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: (A)

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)