Monochromatic light of wavelength `632.8nm` 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). (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon. `h=6.663xx10^(-34)Js,1 a.m.u. =1.66xx10^(-27)kg`.

Explanation

Given , wavelength , `lamda=632.8nm`
`=632.8xx10^(-9)m`
Power emitted , `P = 9.42m W = 9.42xx10^(-3)W`
(a) Energy of each photon is
`E=hc/lamda`
`impliesE=(6.63xx10^(-34)xx3xx10^(8))/(632.8xx10^(-9))=3.14xx10^(-19)J`
Momentum is given by
`p=E/c=(3.14xx10^(-19))/(3xx10^8)`
`=1.05xx10^(-27)"kg ms"^(-1)`
(b) If n is the number of photons emitted per second, then
`n=P/E`
`impliesn =(9.42xx10^(-3))/(3.14xx10^(-19))=3xx10^(-16) ` photons//s
(c) Velocity of hydrogen atom
(c) Velocity of hydrogen atom
`v=p/m=(1.05xx10^(-27))/(1.66xx10^(-27))`
`=0.63" ms"^(-1)`