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A radiation of wavelength 200nm is propa...

A radiation of wavelength 200nm is propagating in the form of a parallel surface. The power of the beam is 5mW and its cross-sectional area is 1.0`mm^(2)`. Find the pressure exerted by radiation on the metallic surface if the radiation is completely reflected.

A

`3.33xx10^-5Nm^(-2)`

B

`4.33xx10^-5Nm^(-2)`

C

`5xx10^-2Nm^(-2)`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
Energy of one photon `E=(hc)/(lamda)`
If power of source is P, the number of photons incident on the metallic surface is
`(P)/(E)=(lamdaP)/(hc)`
Momentum of incident photons`=(h)/(lamda)`
Change in momemtum due to reflection `=(2h)/(lamda)`
The total momentum imparted to the suface per second is
`(2h)/(lamda)(lamdaP)/(hc)=(2P)/(c)`
pressure `=("force")/("Area")(((2P)/(c)))/(A=(2P)/(cA))`
`(2xx5xx10^(-3))/(3xx10^(8)xx10^(-6))=3.33xx10^(-5)Nm^(-2)`
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