Question

The stable nucleus that has a radius $\frac{1}{3}$ that of $O{s}^{189}$ is-

• A. ${}_{3}L{i}^7$
• B. ${}_{2}H{e}^4$
• C. ${}_5{B}^{10}$
• D. ${}_6{C}^{12}$

Answer 1

The correct option is A ${}_{3}L{i}^7$

$\begin{array}{c}\text{We Know'}\\ \text{Radius of atom}=R_0(A{)}^{\frac{1}{3}}\end{array}$

$\begin{array}{c}\text{Radius of}O{s}^{189}=R_0(A{)}^{\frac{1}{3}}\\ \text{and}\\ \text{Radius of stable nuclei}=\frac{1}{3}R\left(Os\right)\end{array}$

$\begin{array}{c}=\frac{1}{3}{R}_0(A{)}^{\frac{1}{3}}\\ =R_0{\left(\frac{4}{27}\right)}^{\frac{1}{3}}\\ =R_0{\left(\frac{189}{27}\right)}^{1/3}\\ =R_0(7{)}^{\frac{1}{3}}\end{array}$

$\begin{array}{c}\text{So, Atomic mass of stable nuclei will be}7\\ \text{so, option (A)}\end{array}$