Thank you for reporting, we will resolve it shortly
Q.
Which transition in $Li^{2+}$ would have the same wavelength as the $2\to 4$ transition in $He^{+}$ ion?
Structure of Atom
Solution:
$\left(He^{+}\right)_{2\to4}=\left(Li^{2+}\right)_{n_4\to n_3}$
$\therefore \frac{Z_{1}}{Z_{2}}=\frac{n_{2}}{n_{4}}=\frac{n_{1}}{n_{3}}$
or $\frac{2}{3}=\frac{2}{n_{4}}=\frac{4}{n_{3}}$
$\therefore n_{4}=3$ and $n_{3}=6$
$\therefore $ Transition in $Li^{2+}$ ion $= 3 \to 6$