Question

(a) Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the $n=$1, 2, and 3 levels.

(b) Calculate the orbital period in each of these levels.

Answer 1

(a) $v$ is the orbital speed of the electron in the hydrogen atom in level $n$.

$v=\frac{e^2}{n_{1}4\pi {ϵ}_o\left(h/2\pi \right)}$

For $n=1$, $\to v_1=2.18\times {10}^{6}m/s$

For $n=2$, $\to v_1=1.09\times {10}^{6}m/s$

For $n=3$, $\to v_1=7.27\times {10}^{5}m/s$

(b) Orbital perios is given by $T=\frac{2\pi r}{v};v=velocity$

Radius, $r=\frac{n^2{h}^2{ϵ}_o}{\pi m{e}^2}$

So,

$T_1=1.527\times {10}^{-16},n=1$

$T_2=1.22\times {10}^{-15},n=2$

$T_3=4.12\times {10}^{-15},n=3$