An electron in a hydrogen atom makes a transition n1→n2 where n1 and n2 a

Question

An electron in a hydrogen atom makes a transition

n_{1} \to n_{2}

where

n_{1}

and

n_{2}

are principal quantum numbers of the states. Assume the Bhor's model to be valid. The time period of the electron in the initial states is eight times to that of final state. What is ratio of

\frac{n_{1}}{n_{2}}

Options:

A . 8 : 1

B . 4 : 1

C . 2 : 1

D . 1 : 2

Answer: Option C
:
C

T_{n} \propto n^{3}

n \propto T^{\frac{1}{3}}

\frac{n_{1}}{n_{2}} = {[\frac{T_{1}}{T_{2}}]}^{\frac{1}{3}} = {[\frac{8}{1}]}^{\frac{1}{3}}

n_{1} : n_{2} = 2 : 1

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