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Q.

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

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a

n1=6 and n2=2

b

n1=8 and n2=1

c

n1=8 and n2=2

d

n1=4 and n2=2

answer is D.

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Detailed Solution

The time period T of an electron in a Bohr orbit of principal quantum number n isT=4ε02h3n3me4 T∝n3 ∴  T1T2=n13n23  As T1=8T2 , the above relation gives  n1n23=8   or   n1=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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