An electron in a hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon…

Let us assume that the electron in the lithium-ion is knocked off from the $n^{\mathrm{th}}$ energy level, then

$R{\left(Z_{\mathrm{H}}\right)}^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=R\frac{{\left(Z_{\mathrm{Li}}\right)}^2}{n^2}$

$R{\left(1\right)}^2\times \frac{3}{4}=R{\left(3\right)}^2\left[\frac{1}{n^2}\right]$

$\frac{3}{4}=\frac{9}{n^2}$

$n=\sqrt{12}\approx 3.5$

Hence the least quantum number must be $4$.