Photon emissions from hydrogen

AI Thread Summary
The discussion focuses on calculating the number of different photon emissions a hydrogen atom can produce when transitioning from excited state 5 to ground level. The user initially counted 10 emissions but sought a more elegant formula. It was clarified that the excited state corresponds to n=6, allowing for a total of 15 possible transitions calculated using the formula (1+n)*n/2. The conversation concludes with the user confirming their understanding of the formula for determining photon emissions from excited states. This highlights the importance of using mathematical equations to simplify complex calculations in atomic physics.
natugnaro
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[SOLVED] Photon emissions from hydrogen

Homework Statement


How many different photon emissions can hydrogen atom make going down from excited state 5 to ground level ?



Homework Equations



Thats what I'm lookin for.

The Attempt at a Solution



Simply by counting I got 10 different photon emissions.
But is there some equation for doing this elegantly ?
 
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Isn't excited state 5 energy level n=6? So shouldn't there be 5+4+3+2+1 photons possible since from n=6, the electron can make 5 transitions, and from n=5 it can make 4 transitions, etc?
 
thanks, I got it
 
For excited state n there is (1+n)*n/2 possible different photon emissions.
 
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