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Standard XII

Physics

Characteristics of Bohr's Atomic Model

An electron i...

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

8 : 1

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4 : 1

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2 : 1

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1 : 2

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Solution

The correct option is C 2 : 1
$T_{n} \propto n^{3}$ $n \propto T^{\frac{1}{3}}$
$\frac{n_{1}}{n_{2}} = {[\frac{T_{1}}{T_{2}}]}^{\frac{1}{3}} = {[\frac{8}{1}]}^{\frac{1}{3}}$
$n_{1} : n_{2} = 2 : 1$

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An electron in a hydrogen atom makes a transition n1→n2 where n1 and n2 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 n1n2

The correct option is C 2 : 1Tn∝n3 n∝T13 n1n2=[T1T2]13=[81]13 n1:n2=2:1

The correct option is C 2 : 1
$T_{n} \propto n^{3}$ $n \propto T^{\frac{1}{3}}$
$\frac{n_{1}}{n_{2}} = {[\frac{T_{1}}{T_{2}}]}^{\frac{1}{3}} = {[\frac{8}{1}]}^{\frac{1}{3}}$
$n_{1} : n_{2} = 2 : 1$