Explanation

(b) By using $\frac{1}{\lambda} = RZ^{2}\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack$
For Hydrogen atom $\frac{1}{\left( \lambda_{\min} \right)_{H}} = R\left\lbrack \frac{1}{1^{2}} - \frac{1}{\infty} \right\rbrack = R$
$\Rightarrow \left( \lambda_{\min} \right)_{H} = \frac{1}{R}$ …(i)
For hydrogen like atom $\left( \frac{1}{\lambda_{\min}} \right)_{atom} = RZ^{2}\left( \frac{1}{2^{2}} - \frac{1}{\infty} \right)$
$\Rightarrow \left( \lambda_{\min} \right)_{atom} = \frac{4}{RZ^{2}}$ …(i)
From equation (i) and (ii), $\frac{1}{R} = \frac{4}{RZ^{2}} \Rightarrow Z = 2$