According to classical theory, the proposed path of an electron in Rutherford atomic model was spiral.
According to Maxwell theory of electromagetic radiation, when a charged particle evolves, it gives out radiation and loses energy. An electron revolving around the nucleus should continuously emit radiation and lose energy. The electron should come closer to the nucleus by following spiral path and ultimately fall into the nucleus

According to classical theory, the path of an electron in Rutherford's atom is a spiral. This means that the electron moves in a spiral trajectory around the nucleus, rather than any of the other options provided (circular, parabolic, or straight line).

There are several reasons why the electron's path is believed to be a spiral according to classical theory:

1. Electromagnetic Radiation: According to classical electromagnetic theory, an accelerated charged particle emits electromagnetic radiation. As the electron orbits the positively charged nucleus, it experiences acceleration due to the electrostatic attraction between the two. This acceleration causes the electron to emit electromagnetic radiation continuously.

2. Energy Loss: The emission of electromagnetic radiation by the electron results in energy loss. According to classical theory, as the electron loses energy, it moves to a lower energy level and spirals closer to the nucleus. This spiraling motion is a consequence of the continuous energy loss due to radiation.

3. Stability of the Atom: In classical theory, if the electron were to move in a circular path, it would continuously lose energy and spiral into the nucleus, leading to the collapse of the atom. However, the observed stability of atoms suggests that the electron must be in a stable orbit. The spiral path allows the electron to continuously lose energy without collapsing into the nucleus.

4. Experimental Observations: Rutherford's famous gold foil experiment provided evidence for the existence of a small, dense, positively charged nucleus at the center of an atom. The scattering of alpha particles in this experiment supported the idea of a spiral path for the electron, as the deflection of the alpha particles indicated the presence of a concentrated positive charge at the center.

Overall, classical theory suggests that the path of an electron in Rutherford's atom is a spiral due to the emission of electromagnetic radiation and the continuous loss of energy. This spiral motion allows for the stability of the atom while accommodating the observed experimental evidence.