If an electron in a hydrogen atom jumps from the orbit to the orbit, it emits a photon of wavelength . When it jumps from the orbit to the orbit, the corresponding wavelength of the photon will be [2016]

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Solution

Q.
If an electron in a hydrogen atom jumps from the $3^{rd}$ orbit to the $2^{nd}$ orbit, it emits a photon of wavelength $λ$ . When it jumps from the $4^{th}$ orbit to the $3^{rd}$ orbit, the corresponding wavelength of the photon will be [2016]

1 $\frac{16}{25} λ$

2 $\frac{9}{16} λ$

3 $\frac{20}{7} λ$

4 $\frac{20}{13} λ$

Ans.
(3)

When electron jumps from higher orbit to lower orbit, then the wavelength of emitted photon is given by,

$\frac{1}{λ} = R (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$

so, $\frac{1}{λ} = R (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = \frac{5 R}{36} and \frac{1}{λ'} = R (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = \frac{7 R}{144}$

$∴$ $λ' = \frac{144}{7} \times \frac{5 λ}{36} = \frac{20 λ}{7}$

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