Question

Orbital acceleration of electron in first orbit of hydrogen atom is:

• A. $\frac{h}{2{\pi }^2{m}^2{r}^3}$
• B. $\frac{h^2}{2{\pi }^2{m}^2{r}^3}$
• C. $\frac{h^2}{4{\pi }^2{m}^2{r}^3}$
• D. $\frac{h^2}{4{\pi }^2{m}^2{r}^2}$

Answer 1

The correct option is C $\frac{h^2}{4{\pi }^2{m}^2{r}^3}$

Orbital Angular momentum

$mvr=\frac{nh}{2\pi }$ n=1

$mvr=\frac{h}{2\pi }$

$v=\frac{h}{2\pi mr}$

$v^2={\left(\frac{h}{2\pi mr}\right)}^2$

$a=\frac{V^2}{r}=\frac{h^2}{4{\pi }^2{m}^2{r}^3}$