Question

$n\times {10}^{27}$ photons of wavelength $\lambda =6600\text{nm}$ must strike a totally reflecting surface per second at normal incidence to exert a force of $1\text{N}.$ The value n is (integer only)

Answer 1

Given,

$\lambda =6600\text{nm};F=1\text{N}$

When radiation normal incident on a surface perfectly reflecting surface, the magnitude of momentum delivered to the surface is,

$\Delta P=\frac{2E}{c}=\frac{2nh}{\lambda }[\because E=\frac{nhc}{\lambda }]$

Let $n$ be the number of photons falling per second on the surface, then force exerted on it will be,

$F=\frac{\Delta P}{\Delta t}=\frac{2nh}{\lambda }$

$\Rightarrow n=\frac{F\lambda }{2h}=\frac{1\times 6600\times {10}^{-9}}{2\times 6.6\times {10}^{-34}}=5\times {10}^{27}$

Hence, $n=5$