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Question -

Monochromatic light ofwavelength 632.8 nm is produced by a helium-neon laser. The power emitted is9.42 mW.

(a) Find the energy andmomentum of each photon in the light beam,

(b) How many photons persecond, on the average, arrive at a target irradiated by this beam? (Assume thebeam to have uniform cross-section which is less than the target area), and

(c) How fast does a hydrogen atom have to travel inorder to have the same momentum as that of the photon?



Answer -

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 photonis given as:

The momentum of eachphoton is given as:

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

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

Hence, the equation forpower can be written as:

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

Momentum is given as:

Where,

v = Speed of the hydrogen atom

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