Question

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. (a) Find the energy and momentum of each photon in the light beam, (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

Answer 1

given, λ = 632.8 nm = 6.328 × 10^-7 m

power emitted, P = 9.42 mW = 9.42 × 10^-3 W

(a) Energy of each photon, E = hc/λ

= (6.63 × 10^-34 × 3 × 10^8)/(6.328 × 10^-7)

= 3.14 × 10^-19 J

momentum of each photon = h/λ [ from De-broglie's equation]

= (6.63 × 10^-34)/(6.328 × 10^-7)

= 1.05 × 10^-27 Kgm/s .....(1)

(b) number of photons arriving per second at the target,

N = P/E = (9.42 × 10^-3)/(3.14 × 10^-19)

= 3 × 10^16 photons per second

(c) As we know,

momentum = mass × velocity

so, velocity of hydrogen = momentum/mass of hydrogen atom.

here, momentum = 1.05 × 10^-27 Kg m/s [ from equation (1)]

and mass of hydrogen atom = 1.67 × 10^-27 Kg

= (1.05 × 10^-27 Kgm/s)/(1.67 × 10^-27kg) = 0.63 m/s