Solution7

Solution7 - PHYS 434: Assignment 7 solutions Problem 7.10:...

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PHYS 434: Assignment 7 solutions Problem 7.10: With no stimulated emission, the term B 21 in Equation 7.13 is zero giving u ( f ) = A 21 / B 21 e hf / k B T . This occurs when the photon energy is much larger than k B T . In this case, the photon density is very small, and emission is unlikely to be stimulated before spontaneous emission occurs. This can be seen from Equation 7.15; the ratio of spontaneous to stimulated emission becomes large when the frequency is large. Problem 7.11: Assume that the gas particles are described by a Maxwell Boltzmann distribution of energies : f ( E ) = Ce E / k B T where C is a normalization constant. (a) Normalize the distribution: f ( E ) dE = C 0 e E / k B T dE = C k B Te E / k B T ( ) 0 0 = Ck B T = 1 C = 1 k B T (b) Calculate the average energy: E = E f ( E ) ( ) dE = 0 E 1 k B T e E / k B T dE 0 Integrate by parts: U = E dV = 1 k B T e E / k B T dU = dE V = e E / k B T giving E = Ee E / k B T ( ) 0 e E / k B T ( ) dE 0 = 0 + e E / k B T dE 0 = k B Te
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Solution7 - PHYS 434: Assignment 7 solutions Problem 7.10:...

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