JEE MAIN - Chemistry (2025 - 2nd April Morning Shift - No. 16)

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

Radius of $4^{\text {th }}$ orbit is four times larger than that of $2^{\text {nd }}$ orbit

Radius of $8^{\text {th }}$ orbit is four times larger than that of $4^{\text {th }}$ orbit

Radius of $6^{\text {th }}$ orbit is three times larger than that of $4^{\text {th }}$ orbit

Radius of $3^{\text {rd }}$ orbit is nine times larger than that of $1^{\text {st }}$ orbit

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

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

C: $\displaystyle \frac{r_6}{r_4} = \frac{6^2}{4^2} = \frac{36}{16} = 2.25\;\bigl(\neq3\bigr)$ → incorrect

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

Therefore the incorrect statement is Option C.