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

<p>In Bohr’s model the radius of the $n$th orbit is </p> <p>$r_n = n^2\,a_0$ </p> <p>where $a_0$ is the Bohr radius. Hence for any two orbits $m$ and $n$: </p> <p>$\frac{r_m}{r_n} = \frac{m^2}{n^2}\,.$ </p> <p>Let’s check each option:</p> <p><p>A: $\displaystyle \frac{r_4}{r_2} = \frac{4^2}{2^2} = \frac{16}{4} = 4$ → correct </p></p> <p><p>B: $\displaystyle \frac{r_8}{r_4} = \frac{8^2}{4^2} = \frac{64}{16} = 4$ → correct </p></p> <p><p>C: $\displaystyle \frac{r_6}{r_4} = \frac{6^2}{4^2} = \frac{36}{16} = 2.25\;\bigl(\neq3\bigr)$ → incorrect </p></p> <p><p>D: $\displaystyle \frac{r_3}{r_1} = \frac{3^2}{1^2} = 9$ → correct </p></p> <p>Therefore the incorrect statement is Option C.</p>