The wave number of the energy emitted when electron comes from fourth orbit to s

Question

The wave number of the energy emitted when electron comes from fourth orbit to second orbit in hydrogen is

20, 397 c m^{- 1}

. The wave number of the energy for the same transition in

H e^{+}

Options:

A . 5,099 cm−1

B . 20,497 cm−1

C . 40,994 cm−1

D . 81,588 cm−1

Answer: Option D
:
D
Using

\frac{1}{λ} = ¯ v = R Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) \Rightarrow ¯ v \infty Z^{2} \Rightarrow \frac{_{2}}{_{1}} = {(\frac{Z_{2}}{Z_{1}})}^{2} = {(\frac{Z}{1})}^{2} = 4 \Rightarrow_{2} = ¯ v \times 4 = 81588 c m^{- 1}

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