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. c.) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon? Given, m = 4.74 × 1014Hz (a) Energy of a photon, E = hv = 6.63 × 10-34× 4.74 × 1014J= 3.14 × 10-19J. Momentum of each photon, p (momentum) = hλ = 6.63 × 10-34632.8 × 10-9 = 1.05 × 10-27 kg ms-1 (b) Power emitted, P = 9.42 mW = 9.42 x 10–3 W n = PE = 9.42 × 10-3W3.14 × 10-19J = 3 × 1016 photons/sec. Thus, these many number of protons arrive at the target.(c) Velocity of hydrogen atom = Momentum 'p' of H2 atom (mv)Mass of H2 atom(m) v = 1.05 × 10-271.673 × 10-27ms-1 = 0.63 ms-1. Thus, the hydrogen atom travel at a speed of 0.63 m/s to have the same momentum as that of the photon. |