Blackbody radiation - derive expression for T

AI Thread Summary
The discussion focuses on deriving the temperature of an ideal blackbody that emits light at a peak intensity wavelength capable of exciting an electron from the ground state to the fourth excited state. The relevant equations include the Stefan-Boltzmann law and the relationship between temperature and peak wavelength. A participant suggests using the Rydberg formula for energy levels, assuming the ground state refers to hydrogen. They derive a temperature expression, T = -2.9*10^-3 * R * (1/12 - 1/42), and seek confirmation of its correctness. Additionally, there is a brief inquiry about how to delete a post, with guidance provided on the process.
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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
λm*T = 2.9 * 10-3 m * K
E = hf = hc/λ

The Attempt at a Solution


Well, the peak intensity wavelength is at λm = 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!
 
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The ground state of what?
 
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.
 
mbradar2 said:
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 :redface:) 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.
 
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