Electrostatic Potential Energy of a system of Two Point Charges
In a hydrogen atom, the electron and proton are bound at a distance of about `0.53Å`
Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinity sepration of the electron from proton.
The potential energy of any object at any point is equal to the difference in its potential energy at infinity and at that point. Work done is equal to the total energy of the system.

Explanation

Charge on electron, `q_(e)=-1.6xx10^(-19)C` and charge on proton, `q_(p)=1.6xx10^(-19)C`

Potential energy of the system = Potential energy at infinity - Potential energy at a distance of `0.53Å`
`=0-(1)/(4piepsilon_(0))*(q_(e)q_(p))/(r)`
`=0-(9xx10^(9)xx1.6xx10^(-19)xx1.6xx10^(-19))/(0.53xx10^(-10))`
`=43.47xx10^(-19)J`
`=(43.47xx10^(-19))/(1.6xx10^(-19))" "(because1" eV "=1.6xx10^(-19)J)`
`=-27.16" eV"`