How Does Temperature Affect Vibrational State Populations in Molecules?

[SilentBob1988]

Homework Statement

Use the Boltzmann expression where v is the vibrational quantum number to complete the following table.

Vibrational State Populations

Molecule

D2 (v=3115)
F2 (v=917)
I2 (v=214.5)

Find Nv/No for 389 K and 1899 K

Assume gv = go = 1

Homework Equations

Nv/No=(gv/go)* e^(– (Ev –Eo) /kT)

The Attempt at a Solution

I have no idea how to even start. :(

I'm not sure how to do it but the Ev-Eo term aren't Es, they are Epsilon symbols.

 

[Adrmay]

So it's the energy difference between vibrational states. And the kT term is referred to as the Boltzmann factor. For D2:Nv/No (389 K) = (1/1)* e^(– (3115 - 0) / (1.38x 10^-23 x 389)) = 0.0059Nv/No (1899 K) = (1/1)* e^(– (3115 - 0) / (1.38x 10^-23 x 1899)) = 0.0001For F2:Nv/No (389 K) = (1/1)* e^(– (917 - 0) / (1.38x 10^-23 x 389)) = 0.0178Nv/No (1899 K) = (1/1)* e^(– (917 - 0) / (1.38x 10^-23 x 1899)) = 0.0004For I2:Nv/No (389 K) = (1/1)* e^(– (214.5 - 0) / (1.38x 10^-23 x 389)) = 0.0762Nv/No (1899 K) = (1/1)* e^(– (214.5 - 0) / (1.38