Rutherford's Atomic Model

Structure of Atoms and Nuclei · Maharashtra HSC

Theory

In Thomson's model the positive charge is uniformly spread over the whole sphere of the atom, so its volume density of positive charge is very small.
Such a diffuse charge can deflect an incoming alpha particle only through a very small angle; it can never turn one back.
The observed backscattering therefore ruled the model out.

An alpha particle that is deflected back must have encountered a massive particle carrying a large positive charge, which repelled it.
Since an extremely small number of alpha particles turned back while nearly all passed through almost undeflected, that positively charged particle must be very small in size and must contain most of the mass of the atom.
From the experimental data its size came out as about $10\ \text{fm}$ ( $1\ \text{fm} = 10^{-15}\ \text{m}$ ), about $10^{-5}$ times the size of the atom, so about $10^{-15}$ times its volume. Rutherford called it the nucleus.

The entire positive charge and most ( $99.9\%$ ) of the mass of an atom is concentrated in a central nucleus.
The electrons revolve around the nucleus in circular orbits, much as the planets revolve round the Sun.
The revolution is essential: without it, the electrons would be pulled straight into the positively charged nucleus and the atom would collapse.
The space between the electron orbits, which fix the size of the atom, and the tiny nucleus is mostly empty. Alpha particles that go through this empty space are undeflected; the very few that are in direct line with the nucleus or pass extremely close to it are repelled and deflected through large angles.
The model also explains why atoms emit electrons but never positive particles: the nucleus is so massive that it is not affected by forces applied to the atom.
Diagram in words: a small dark circle at the centre labelled nucleus, with two or three concentric circular orbits drawn round it, an electron marked on each orbit with an arrow showing the direction of revolution, and the vast empty space between orbits and nucleus indicated.

From Maxwell's equations, an accelerated charge emits electromagnetic radiation. The electron moves uniformly along a circular orbit, and even though the magnitude of its velocity is constant, its direction changes continuously, so its motion is accelerated. It should therefore radiate continuously.
As it radiates it loses energy, so the radius of its orbit must decrease continuously; the electron would spiral into the nucleus and the atom would collapse, losing its atomic properties.
As the electron loses energy its speed changes continuously, so the frequency of the emitted radiation would also change continuously, giving a continuous spectrum.
None of this is observed. Atoms are very stable; they do not constantly emit radiation, and certainly not of continuously varying frequency. They emit only when given energy, for instance by heating, and even then only at particular frequencies.
The model also cannot explain the observed line spectra of atoms.