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

In Bohr’s model of the hydrogen atom the radius of the $$n^{\text{th}}$$ orbit is

$$r_n = r_1 n^{2}$$

where $$r_1$$ is the radius of the first orbit. Hence the ratio of radii of any two orbits is

$$\frac{r_n}{r_m} = \left(\frac{n}{m}\right)^{2}$$

Using this relation for every option:

Case A:
$$\frac{r_3}{r_1} = \left(\frac{3}{1}\right)^{2} = 9$$.
The radius of the 3rd orbit is nine times that of the 1st orbit.
Statement A is correct.

Case B:
$$\frac{r_8}{r_4} = \left(\frac{8}{4}\right)^{2} = 2^{2} = 4$$.
The radius of the 8th orbit is four times that of the 4th orbit.
Statement B is correct.

Case C:
$$\frac{r_6}{r_4} = \left(\frac{6}{4}\right)^{2} = \left(\frac{3}{2}\right)^{2} = \frac{9}{4} = 2.25$$.
The radius of the 6th orbit is only 2.25 times that of the 4th orbit, not three times.
Statement C is incorrect.

Case D:
$$\frac{r_4}{r_2} = \left(\frac{4}{2}\right)^{2} = 2^{2} = 4$$.
The radius of the 4th orbit is four times that of the 2nd orbit.
Statement D is correct.

Only Statement C contradicts the Bohr radius relation. Therefore the incorrect statement is

Option C.