Partition Function Homework: Find En at 290K

[lmanri]

Homework Statement

Consider a system at 290 K for which the energy of the n^th state is E_n=n(.01 eV). Using 1+a+a²+a³...=1/(1-a) for a <1 where necessary, Find the value of the partition function.

Homework Equations

The Attempt at a Solution

Z=∑e^-βE$_{}n$

β=1/κT

I don't know what the energy of the state would be so I can't figure out the problem.

 

[tman12321]

What do you mean you don't know what the energy of the state is? You wrote it already: E(n) = (0.01 eV)*n. It is linear in n.

 

[lmanri]

So, I would then have
Z=(sum)e^(-(1/((1.38*10^-23)(290)))(n(0.01))

 

[tman12321]

No. You have incompatible units.

 

[lmanri]

I don't understand it.

 

[Matterwave]

tman means, your units of energy is in eV, but your Boltzmann constant is using units of J/K. You should convert one or the other to have the same units.

 

[lmanri]

Oh ok, which is 8.625*10^-5 eV/K