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