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 nhλmGiven 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=pf−pi ⇒Δp=hλ−0=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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