Question

The force on a hemisphere of radius $1$ cm if a parallel beam of monochromatic light of wavelength $500$ nm. falls on it with an intensity of $0.5$ W/cm${}^2$, striking the curved surface in a direction which is perpendicular to the flat face of the hemisphere is:

(Assume the collisions to be perfectly inelastic)

• A. $5.2\times {10}^{-13}N$
• B. $5.2\times {10}^{-12}N$
• C. $5.22\times {10}^{-9}N$
• D. $0$ N

Answer 1

The correct option is C $5.22\times {10}^{-9}N$

Momentum of each photon $\Rightarrow p=\frac{h}{\lambda }=\frac{6.62\times {10}^{-34}}{500\times {10}^{-9}}=1.324\times {10}^{-27}kg.m/s$

Number of photons per sq. cm $\Rightarrow n=\frac{0.5\lambda }{hc}=\frac{0.5}{3\times {10}^8}\times \frac{1}{1.324\times {10}^{-27}}=1.258\times {10}^{18}photons/c{m}^2$

As the beam is a parallel beam, photons strike on the circular area of the hemisphere $\Rightarrow A=\pi r^2$.

Force $=$ Number $\times$ Momentum$\times$ Area $=1.258\times 1.324\times 3.14\times 1^2\times {10}^{-9}N$

$F=5.22\times {10}^{-9}N$