Question

If the radius of a nucleus of mass number $3$ is $R$ ,then the radius of a nucleus of mass number $81$ is

• A. $3\,R$
• B. $9\,R$
• C. $(27)^{1/2}\,R$
• D. $27\,R$

Answer 1

Answer: (A)

$3\,R$

Answer 2

Nuclear radius is proportional to $A^{1 / 3}$ where, $A$ is mass number of nucleus. ie, $R \propto A^{1 / 3}$
$\frac{R_{1}}{R_{2}}=\left[\frac{A_{1}}{A_{2}}\right]^{1 / 3}$
$\frac{R}{R_{2}}=\left[\frac{3}{81}\right]^{1 / 3}$
or $\frac{R}{R_{2}}=\frac{1}{3}$
or $R_{2}=3\, R$