Question

If the radius of a nucleus with a mass number $7$ is $2\text{fm}$, then the radius of the nucleus with mass number $189$ is

• A. $3\text{fm}$
• B. $6\text{fm}$
• C. $25\text{fm}$
• D. $27\text{fm}$

Answer 1

The correct option is B $6\text{fm}$

Given:
$A_1=7$ , $A_2=189$
$R_1=2\text{fm}$, $R_2=?$

We know that, the expression for nuclear radius is given by,

$R=R_0{A}^{\frac{1}{3}}$

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

$\Rightarrow \frac{R_2}{2\text{fm}}={\left[\frac{189}{7}\right]}^{\frac{1}{3}}=(27{)}^{\frac{1}{3}}$

$\Rightarrow R_2=3\times 2\text{fm}$

$\begin{array}{c}{R}_2=6\text{fm}\end{array}$

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