Rutherford atom model doesn't explain stability of an atom properly. Following are the two drawbacks of Rutherford’s
(i) Centripetal acceleration is experienced by an electron when it moves in a circular orbit.According to electromagnetic theory, an accelerated electron must radiate energy in the form of electromagnetic
waves. Therefore, if the accelerated electron lose energy by radiation,
the energy of the electron continuously decreases and it must spiral
down into the nucleus.Thus, the atom cannot
be stable. But, it is well known that most of the atoms are stable.
(ii) According to classical electromagnetic theory, the accelerating
electron must radiate energy at a frequency proportional to the angular
velocity of the electron. Therefore, as the electron spiral towards the
nucleus, the angular velocity tends to become infinity and hence the
frequency of the emitted energy will tend to infinity. This will result in
a continuous spectrum with all possible wavelengths. But experiments
reveal only line spectra of fixed wavelength from atoms.