In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted…
In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $L$. If an electron jumps from $\mathrm{N}$ -shell to the $\mathrm{L}$ -shell, the wavelength of emitted radiation will be:
$\frac{27}{20} \lambda$
$\frac{16}{25} \lambda$
$\frac{25}{16} \lambda$
$\frac{20}{27} \lambda$
Solution
When electron jumps from $\mathrm{M} \rightarrow \mathrm{L}$ shell
$\frac{1}{\lambda}=\mathrm{K}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)=\frac{\mathrm{K} \times 5}{36}$
When eletron jumps from $\mathrm{N} \rightarrow \mathrm{L}$ shell
$\frac{1}{\lambda^{\prime}}=K\left(\frac{1}{2^{2}}-\frac{1}{4^{2}}\right)=\frac{K \times 3}{16}$
solving equation (i) and (ii) we get
$\lambda^{\prime}=\frac{20}{27} \lambda$