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Question

When a hydrogen atom, initially at rest emits a photon resulting in transition n=5n=1,its recoil speed is about :

A
104m/s
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B
2×102m/s
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C
4.3m/s
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D
3.8×102m/s
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Solution

The correct option is B 4.3m/s
Given,
n1=1
n2=5
m=1.6×1027kg
Momentum, P=mv=hλ
recoil speed, v=hmλ. . . . . . . . .(1)
we know that,
1λ=R(1n211n22)
1λ=1.097×107(112152)
λ=9.48×108m
From equation (1),
recoil speed, v=6.67×10341.6×1027×9.48×108=4.3m/s
The correct option is C.


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