Physics - Modern Physics Question with Solution | TestHub

For$H-$atom$\left(n=1\right)$

$\frac{m{v}^2}{r}=\frac{1}{4\pi {ϵ}_o}\frac{e^2}{r^2} ...\left(1\right)$

$mvr=\frac{h}{2\pi } ...\left(2\right)$

On squaring$\left(2\right)$

$m^2{v}^2{r}^2=\frac{h^2}{4{\pi }^2}$

On dividing both sides by$r^3 ,$

$\frac{m^2{v}^2}{r}=\frac{h^2}{4\pi r^3} \Rightarrow \boxed{\frac{v^2}{r}=\frac{h^2}{4{\pi }^2{r}^3{m}^2}}$

Acceleration$= \frac{h^2}{4{\pi }^2{r}^3{m}^2}$.