JEE Main 2025 — Structure Of Atom Question with Solution

In Bohr’s model the radius of the $n$th orbit is

$$r_n=n^2{a}_0$$

where $a_0$ is the Bohr radius. Hence for any two orbits $m$ and $n$:

$$\frac{r_m}{r_n}=\frac{m^2}{n^2}.$$

Let’s check each option:

A: $\frac{r_4}{r_2}=\frac{4^2}{2^2}=\frac{16}{4}=4$ → correct

B: $\frac{r_8}{r_4}=\frac{8^2}{4^2}=\frac{64}{16}=4$ → correct

C: $\frac{r_6}{r_4}=\frac{6^2}{4^2}=\frac{36}{16}=2.25(\ne 3)$ → incorrect

D: $\frac{r_3}{r_1}=\frac{3^2}{1^2}=9$ → correct

Therefore the incorrect statement is Option C.