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 =-13.6 xx1.6xx10^(-19)J=-2.2xx10^(-18)J`.
Thus, `-(e^(2))/(8pi epsi_(0)r)=2.2xx10^(-18)J`
This gives the orbital radius
`r=-(e^(2))/(8pi epsi_(0)E)=-((9xx10^(9)Nm^(2)//C^(2))(1.6xx10^(-19)xxC)^(2))/((2)(-2.2xx10^(-18)J))`
The velocity of the revolving electron can be computed with `m=9.1xx10^(-31) kg`.
`v=(e)/(sqrt(4pi epsi_(0)mr))=2.2xx10^(6)m//s`