Question

The nucleus which has radius one-third of the radius of $O{s}^{189}$ is

• A. $B{e}^9$
• B. $L{i}^7$
• C. $F^{19}$
• D. $C^{12}$

Answer 1

Answer: (B)

Let nucleus be $q^{X^A}$.
Nuclear radius, $R=R_0\left(A^{1/3}\right)$
where $R_0$ is a constant whose value is found to be
$1.2\times 10^{-15}m$ and $A$ is the mass number
$\therefore \frac{R_X}{R_{Os}}={\left(\frac{A}{189}\right)}^{1/3}$
$\Rightarrow \frac{1}{3}={\left(\frac{A}{189}\right)}^{1/3}$
$A=\frac{189}{3^3}=\frac{189}{27}=7$
The given nucleus is $L{i}^7$.