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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)
$5.2\times10^{-13}\, N$
$5.2\times10^{-12}\, N$
$5.22\times10^{-9}\, N$
zero
Solution
$\mathrm{p}=\frac{\mathrm{h}}{\lambda}$ of each photon
$=\frac{6.63 \times 10^{-34}}{500 \times 10^{-9}}=1.33 \times 10^{-27} \mathrm{\,kg}-\mathrm{m} / \mathrm{s}$
and no. of photons
$=\frac{0.5}{\mathrm{hv}} / \mathrm{cm}^{2}=\frac{0.5 \lambda}{\mathrm{hc}} / \mathrm{cm}^{2}$
$=\frac{0.5 \times 500}{1240 \times 1.6 \times 10^{-19}} / \mathrm{cm}^{2}$
$=1.25 \times 10^{18}$ $\mathrm{photons}$ $/ \mathrm{cm}^{2}$
$\therefore$ force $=1.25 \times 10^{8} \times 1.33 \times 10^{-27} \times \pi \times 1^{2}$
$=5.22 \times 10^{-9} \mathrm{\,N}$
