The number of photons falling per second on a completely darkened plate to produce force of `6.62xx10^(-5) N` is n . If the wavelength of the light falling is `5xx10^(-7)` m then n = ............ `xx 10^(22)`.
( `h = 6.62 xx10^(-34)J s` )

Options

A. 1
B. 5
C. 0.2
D. 3.3

Answer

B

Explanation

If `lamda` is the wavelength of the light falling , then momentum of each photon
`=h/lamda` (where h is the Planck's constant)
As n photons falling per second on the plate, the total momentum of all the photons falling per second on the plate
`=(nh)/lamda`
Since the plate is completely darkended, all the photons absorbed by it.
`:.` Rate of change of momentum of photons is
`(dp)/(dt)=(nh)/lamda`
By Newton's second law, force on the plate is
`F=(dp)/(dt)=(nh)/lamda`
or `n=(Flamda)/h=((6.62xx10^(-5)N)(5xx10^(7)m))/((6.62xx10^(-34)Js))=5xx10^(22)`