First slide

Bohr's atom model

Question

The electron in a hydrogen atom makes a transition from n = n₁ to n = n₂ state. 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

Moderate

A

$n_{1} = 4, n_{2} = 2$
B

$n_{1} = 8, n_{2} = 2$
C

$n_{1} = 8, n_{2} = 3$
D

$n_{1} = 6, n_{2} = 2$

Solution

$T^{2} \propto r^{3} and r \propto n^{2} \Rightarrow T^{2} \propto n^{6} \Rightarrow T \propto n^{3}$
$\frac{T_{1}}{T_{2}} = {(\frac{n_{1}}{n_{2}})}^{3} \Rightarrow 8 = {(\frac{n_{1}}{n_{2}})}^{3} or \frac{n_{1}}{n_{2}} = 2$
only (a) satisfies the above, hence this is right choice.

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