First slide

Bohr Model of the Hydrogen atom.

Question

An electron in a hydrogen atom makes a transition n₁ → n₂, where n₁ and n₂ are principal quantum numbers of the states. Assume the Bohr’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 n₁/n₂

Easy

A

8 : 1
B

4 : 1
C

2 : 1
D

1 : 2

Solution

$T \propto n^{3} \Rightarrow \frac{T_{1}}{T_{2}} = {(\frac{n_{1}}{n_{2}})}^{3} \Rightarrow \frac{8 T}{T} = {(\frac{n_{1}}{n_{2}})}^{3}$
$∴ n_{1} : n_{2} = 2 : 1$

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