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Question

An electron of a stationary hydrogen atom passes 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, Rydberg constant and h 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
Here, E5E1=hcλ

and

Rhc25=Rhc=hcλ

2425R=1λ ......................(1)

We have,

P=hλ

Where P is momemtum

Also, P=mv

Where m is mass and v is velocity

mv=hλ

v=hmλ .........................(2)

Substituting the value of 1λ from equation (1) in equation (2), we get

v=24hR25m

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