CBSE Sample Papers NCERT Books
Question 4

# 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?

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 = hc/λ = 3.141 x 10-19 J

The momentum of each photon is given as: P = h/λ = 6.626 x 10-34 / 632.8 = 1.047 x 10-27 kg m 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= nE

n = P/E = 9.42 x 10-3 / 3.141 x 10-19 = 3 x 1016 photons/s (approx)

(c) Momentum of the hydrogen atom is the same as the momentum of the photon,

p = 1.047 x 10-27 kg m s-1

Momentum is given as: p = mv

Where,

v = Speed of the hydrogen atom

v = p/m = 1.047 x 10-27 / 1.66 x 10-27 = 0.621 m/s

## Recently Viewed Questions of Class 12 Physics

#### Write a Comment:

• NCERT Chapter