Question

Using Bohr's postulates of the atomic model, derive the expression for radius of n${}^{th}$ electron orbit. Hence obtain the expression for Bohr's radius.

Answer 1

Centripetal force is provided by the electrostatic force of attraction.

$\frac{m{v}^2}{r}=\frac{e^2}{4\pi {\epsilon }_o{r}^2}$

From bohr's second postulate.

$L_n=m{v}_n{r}_n=\frac{nh}{2\pi }$

Eliminating $v_n$ from above equations.

$r_n=\frac{n^2{h}^2{\epsilon }_o}{\pi m{e}^2}$

Bohr's radius is the radius of the innermost orbit. Hence, $n=1$

$r_1=\frac{h^2{\epsilon }_o}{\pi m{e}^2}$