An electron of stationary Hydrogen atom passes from fifth energy… | MHT CET 2024 (2 May, Shift 2)

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Transitions, Photon Emission & Excitation

An electron of stationary Hydrogen atom passes from fifth energy level to ground level. The velocity that the atom acquired as a result of photo emission is

( $m =$ mass of electron, $R =$ Rydberg's constant)

( $h =$ Planck's constant)

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Answer: (a)

Momentum conservation: $mv = \frac{h}{\lambda}$ , where $m$ is the mass of the recoiling atom.
$\frac{1}{\lambda} = R\left(1 - \frac{1}{25}\right) = \frac{24R}{25}$
$v = \frac{24Rh}{25m}$
So the answer is (a).

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