(a) According to Rutherford, an atom consisting of a central nucleus and revolving electron is stable much like sun-planet system with electro-static force of attraction and object (electron) which moves in a circle is being constantly accelerated – the acceleration being centripetal in nature. 

According to classical electromagnetic theory, an accelerating charged particle emits radiation in the form of electromagnetic waves. The energy of an accelerating electron should therefore, continuously decrease. The electron would spiral inward and eventually fall into the nucleus. Thus, such an atom can not be stable. But most of the atoms in nature are stable which is against Rutherford model. 

(b) According to the classical electromagnetic theory, the frequency of the electromagnetic waves emitted by the revolving electrons is equal to the frequency of revolution. As the electrons spiral inwards, their angular velocities and hence their frequencies would change continuously, and so will the frequency of the light emitted. Thus, they would emit a continuous spectrum, in contradiction to the line spectrum actually observed. 

Rutherford model which depends on the classical ideas are not sufficient to explain the atomic structure.