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

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$\frac{16}{25} λ$

$\frac{27}{20} λ$

$\frac{20}{27} λ$

$\frac{25}{16} λ$

answer is D.

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Detailed Solution

$For \underset{n_{2} = 3}{M} ⟶ \underset{n_{1} = 2}{L} : \frac{1}{λ} = R_{H} [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = \frac{5}{36} R_{H} \underset{n_{2} = 4}{N} ⟶ \underset{n_{1} = 2}{L} : \frac{1}{λ_{1}} = R_{H} [\frac{1}{2^{2}} - \frac{1}{4^{2}}] = \frac{3}{16} R_{H} ∴ λ_{1} = \frac{5}{36} R_{H} \times \frac{16}{3 R_{H}} = \frac{20}{27} λ$