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 × 10^(-19) J = –2.2 xx 10^(–18) J`. Thus from Eq., 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) N m^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 can be computed from Eq.with `m = 9.1 xx 10^(-31) kg,`
`upsilon = - (e)/(sqrt(4 pi epsilon_0 mr)) = 2.2 xx 10^(6) m//s`.