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=-13.6xx1.6xx10^(-19) J=-2.2xx10^(-18)J`
Total energy of the electron in hydrogen atom is
`E=-(e^(2))/(8piepsi_(0)r)`
`:." " -(e^(2))/(8piepsi_(0)E)`
Orbital radius ,` r=-(e^(2))/((8piepsi_(0)E)`
`rArr" " r=((9xx10^(9)Nm^(2)C^(2))(1.6xx10^(-19)C)^(2))/((2)(-2.2xx10^(-18)J))`
`rArr " " r=5.3xx10^(-11)m`
The velocity of the revolving electron is given by
`r=(e^(2))/(4piepsi_(0)mv^(2))`
`rArr" " v=(e)/(sqrt(4piepsi_(0)mr))`
Putting `m=9.1xx10^(-31)kg and r=5.3xx10^(-11)m `
We have `v=((1.6xx10^(-19)))/sqrt(4piepsi_(0)xx9.1xx10^(-31)xx5.3xx10^(-11))`
`v=2.2xx10^(6)m//s`