An electron of stationary hydrogen atom jumps from 4th energy level… | MHT CET 2026 (15 May, Shift 1)

Q9MHT CET 2026 · 15 MAY · SHIFT 1Medium

Transitions, Photon Emission & Excitation

An electron of stationary hydrogen atom jumps from 4th energy level to ground level. The recoil velocity of the atom as a result of electron transition will be

( $h$ = Planck's constant, $R$ = Rydberg's constant, $m =$ mass of hydrogen atom)

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Answer: (d)

Momentum is conserved: atom recoil momentum $mv$ = photon momentum $\frac{h}{\lambda}$ .
$\frac{1}{\lambda} = R\left(1 - \frac{1}{16}\right) = \frac{15R}{16}$
$v = \frac{h}{m\lambda} = \frac{15Rh}{16m}$
So the answer is (d).

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