According to Rutherford the electrons are revolving around the nucleus in circular orbits (now we postulate eliptical orbits). This is very similar to the planetary model of the universe where planets are revolving round the sun in circular orbits. The attraction between the positively changed nucleus and negative electron provide the centripetal force acting on the electron moving in circular orbit.
For an electron of mass m, moving in a circular orbit of radius r, with speed v;
In the Rutherford model all value of r and v are permitted.
Since r and v are continuous variables, E is also a continuous variable. In other words all values of energy of electron in orbit are possible.
