Consider an element with energy levels E0 and E* and degeneracies of those energ
ID: 854613 • Letter: C
Question
Consider an element with energy levels E0 and E* and degeneracies of those energy levels g0 and g*, respectively. If the wavelength difference of the two states is 578.9 nm, g0 = 1, and g* = 3, determine the fraction of atoms of the element in the excited state (N*/N0) at 5497 K.
Consider an element with energy levels E0 and E* and degeneracies of those energy levels g0 and g*, respectively. If the wavelength difference of the two states is 578.9 nm, g0 = 1, and g* = 3, determine the fraction of atoms of the element in the excited state (N*/N0) at 5497 K. N*/No =Explanation / Answer
Boltzmann's distribution equation for degenaracy energy levels,
N*/N0= g*/g0 exp(-delta E/ kT)
detla E = hv=hc/lambda= (6.626*10^-34 J.sec *3*10^8 m/sec)/ 578.9 *10^-9 m
delta E =3.434*10^-19 J, and k=1.381*10^-23 J K-1, T=5497K
Therefore N*/N0 =3/1 exp(-3.434*10^-19J/ 1.381*10^-23 J K-1*5497K)
=3 exp(-4.5236)
N*/N0 = 0.0326