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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)┬аFind the energy andmomentum of each photon in the light beam,

(b)┬аHow 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)┬аHow 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,┬а╬╗┬а=632.8 nm = 632.8 ├Ч 10тИТ9┬аm

Power emitted by the laser,┬аP┬а=9.42 mW = 9.42 ├Ч 10тИТ3┬аW

PlanckтАЩs constant,┬аh┬а=6.626 ├Ч 10тИТ34┬аJs

Speed of light,┬аc┬а= 3 ├Ч 108┬аm/s

Mass of a hydrogen atom,┬аm┬а=1.66 ├Ч 10тИТ27┬аkg

(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 =┬аn

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,┬а

Momentum is given as:

Where,

v┬а= Speed of the hydrogen atom

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