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Making use of Planck's formula, derive the expressions determining the number of photons per 1cm^(3) of a cavity at a temperature T in the spectral intervals (omega, omega + d omega) and (lambda, lambda + d lambda). |
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Answer» Solution :We use the formula `epsilon = cancelh omega` Then the number of photons in the spectral interval `(omega, omega + d omega)` is `n(omega)d omega = (u(omega,T)d omega)/(cancelh omega) = (omega^(2))/(PI^(2)c^(3))(1)/(E^(cancelh omega//kT)-1)d omega` USING `n(omega)d omega =- overset~(n)(LAMBDA) dlambda` we get `d lambda overset~(n)(lambda) = n((2pic)/(lambda)) (2pic)/(lambda^(2))d lambda` `=((2pic)^(3))/(pi^(2)c^(3)lambda^(4))(1)/(e^(2pi cancelh c//klambdaT)-1) dlambda` `= (8pi)/(lambda^(4))(d lambda)/(e^(2picancelh c//lambdakT)-1)` |
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