Physics - Modern Physics Question with Solution | TestHub

By Rutherford's experiment

${\mathrm{R}}_1={\mathrm{R}}_0{\mathrm{A}}_1^{\frac{1}{3}}$.....(i)

${\mathrm{R}}_2={\mathrm{R}}_0\mathrm{ }{\mathrm{A}}_2^{\frac{1}{3}}$......(ii)

Given,

${\mathrm{R}}_1=\text{1.5} \mathrm{fm}$

${\mathrm{A}}_1=125$

${\mathrm{A}}_2=64$

Now,$\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}={\left(\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}\right)}^{\frac{1}{3}}$[from the equation (i) and (ii)]

$\frac{\text{1.5}}{{\mathrm{R}}_2}={\left(\frac{125}{64}\right)}^{\frac{1}{3}}$

$\Rightarrow$$\frac{1.5}{{\mathrm{R}}_2}=\frac{5}{4}$

$\Rightarrow$${\mathrm{R}}_2=\frac{1.5\times 4}{5}=0.3\times 4$

$=\text{1.2}\mathrm{ }\mathrm{fm}$