12. Consider the photons inside an oven. The chemical potential of a photon is z
ID: 504668 • Letter: 1
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12. Consider the photons inside an oven. The chemical potential of a photon is zero. Photons are bosons, so any number of photons may occupy one state. A certain state has energy 0.1 eV. At what temperature would the ratio Pn=1/Pn=0 be equal to e^-1? 12. Consider the photons inside an oven. The chemical potential of a photon is zero. Photons are bosons, so any number of photons may occupy one state. A certain state has energy 0.1 eV. At what temperature would the ratio Pn=1/Pn=0 be equal to e^-1? 12. Consider the photons inside an oven. The chemical potential of a photon is zero. Photons are bosons, so any number of photons may occupy one state. A certain state has energy 0.1 eV. At what temperature would the ratio Pn=1/Pn=0 be equal to e^-1?Explanation / Answer
P n =1 / Pn = 0 = exp ( - dE / kT)
where dE = Energy of particle at n = 1 state - energy of particle at n = 0 state
= 0.1eV - 0 = 0.1eV
= 0.1 x 1.602 x 10^-19 J ( since 1eV = 1.602 x 10^-19 J)
= 1.602 x 10^-20 J
now Pn = 1/ Pn= 0 = exp ( - 1.602 x 10^-20 J / 1.38 x 10^-23 J/K x T )
exp ( -1) = exp ( -1.602 x 10^-20 / 1.38 x 10^-23 x T) ( since it was given Pn = 1/Pn = 0 = exp (-1)
-1 = ( -1.602 x 10^-20) / ( 1.38 x 10^-23 x T)
T = 1161 K
= 1161-273 C = 888 C
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