Question

The acceleration of an electron in the first orbit of the hydrogen atom $(n=1)$ is :

• A. $\frac{h^2}{{\pi }^2{m}^2{r}^3}$
• B. $\frac{h^2}{8{\pi }^2{m}^2{r}^3}$
• C. $\frac{h^2}{4\pi m^2{r}^3}$
• D. $\frac{2{\pi }^{2}km{e}^{2}Z}{\eta h}$

Answer 1

Answer: (C)

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

Orbital Angular momentum

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

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

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

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

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