Physics - Modern Physics Question with Solution | TestHub

The angular momentum of an electron in hydrogen atom$=\frac{h}{\pi }$.

As we know, from Bohr's second postulate,

$mvr=\frac{h}{\pi }\Rightarrow v=\frac{h}{\pi mr}$...(i)

Now, kinetic energy of electron

$=\frac{1}{2}m{v}^2=\frac{1}{2}m\times {\left(\frac{h}{\pi mr}\right)}^2$[from Equation (i)]

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

$=\frac{{\left(6.63\times {10}^{-34}\right)}^2}{2\times {\left(3.14\right)}^2\times 9.1\times {10}^{-31}\times {\left(5.3\times {10}^{-11}\right)}^2\times 1.6\times {10}^{-19}}$

$=3.4 \text{e}\text{V}$