NEET 2022 — Physics solution

NEET2022Physics

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 :

A
4 : 1
B
4 : 9
C
9 : 4
D
1 : 4

Solution

In the Bohr model, the energy of the electron in the $n$ -th level of hydrogen is $E_{n} = - \frac{13.6}{n ^{2}}$ eV.

First excited state corresponds to $n = 2$ , so $T_{1} = - \frac{13.6}{4}$ eV.

Second excited state corresponds to $n = 3$ , so $T_{2} = - \frac{13.6}{9}$ eV.

Taking the ratio of magnitudes: $T_{1} : T_{2} = \frac{1}{4} : \frac{1}{9} = 9 : 4$ .

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