Question

State the postulates of Bohr atom model. Obtain the expression for the radius of the $n^{th}$ orbit of an electron based on Bohr's theory.

Answer 1

Bohr's postulates
two postulate
radius of electron in nth orbit
Explanation
Electrostatic force $F=\frac{1}{4\pi {\epsilon }_0}\frac{z{e}^2}{r_n^2}$
upto ${\omega }_n^2=\frac{z{e}^2}{4\pi {\epsilon }_{0}m{r}_n^3}$
$L=m{v}_n{r}_n=m{r}_n{\omega }_n^2$ (or) $L=\frac{nh}{2\pi }$
upto ${\omega }_n^2=\frac{n^2{h}^2}{4{\pi }^2{m}^2{r}_n^4}$
Up to $r_n=\frac{n^2{h}^2{\epsilon }_o}{\pi mz{e}^2}$