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Question

An electron of a stationary hydrogen atom makes a transition from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be (m is the mass of the electron, R is the Rydberg constant and h is the Planck's constant)

A
24hR25m
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B
25hR24m
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C
25m24hR
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D
24m25hR
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Solution

The correct option is A 24hR25m
According to Rydberg formula
1λ=R[1nf21ni2]
Here, nf=1, ni=5
1λ=R[112152]=R[11125]
=2425R
According to conservation of linear momentum, we get
Momentum of photon = Momentum of atom
hλ=mv
or v=hmλ=hm(24R25)=24hR25m

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