It is found experimentally that 13.6 eV energy is required to separate a hydrogen atom into a proton and an electron . Compute the orbital radius and the velocity of the electron in a hydrogen atom.

Explanation

Total energy of the electron in hydrogen atom is - 13.6 eV=- 13.6 `xx 1.6 xx 10^(-19) J = -2.2 xx 10^(-18)`J.
We have E = `(e^(2))/(8 pi epsilon_(0)r) = - 2.2 xx 10^(-18) `J.
This gives the orbital radius .
r = `(e^(2))/(8 pi epsilon_(0) E) = - ((9 xx 10^(9) Nm^(2) // C^(2)) (1.6 xx 10^(-19) C)^(2))/((2) (-2.2 xx 10^(-18)J))`
=` 5.3 xx 10^(-11)`m
The velocity of the revolving electron
`v (e)/(sqrt(4 pi epsilon_(0)mr)) = 2.2 xx 10^(6) `m//s