Wavelength of monochromatic light \lambda = 632.8nm = 632.8 * 10^{-9} m
Power emitted P = 9.42 mW = 9.42 * 10^{-3} W
a) Find the energy and momentum of each photon in the light beam.
Energy of proton E=h\upsilon\ =\ \frac{hc}{\lambda}
Where, h - Planck's constant (6.626*10^{-34}), speed of light c = 3*10^{8} m/s and \upsilon - frequency
E = \frac{6.626 *10^{-34} * 3*10^8}{632.8 * 10^{-9}}
E = 3.14*10^{-19} J
Momentum of each photon p = \frac{h}{\lambda}
p = \frac{6.626 *10^{-34}}{632.8 * 10^{-9}}
p = 1.047*10^{-27} kg m/s
(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).
Relation between power and energy of photon
P = nE
n = \frac{P}{E}
n = \frac{9.42 * 10^{-3}}{3.14*10^{-19}}
n = 3.42 * 10^{16} potons/sec
c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
Momentum p = 1.047*10^{-27} kg m/s
Mass of hydrogen atom m = 1.66 * 10^{-27}
Momentum formula p = mv
v = \frac{p}{m}
Velocity v = \frac{1.047*10^{-27}}{1.66 * 10^{-27}}
v = 0.621 m/s
Hence, Speed of hydrogen atom v = 0.621 m/s