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Question

The energies of three conservative energy levels L3,L2 and L1 of hydrogen atom are E0,4Eo9 and E14 respectively. A photon of wavelength λ is emitted for a transition L3 to L1. What will be the wavelength of emission for transition L2 to L1?

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Solution

ATQ, EL3=εEL2=4ε9EL1=ε4
In case-1, when the transition is from L3 to L1, the wavelength λ is given by,
hcλ=εε4=3ε4λ=4hc3ε

The wavelength of photon when transition is from L2 to L1 is given by,
hcλ=EL2EL1=4ε9ε4=16ε9ε36=7ε36orλ=36hc7ελ=277λ


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