1. In Bohr’s model, the radius of the $n$th stationary orbit is

$r_n \propto n^2$

More specifically,

$r_n = a_0 n^2$

where $a_0$ is the Bohr radius.

2. Given that the radius of the second orbit is $R$:

$r_2 = a_0(2)^2 = 4a_0 = R$

3. The radius of the third orbit is

$r_3 = a_0(3)^2 = 9a_0$

4. Now compare $r_3$ with $r_2$:

$\frac{r_3}{r_2} = \frac{9a_0}{4a_0} = \frac{9}{4}$

So,

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

5. Checking options:

• A: $2.25R$ ✅
• B: $3R$ ❌
• C: $\frac{R}{3}$ ❌
• D: $9R$ ❌

Therefore, the correct answer is A.