Obtain an expression for the total energy of an electron in the `n^(th)` orbit of hydrogen atom in terms of absolute constants.

Explanation

Consider an electron of mass m and charge - e revolving round the nucleus of an atom of atomic number Z in the `n^(th)` orbit of radius Let v be the velocity of the electron. The electron possesses potential energy, because, it is in the electrostatic field of the nucleus. The electron also possesses kinetic energy by virtue of its motion. Potential energy of the electron is given by,
`E_(p)=(-Ze^(2))/(4pi epsilon_(0)^(r ))`
Kinetic energy of the electron is given by
`E_(k)=1/2 mv^(2)`
Substituting this value of `mv^(2)` in equation (2)
Total energy of the electron revolving in the nth orbit is given by En = Ep + Ek
`=-(Ze^(2))/(4piepsilon_(0)r )[01/1+1/2]=(ze^(2))/(4pi epsilon_(0)r )[-1/2]`