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A. How many photons of a tradiation of w...

A. How many photons of a tradiation of wavelength `lamda=5xx10^(-7)` m must fall per second on a blackened plate in order to produce a force of `6.62xx10^(-5)`N?
B. At what rate will the temperature of plate rise if its mass is 19.86kg and specific heat is equal to `2500J(kgK^(-1))`?

Text Solution

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A. If n is the number of photons falling per second on the plate, then the total momentum per second of the incident photons is `P=nxx(h)/(lamda)`.
Since the plate is blackened, all photons are absorbed by it.
`(triangleP)/(trianglet)=n(h)/(lamda)`
Since `F=(triangleP)/(trianglet)=n(h)/(lamda)impliesn=(F.lamda)/(h)`
or `n=(6.62xx10^(-5)xx5xx10^(-7))/(6.62xx10^(-34))=5xx10^(22)` B. Energy of each photon `=(hc)/(lamda)`
Since n photons fall on the plate per second, the total energy absorbed by the plates in one second is
`E=nxx(hc)/(lamda)=1986Js^(-1)`
i.e., `(dQ)/(dt)=1986Js^(-1)`
`mc(dT)/(dt)=1986`
`implies(dT)/(dt)=(1986)/(19.86xx2500)=4xx10^(-2) C``s^(-1)`
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