Question

The radius of an orbit of hydrogen atom is $0.85nm$. Calculate the velocity (in m/sec) of electron in its orbit.

Answer 1

radius = 0.85nm
This is the radius of 4th orbit of hydrogen atom.
Z= 1 ( for hydrogen atom)
Now, $mvr=\frac{nh}{2\pi }v=\frac{nh}{2\pi \left(mr\right)}----\left[I\right]r_n=\frac{n^2{h}^2}{4{\pi }^{2}km{e}^2}----\left[II\right]$
Substituting eq2 in eq1,
$V=\frac{nh\times 4\pi \times km{e}^2}{2\pi \left(m{n}^2{h}^2\right)}v=\frac{2\pi k{e}^2}{nh}$
We know the value of constants
$k=9.0\times {10}^{9}Jm/C^{2}h=6.626\times {10}^{-34}Jsn=orbitnumber=4e=1.6\times {10}^{-19}C\pi =3.14v=\frac{2\times 3.14\times 9\times {10}^9\times {(1.6\times {10}^{-19})}^2}{6.626\times {10}^{-34}\times 4}v=\frac{144.69\times {10}^{-29}}{26.05\times {10}^{-34}}v=5.55\times {10}^{5}m/s$