Consider an element with energy levels E0 and E* and degeneracies of those energ

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 546.0 nm, g0=1, and g*=4, determine the fraction of atoms of the element in the excited state (N*/N0) at 5845 K.

onsider an element with energy levels Eo and E* and degeneracies of those energy levels go and g. respectively. If the wavelength difference of the two states is 546.0 nm, 90 1, and g - 4, determine the fraction of atoms of the element in the excited state (N*/No) at 5845 K. AV Number 0.0019 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 *3*10^8 )/ 546 *10^-9 m
= 3.64*10^-19

k=1.381*10^-23 J K-1,
And temperature , T=5845K
N*/N0 =4/1 exp(-3.64*10^-19/ 1.381*10^-23*5845)
=4 exp(-4.51)

N*/N0 = 0.044. (Ans)

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