Boltzmann distribution and energy difference

[schu9600]

Homework Statement

The first excited state of Ca is reached by absorption of 422.7-nm light.
• Find the energy difference (kJ/mol) between ground and excited states.
• The degeneracies are g*/g0 = 3 for Ca. Find N*/N0 at 2 500 K.
• By what percentage will N*/N0 change with a 15-K rise in temperature?
• Find N*/N0 at 6 000 K.

Homework Equations

N2/N1 =(g2/g1 )^(-∆E/kT) (boltzmann distribution equation)

The Attempt at a Solution

I know that g* is 2 and g. is 1
The Boltzmann constant is 1.381 x 10 -23 j/K
However I'm not sure how to get the energy from this information. If someone could help me out to get me started I would greatly appreciate it. Thanks.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[schu9600]

After thinking about it a bit more would the energy difference just be the energy of a photon of light with the wavelength of 422.7 nm?

If someone could confirm this I'm pretty sure I could figure the rest out.

 

[Ygggdrasil]

Yes, that is correct (remember to multiply by Avogadro's constant to get the energy per mole of photons, however).

 

[schu9600]

Okay so I've figured out the energy to be 282.15 kj/mol

For the rest of the parts I seem to get 0 for all of them. This doesn't seem right to me. Any advice?

I've been doing N2/N1 = 3^-(282150J)/[(1.381x10^-23J/K)(2500K)]
Using this I get an answer of 0
I get the same answer with a temperature of 2515K and 6000K.

 

[Ygggdrasil]

Your units need to match. If you are expressing your units of energy in J/mol then you need to use a Boltzmann constant with units of J/mol K (8.314 J/mol K). Alternatively, you could express your ΔE in terms of J and use the 1.381x10^-23 J/K value for the Boltzmann constant.

 

[schu9600]

Thanks that cleared up that question.