The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]

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Solution

Q.
The radius of electron’s second stationary orbit in Bohr’s atom is R. The radius of 3rd orbit will be [2023]

1 $\frac{R}{3}$

2 $2.25 R$

3 $3 R$

4 $9 R$

Ans.
(2)

$r \propto \frac{n^{2}}{Z}$

$\frac{r_{2 nd}}{r_{3 rd}} = {(\frac{n_{2}}{n_{3}})}^{2}$

$\Rightarrow \frac{R}{r_{3 rd}} = {(\frac{2}{3})}^{2}$

$\Rightarrow r_{3 rd} = \frac{9}{4} R = 2.25 R$

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