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Question

Identical photons are incident on a perfectly black body of mass m kept at rest on a smooth horizontal surface. If n number of photons are incident per second, then the acceleration of the body will be :

(Assume wavelength of photon to be λ)

A
nh2πλm
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B
nhλm
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C
2πnhλm
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D
λmnh
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Solution

The correct option is B nhλm
Given the wavelength of incident photon is λ.

The momentum associated with each photon is:
p=hλAfter the photon strikes black body, the energy of the photon is completely absorbed by the black body.

Hence, the change in momentum of black body will be,

Δp=pfpi

Δp=hλ0=hλ

If n photons per second strikes the black body, then,

ΔpΔt=nhλ

From Newton's second law, the force experienced by the black body will be,

F=ΔpΔt=nhλ

a=Fm=nhλm

Hence, option (B) is correct.
Why this question ?

Tip: The presence of a perfect black body gives clue that all the incident energy will get absorbed completely by black body.


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