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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 4B / c / Solution

The higher state has principal quantum number

l + 2

and the lower one

l + 1

. Energy conservation for the emitted photon gives

ν = \frac{m e ^{4}}{2 h ( 4 π ε _{0} ) ^{2} ℏ ^{2}} (\frac{1}{( l + 1 ) ^{2}} - \frac{1}{( l + 2 ) ^{2}}) .

Solved by gpt-5.6-sol high.

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