First slide

Bohr's atom model

Question

When the hydrogen atom emits a photon in going from n = 5 to n = 1 state, its recoil speed is nearly

Moderate

A

$10^{- 4} {ms}^{- 1}$
B

$2 \times 10^{- 2} {ms}^{- 1}$
C

$4 {ms}^{- 1}$
D

$8 \times 10^{2} {ms}^{- 1}$

Solution

$Photon energy = h f = 13.6 [1 - \frac{1}{25}] eV = 13 eV$
Photon momentum = momentum of hydrogen atom:
$\Rightarrow p = \frac{h f}{c} or m v = \frac{h f}{c}$
$\Rightarrow v = \frac{h f}{m c} = \frac{E}{m c} = \frac{13 \times 1.6 \times 10^{- 19}}{1.67 \times 10^{- 27} \times 3 \times 10^{8}} = 4 {ms}^{- 1}$

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