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The electron in a hydrogen atom makes a transition n1n2, where n1 and n2 are the principal quantum numbers of the two energy states. Assume Bohr's model to be valid. The time period of the electron in the initial state is eight times that in the final state. What are the possible values of n1 and n2?

Solution
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Here, Z=1. We can derive the expression for the time period of electron in nth orbit as
Tn=1fnn3
Hence
T1T2=n31n32. As T1=8T2, therefore we get
8=(n1n2)3n1=2n2
Thus, the possible values of n1 and n2 are n1=2,n2=1;n1=4,n2=2;n1=6,n2=3 and so on.

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