What are the Boltzmann factors?
1 Answer
A general ratio of the population of states can be written in statistical mechanics as:
#N_i/N = (g_i e^(-betaepsilon_i))/(q) = (g_i e^(-betaepsilon_i))/(sum_i g_i e^(-betaepsilon_i))# where:
#g_i# is the degeneracy of state#i# with energy#epsilon_i# .#beta = 1/(k_BT)# is a constant containing the Boltzmann constant and temperature.#N_i# is the number of particles in state#i# and#N# is the total number of particles.
If we then consider a single state relative to energy zero, we have two states such that:
#N_1/N_0 = N_1/N cdot N/N_0#
#= (g_1 e^(-betaepsilon_1))/cancel(g_0 e^(-betaepsilon_0) + g_1 e^(-betaepsilon_1)) cdot cancel(g_0 e^(-betaepsilon_0) + g_1 e^(-betaepsilon_1))/(g_0 e^(-betaepsilon_0))#
Since the
#(N_i)/(N_0) = (g_i)/(g_0) e^(-betaepsilon_i)#
Thus, the population of state
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