Question

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

Answer 1

Total energy of the electron in hydrogen atom is `-13.6 eV=-13.6 xx 1.6xx10^(-19)J`
`=-2.2xx10^(-18)J`.
Thus from Equation, `E=(e^(2))/(8 pi epsi_(0)r)` we have
`-(e^(2))/(8pi epsi_(0)r)=2.2 10^(-18)J`
This gives the orbital radius
`r=-(e^(2))/(8pi epsi_(0)E)=((9xx10^(9)Nm^(2)//C^(2))(1.6xx10^(-19)C)^(2))/((2)(-2.2xx10^(-18)J)`
`=5.3xx10^(-11)m.`
The velocity of the revolving electron can be computed from Equation `r=-(e^(2))/(4pi epsi_(0)rmv^(2))` with `m=9.1xx10^(-31)kg.`
`v=(e)/(sqrt(4pi epsi_(0)mr))=2.2xx10^(6) m//s`