Assuming the expression for radius of the orbit, derive an expression for total energy of an electron in hydrogen atom.

Explanation

As per Rutherford.s model :
`(mv^(2))/(r)=(1)/(4piepsi_(0)).(Ze^(2))/(r^(2))`
`impliesmv^(2)=(1)/(4piepsi_(0)).(Ze^(2))/(r)`

Total energy =P.E +K.E.
`=-(1)/(4piepsi_(0)).(Ze^(2))/(r)+(1)/(2)mv^(2)=(-1)/(4piepsi_(0)).(Ze^(2))/(r)+(1)/(8piepsi).(Ze^(2))/(r)`
`=-(1)/(2).(1)/(4piepsi_(0)).(Ze^(2))/(r)=-(1)/(8piepsi_(0)).(Ze^(2))/(r)`
Negative sign implies that electron - nucleus form a bound system.