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 - `13.6eV=-13.6xx1.6xx10^(-19)J=-2.2xx10^(-18)J`.
we have `E=(e^(2))/(8pi epsilon_(0)r)=2.2xx10^(-16)J`.
This gives the orbital radius
`r=-(e^(2))/(8pi epsilon_(0)E)=((9xx10^(9)Nm^(2)//C^(2))(1.6xx10^(-19)C)^(2))/((2)(-2.2xx10^(-18)J))`
`=5.3xx10^(-31)m`
The velocity of the revolving electron
`v=(e)/(sqrt(4pi epsilon_(0)mr))=2.2xx10^(6)m//s`