JEE Physics 2023 Question with Solution

Given: The radius of electron's second stationary orbit is $R$.

Find: The radius of the $3$rd orbit.

In Bohr's model, the radius of the $n$-th orbit is given by

$$r_n = n^2 r_1$$

where $r_1$ is the radius of the first orbit.

For the second orbit,

$$r_2 = 2^2 r_1 = 4r_1$$

But $r_2 = R$, so

$$R = 4r_1$$

Hence,

$$r_1 = \frac{R}{4}$$

Now for the third orbit,

$$r_3 = 3^2 r_1 = 9r_1$$

Substituting $r_1 = \frac{R}{4}$,

$$r_3 = 9 \times \frac{R}{4} = \frac{9R}{4} = 2.25R$$

Therefore, the radius of the third orbit is $2.25R$. The correct option is B.