Question

In Bohr?s model, the atomic radius of the first orbit is $r_0$ . The radius of the third orbit, is

• A. $9 r_{0}$
• B. $3 r_{0}$
• C. $r_{0}$
• D. $\frac{r_{0}}{3}$

Answer 1

Answer: (D)

$\frac{r_{0}}{3}$

Answer 2

Here : Radius of first orbit $=r_{0}$ The radius of $n$ the orbit is given by, $r_{n}=\frac{\varepsilon_{0} h^{2}}{\pi m Z_{e}^{2}} \times n^{2} \propto n^{2}$ Hence, $\frac{r_{1}}{r_{2}}=\left(\frac{n_{1}}{n_{2}}\right)^{2}$ $=\frac{1}{9}$ or $r_{3}=9 r_{1}=9 r_{0}$ (where $r_{3}$ is the radius of 3rd orbit)