Radiations of wavelength 200 nm propagation in the form a parallel beam, fall normally on a plane metallic surface. The intensity of the beam is 5 mW and its cross sectional area 1.0 mm2. Find the pressure exerted by the radiation on the metallic surface, if the radiation is completely reflected.

Q: Radiations of wavelength 200 nm propagation in the form a parallel beam, fall normally on a plane metallic surface. The intensity of the beam is 5 mW and its cross sectional area 1.0 mm2. Find the pressure exerted by the radiation on the metallic surface, if the radiation is completely reflected.

Sol: $\large E = \frac{12400}{\lambda (A^o)} \; eV$

$\large E = \frac{12400}{2000} = 6.2 eV \approx 10^{-18} J$

Number of photons passing a point per second is ,

$\large n = \frac{P}{E} = \frac{5 \times 10^{-3}}{10^{-18}} $

n = 5 x 1015

Momentum of each photon , $\large p = \frac{E}{c} = 3.3 \times 10^{-27} J/s$

Change in momentum after each strike = 2 p = 6.6 × 10-27 J/s

Total change in momentum per second is ,

$\large \frac{dp}{dt} = F = n \times \frac{2p}{t}$

F = = 5 × 1015 × 6.6 × 10-27 = 33 × 10-12 N

$\large Pressure = \frac{F}{A} = \frac{33 \times 10^{-12}}{10^{-6}} $

= 33 × 10-6 N/m2