Using Rutherford model of the atom, derive the expression for the total energy of the electron in a hydrogen atom. What is the significance of the total negative energy possessed by the electron?

Let the atomic number of the element be Z. Then, the centripetal force on the electron will be equal to the electrostatic force between the electron and the nucleus. Centripetal force at a distance r will be: F = (mev^2)/r = (KZe^2)/r^2. Solving for v, we get: v = √[(KZe^2)/(mer)].

Potential energy of the electron is given by: PE = −(KZe^2)/r

Kinetic energy of the electron is given by: KE = (1/2)mev^2
KE = (1/2)me[(KZe^2)/(mer)]
KE = (KZe^2)/(2r)

Total energy is given by: E = KE + PE
E = (KZe^2)/(2r) − (KZe^2)/r
E = −(KZe^2)/(2r)

The negative sign indicates that the revolving electron is bound to the positive nucleus.