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.

Explanation

Total energy of the electron in hydrogen atom is - 13.6 eV = `13.6 xx1.6 xx10^(-19)J=-22xx10^(-18)J` Thus from Eq. (12.4), we have `-(e^(2))/(8piepsilon_(0
)r)=-2.2 xx 10^(-18) J`
This gives the orbital radius
`r=-(e^(2))/(8piepsilon_(0)E)=-((9xx10^(9)Nm^(2)//C^(2))(1.6 xx 10^(-19)C)^(2))/((2)(-2.2xx10^(-18)J))`
= `5.3 xx 10^(-11)m`.
The velocity of the revolving electron can be computed from Eq. (12.3) with m = `9.1 xx 10^(-31) kg`,
`upsilon=(e)/(sqrt(4piepsilon_(0)mr))=2.2 xx 10^(6)m//s`.