Monichromatic light of wavelength 632.8 nm Is produced by a helium-neon laser.The power emitted is 9.42 mW.
(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 moementum as that of the photon?

Explanation

Here `lambda=632.8 nm=632.8xx10^(-9)m`
`P=9.42 mW=9.42xx10^(-3)W`
`h=6.63xx10^(-34)Js,c=3xx10^(8) ms^(-1)`
(a)energy of each photon,
`E=(hc)/(lambda)`
`therefore E=(6.63xx10^(-34)xx3xx10^(8))/(632.8xx10^(-9))`
`=0.031431xx10^(-17)J`
`therefore E~~3.14xx10^(-19)J`
`therefore` Momentum of each photon,
`impliesp=(h)/(lambda)`
`therefore p=(6.63xx10^(-34))/(632.8xx10^(-9))`
`therefore p=0.010477xx10^(-25)`
`therefore p~~1.05xx10^(-27) kg ms^(-1)`
(b)Let no. of photon reaching to target envery second =N
P=(no. of photon N)
`P=NExx("energy of each photon E")`
`therefore N=(P)/(E)=(9.42xx10^(-3))/(3.14xx10^(-19))`
`therefore N=3x10^(16)"photon//second"`
(c )Momentum of hydrogen atom=momentum of photon,
`therefore` mv=p
`therefore v=(p)/(m)=(1.05xx10^(-27))/(1.67xx10^(-27))`
`therefore v=0.62874 therefore v~~0.63 m^(-1)`