Question

If $a$ is the radius of first Bohr orbit in a hydrogen atom, the radius of the third orbit is

• A. $3a$
• B. $9a$
• C. $27a$
• D. $81a$

Answer 1

Answer: (B)

Radius of Bohr orbit is given by
$r_n=$ $\left(\frac{{ϵ}_0{h}^2}{\pi m{e}^2}\right)n^2$
The quantities in the bracket are constant
$\therefore r_n\propto n^2$
The expression gives the radius of the nth Bohr orbit
$\frac{r_1}{r_2}=\frac{n_1^2}{n_2^2}$
$\frac{a}{r_2}=\frac{1}{3^2}$
$r_2=9a$