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 < target area).
$(c)$ How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

(N/A) Given: Wavelength $\lambda = 632.8 \; nm = 632.8 \times 10^{-9} \; m$,Power $P = 9.42 \; mW = 9.42 \times 10^{-3} \; W$.
$(a)$ Energy of a photon $E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34} \; J \cdot s)(3 \times 10^8 \; m/s)}{632.8 \times 10^{-9} \; m} \approx 3.14 \times 10^{-19} \; J$.
Momentum of a photon $p = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34} \; J \cdot s}{632.8 \times 10^{-9} \; m} \approx 1.05 \times 10^{-27} \; kg \cdot m/s$.
$(b)$ Number of photons per second $N = \frac{P}{E} = \frac{9.42 \times 10^{-3} \; W}{3.14 \times 10^{-19} \; J} = 3 \times 10^{16} \; \text{photons/second}$.
$(c)$ Momentum of a hydrogen atom $p = mv$. Given $p = 1.05 \times 10^{-27} \; kg \cdot m/s$ and mass of hydrogen atom $m \approx 1.67 \times 10^{-27} \; kg$.
$v = \frac{p}{m} = \frac{1.05 \times 10^{-27}}{1.67 \times 10^{-27}} \approx 0.63 \; m/s$.