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

Answer 1

Answer: (C)

$v=\frac{l^{2}}{2 h \varepsilon_{0}}$
$r=\frac{h^{2} \varepsilon_{0}}{\pi m e^{2}}$
$ \Rightarrow \varepsilon_{0}=\frac{r \pi m e^{2}}{h^{2}}$
$\frac{v^{2}}{r}=\frac{l^{2} \pi m}{4 h^{4} \varepsilon_{0}^{3}}=\frac{h^{2}}{4 r^{3} \pi^{2} m^{2}}$