$

$\Rightarrow \frac{R_1}{R_2}={\left(\frac{8}{64}\right)}^{\frac{1}{3}}=\frac{1}{2}$

As the density is independent of mass number $A$,

$\frac{{\rho }_1}{{\rho }_2}=1$

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