12.7 (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.

12.7 Let $v_1$ be the speed of the electron of the hydrogen atom in the ground state level, $n_1=1.$ For charge e of an electron, $v_1$ is given by the relation

$v_1=\frac{e^2}{n_{1}4?{?}_0\left(\frac{h}{2?}\right)}$ = $\frac{e^2}{2n_1{?}_{0}h}$

$where$ , e = 1.6 $*{10}^{-19}$ C 

${?}_0=$ Permittivity of free space = 8.85 $*{10}^{-12}$ $N^{-1}{C}^2{m}^{-2}$

$h$ = Planck's constant = 6.626 Js $*{10}^{-34}$

$Hence$ $v_1=\frac{e^2}{2n_1{?}_{0}h}$ $\frac{{(1.6*{10}^{-19})}^2}{2*1*8.85*{10}^{-12}*6.626*{10}^{-34}}$ = 2.182 $*{10}^6$ m/s

For level 2, $n_2=2$ ,

$v_2=\frac{e^2}{2n_2{?}_{0}h}$ = $\frac{{(1.6*{10}^{-19})}^2}{2*2*8.85*{10}^{-12}*6.626*{10}^{-34}}$ = 1.091 $*{10}^6$ m/s

For level