Question

If the radius of a nucleus with mass number $ 125 $ is $ 1.5 $ fermi, then radius of a nucleus with mass number $ 64 $ is

• A. 0.48 fermi
• B. 0.96 fermi
• C. 1.92 fermi
• D. 1.2 fermi

Answer 1

Answer: (D)

By Rutherford's experiment
$R_{1} =R_{0}\, A_{1}^{1 / 3}\,\,\,...(i)$
$R_{2} =R_{0}\, A_{2}^{1 / 3}\,\,\,....(ii)$
Given
$R_{1}=1.5 $ fermi
$A_{1}=125 $
$A_{2}=64 $
$R_{2}=?$
Now, $\frac{R_{1}}{R_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{1 / 3} \,\,\,$ [from the Eqs. (i) and (ii)]
$ \frac{1.5}{R_{2}}=\left(\frac{125}{64}\right)^{1 / 3}$
$\Rightarrow \frac{1.5}{R_{2}}=\frac{5}{4}$
$\Rightarrow R_{2}=\frac{1.5 \times 4}{5}=0.3 \times 4 $
$=1.2$ fermi