An electron in a hydrogen atom makes a transition from n = 2 to n =...

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

$R{\left({Z}_{H}\right)}^{2}\left(\dfrac{1}{{1}^{2}} - \dfrac{1}{{2}^{2}}\right) = R\dfrac{{\left({Z}_{Li}\right)}^{2}}{{n}^{2}}$

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

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

$n = \sqrt{12} \approx 3 . 5$

Hence the least quantum number must be $4$.