Question

Calculate the frequency of the electron in the 1st Bohr orbit in a H-atom.

Answer 1

Velocity in Bohr's first orbit is given by $mvr=\frac{nh}{2\pi }$

For Bohr's first orbit $n=1$

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

Radius $r$ is given by, $r_n=0.53\times {10}^{-10}\times n^{2}meter$

For Bohr's first orbit $n=1$

$r=0.53\times {10}^{-10}meter$

Frequency $\nu$ is given by $\nu =\frac{v}{2\pi r}=\frac{h}{4{\pi }^{2}m{r}^2}$

Mass of electron $m=9.1096\times {10}^{-31}kg$

$\nu =\frac{6.62\times {10}^{-34}}{4{\pi }^2\times 9.1096\times {10}^{-31}\times (0.53\times {10}^{-10}{)}^2}=6530\times {10}^{12}Hz$