Blackbody radiation - derive expression for T

[accountkiller]

Homework Statement

Derive an expression for the temperature of an ideal blackbody so that its radiated light at the peak intensity wavelength has exactly enough energy to excite the ground state to fourth excited state.

Homework Equations

I = σ*T⁴
λ_m*T = 2.9 * 10^-3 m * K
E = hf = hc/λ

The Attempt at a Solution

Well, the peak intensity wavelength is at λ_m = 2.9*10^-3 / T.
I'm not sure what to do with the energy levels... the energy difference between levels is hf... do I use that Rydberg formula with n's?

I've got bits and pieces of information but I can't pull it all together. Could someone guide me in the right direction? Thanks!

 

[D H]

The ground state of what?

 

[accountkiller]

See, it doesn't say the ground state of what, that's also what confused me, but I assumed it was hydrogen since that's the simplest and that's the only thing we've done so far.

But I worked through it and got:

T = -2.9*10^-3 * R * (1/1² - 1/4²)

Can anyone confirm that is correct?

Also, how do I delete a post? I can't seem to find the 'delete' button.

 

[Redbelly98]

T = -2.9*10^-3 * R * (1/1² - 1/4²)

Can anyone confirm that is correct?

Looks good, assuming you use appropriate units and that they meant hydrogen.

Also, how do I delete a post? I can't seem to find the 'delete' button.

Members can delete their own posts for some limited time after posting. (I should know what that time limit is, but I don't ) Otherwise, you can hit the Report button and request that a moderator delete the post -- but you should provide a reasonable justification for doing so, or we will simply leave it intact.