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Question

How many photons of a radiation of wavelength $$\lambda=5\times 10^{-7}$$ m must fall per second on a blackened plate in order to produce a force of $$6.62\times 10^{-5}N$$?


A
3×1019
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B
5×1022
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C
2×1022
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D
1.67×1018
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Solution

The correct option is B $$5\times 10^{22}$$
Momentum of photon is given by,

$$p=\dfrac{h}{\lambda}$$

Momentum of n photons, $$=n\dfrac{h}{\lambda}$$

Force is the change in momentum. Since, the plate is blackened, all the photons are being absorbed. Thus, change in momentum and hence the force is given by

$$F=\dfrac{dp}{dt}=n\dfrac{h}{\lambda}$$

$$n=F\dfrac{\lambda}{h}=\dfrac{6.62\times{10}^{-5}\times 5\times {10}^{-7}}{6.62\times{10}^{-34}}=5\times{10}^{22}$$

Physics
NCERT
Standard XII

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