Which among the following has a Hydrogen-like spectrum and whose...

For Hydrogen like atom, $\dfrac{1}{\lambda '}=R Z{}^{2} \left(1{n}_{1}^{2} - 1{n}_{2}^{2}\right) ...(i)<br /><br />For Hydrogen atom, \dfrac{1}{λ}= R \left(1{n}_{1}^{2} - 1{n}_{2}^{2}\right) ...(ii)<br /><br />Dividing Eqn (ii) by Eqn (i), we get<br /><br /> \dfrac{\lambda '}{λ} =\dfrac{R \left(1{n}_{1}^{2} - 1{n}_{2}^{2}\right)}{{RZ}^{2}\left(1{n}_{1}^{2} - 1{n}_{2}^{2}\right)}$

$\text{or}\dfrac{\lambda '}{λ} =\dfrac{1}{Z{}^{2}}$

According to problem, ${λ}^{'} = \dfrac{λ}{4}$

∴ $\dfrac{\lambda '}{4{λ}^{'}} = \dfrac{1}{Z{}^{2}}$

$∴ Z = 2$

The atomic number of Helium atom is $2$. Hence, the required element is Helium.