Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser.

Solution:

Wavelength of the monochromatic light, λ = 632.8 nm = 632.8 × 10−9 m

Power emitted by the laser, P = 9.42 mW = 9.42 × 10−3 W

Planck’s constant, h = 6.626 × 10−34 Js

Speed of light, c = 3 × 108 m/s

Mass of a hydrogen atom, m = 1.66 × 10−27 kg

(a)The energy of each photon is given as:

$E=\frac{h c}{\lambda}$

$=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{632.8 \times 10^{-9}}=3.141 \times 10^{-19} \mathrm{~J}$

The momentum of each photon is given as:

$P=\frac{h}{\lambda}$

$=\frac{6.626 \times 10^{-34}}{632.8}=1.047 \times 10^{-27} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$

(b)Number of photons arriving per second, at a target irradiated by the beam = n

Assume that the beam has a uniform cross-section that is less than the target area.

 

Hence, the equation for power can be written as:

$P=n E$

$\therefore n=\frac{P}{E}$

$=\frac{9.42 \times 10^{-3}}{3.141 \times 10^{-19}} \approx 3 \times 10^{16}$ photon/s

(c) Momentum of the hydrogen atom is the same as the momentum of the photon, $p=1.047 \times 10^{-27} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ Momentum is given as:

$p=m v$

Where,

 

v = Speed of the hydrogen atom

$\therefore v=\frac{p}{m}$

$=\frac{1.047 \times 10^{-27}}{1.66 \times 10^{-27}}=0.621 \mathrm{~m} / \mathrm{s}$