Hyperfine and fine structure ENERGIES

AI Thread Summary
The discussion focuses on comparing energy differences in hydrogen, specifically between the n = 1 to n = 2 transition, rest mass energy of an electron, fine structure splitting, and hyperfine structure splitting. Participants suggest using the Rydberg formula to calculate energy differences and emphasize understanding the relative sizes of these energies. It is noted that the fine structure splitting is approximately 1000 times smaller than the energy difference between the n = 1 and n = 2 states. The conversation also highlights the need for clarity on how these energy comparisons relate to each other. Overall, the thread seeks to clarify the relationships and calculations involving these fundamental energy values in hydrogen.
student1938
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What are the approximate relative sizes of the following energies?

a) The n = 1 to n = 2 energy difference in hydrogen and the rest mass mc^2 of an electron

b) The n = 1 to n = 2 energy difference in hydrogen and a typical fine structure splitting in hydrogen

c) A typical fine structure splitting in hydrogen and a typical hyperfine structure splitting in hydrogen

a) I know that E = -Ryd/n^2 where Ryd is Rydberg = -(m*e^4)/(2hbar^2)...do I just plug in constants and explain the difference between the two energies

b) and c ) I know that uI is approximately 1000 times smaller than uE but what does that have to do with energies?

Depsarately need help !
 
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Originally posted by student1938

a) I know that E = -Ryd/n^2 where Ryd is Rydberg = -(m*e^4)/(2hbar^2)...do I just plug in constants and explain the difference between the two energies

b) and c ) I know that uI is approximately 1000 times smaller than uE but what does that have to do with energies?

Depsarately need help ! [/B]

a) yes... and you should be able to work out the rest mass of an electron fairly easily.
 

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