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A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly absorbing surface. The power through any cross–section of the beam is 10 W. Find (a) the number of photons absorbed per second by the surface and (b) the force exerted by the light beam on the surface.

A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross–section of the beam is 10 W. Find (a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.

Grade:12

1 Answers

Arun
25758 Points
4 years ago
(a) Energy of each photon is
E = hc / \lambda 
 = 1242 eV – nm/ 500 nm
 = 2.48 eV
In one second 10 J energy passes through any cross section of the beam,
Thus the no. of photons crossing a cross section is = 
 n = 10 J / 2.48 eV
n = 2.52 * 1019
 
(b)
total momentum of all the photons = 
 p = nh/ \lambda = nh \nu/ c = 10 J / 3*108
 = 3.33 * 10 –8 N-sec
 
hence total force F = dP/dt = 3.33 *10 –8 Newton

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