Question

Using Bohr's atomic model, derive an equation for radius of orbit of an electron.

Answer 1

$mvr=\frac{nh}{2\pi }⟶\left(1\right)$

$\frac{{mv}^2}{r}=\frac{K{ze}^2}{r^2}⟶\left(2\right)$

$\Rightarrow r=\frac{Kz{e}^2}{{mv}^2}$ (from (2))

$v=\frac{nh}{2\pi \times mr}$ (from (1))

Put ${}^{\prime }{v}^{\prime }$ ${}^{\prime }{m}^{\prime }$ ${}^{\prime }{r}^{\prime }$ :-

$r=\frac{K{ze}^2\times {\left(2\pi \right)}^2{m}^2{r}^2}{m\times {\left(nh\right)}^2}$

$r=\frac{m{\left(nh\right)}^2}{{Kze}^2\left({4\pi }^2\right)m^2}$

$r=\left(\frac{h^2}{mK{ze}^{2}4{\pi }^2}\right)\frac{n^2}{z}x$