Number of identical photons are incident on a perfectly black body of mass $m$ kept at rest on smooth horizontal surface. Then the acceleration of the body if $n$ number of photons incident per second is (assume wavelength of photon to be $λ$ ):

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$\frac{2 π n h}{λ m}$

$\frac{n h}{λ m}$

$\frac{n h}{2 π λ m}$

$\frac{λ m}{m h}$

answer is B.

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Detailed Solution

Change in momentum due to a single photon $= \frac{h}{λ}$

Force $F =$ rate of change of momentum

$\Rightarrow F = n \frac{h}{λ} = m a$

$\Rightarrow a = \frac{n h}{λ m}$

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