Q79 / 90 · JEE Main 2023 (31 Jan Shift 2) · Physics

The radius of electron's second stationary orbit in Bohr's atom is $R$ . The radius of $3^{r d}$ orbit will be

Solution

As we know, radius of hydrogen like atom $r \propto \frac{n^{2}}{Z}$ .

Therefore,

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

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

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

$= 2.25 R$

Hence, the correct answer is option: 'B'.