Question

In a hydrogen like atom, when an electron jumps from the $M-$shell to the $L-$shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N-$shell to the $L-$shell, the wavelength of emitted radiation will be:

• A. $\frac{27}{20}\lambda$
• B. $\frac{16}{25}\lambda$
• C. $\frac{25}{16}\lambda$
• D. $\frac{20}{27}\lambda$

Answer 1

The correct option is D $\frac{20}{27}\lambda$

When electron jumps from $M\to L$ shell
$\frac{1}{\lambda }=R(\frac{1}{2^2}-\frac{1}{3^2})=\frac{R\times 5}{36}......\left(i\right)$

When electron jumps from $N\to L$ shell
$\frac{1}{{\lambda }^{\prime }}=R(\frac{1}{2^2}-\frac{1}{4^2})=\frac{R\times 3}{16}......\left(ii\right)$

solving equation $\left(i\right)$ and $\left(ii\right)$, we get,
${\lambda }^{\prime }=\frac{20}{27}\lambda$

Hence, $\left(D\right)$ is the correct answer.