In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell,

(4) When electron jumps from $M \rightarrow L$ shell

$\frac{1}{\lambda}=K\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)=\frac{K \times 5}{36}$  ...(1)

When eletron jumps from $\mathrm{N} \rightarrow \mathrm{L}$ shell

$\frac{1}{\lambda^{\prime}}=\mathrm{K}\left(\frac{1}{2^{2}}-\frac{1}{4^{2}}\right)=\frac{\mathrm{K} \times 3}{16}$   ...(2)

solving equation (i) and (ii) we get

$\lambda^{\prime}=\frac{20}{27} \lambda$