Question

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentun transferred to the surface is

• A. $E/c$
• B. $2E/c$
• C. $Ec$
• D. $E/c^2$

Answer 1

The correct option is B $2E/c$

Let initial momentum is $p_i$and final reflected momentum is $p_f$such that

Energy, $E=\frac{hc}{\lambda }.....\left(1\right)$

$p_i=\frac{h}{\lambda }=\frac{E}{c}\left(from1\right)$

$p_f=\frac{-h}{\lambda }=\frac{-E}{c}$

So, net change in momentum is

$\Delta p=p_f-p_i$

$\Delta p=\frac{-E}{c}-\frac{E}{c}$

$\Delta p=-\frac{2E}{c}$

The momentum transferred to the surface is$\frac{2E}{c}$