Let and be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio is [2022]

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Solution

Q.
Let $T_{1}$ and $T_{2}$ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio $T_{1} : T_{2}$ is [2022]

1 1 : 4

2 4 : 1

3 4 : 9

4 9 : 4

Ans.
(4)

For $1^{st}$ excited state, n = 2

For $2^{nd}$ excited state, n = 3

$∴$ $\frac{T_{1}}{T_{2}} = \frac{n_{2}^{2}}{n_{1}^{2}} = \frac{3^{2}}{2^{2}} = \frac{9}{4}$

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