Rutherford’s model of the atom was unstable because

The correct answer is Option (3) → the orbiting electron radiates energy

In Rutherford’s model the electron revolves round the nucleus, held in its orbit by the electrostatic attraction of the nucleus.

Option (1) the nucleus would break down — Incorrect. The model says nothing about the nucleus breaking up. Its problem lies in the motion of the electron around the nucleus.

Option (2) the electrons move in circular orbits — Incorrect. Motion in a circle is not unstable in itself. The planets move round the sun in stable orbits. The trouble comes only because the orbiting electron is a charged particle.

Option (3) the orbiting electron radiates energy — Correct. An electron moving in a circle is constantly accelerated. By classical electromagnetic theory, an accelerating charge emits electromagnetic waves. So the energy of the electron would keep decreasing. It would spiral inward and fall into the nucleus, and such an atom cannot be stable.

Option (4) the electrons are repelled by the nucleus — Incorrect. The electrons are negative and the nucleus is positive, so the force between them is an attraction. This attraction provides the centripetal force of the orbit.

NCERT (2026-27):
Points to Ponder – “1. Both the Thomson’s as well as the Rutherford’s models constitute an unstable system. Thomson’s model is unstable electrostatically, while Rutherford’s model is unstable because of electromagnetic radiation of orbiting electrons.”