Why Rutherford's atom fails

Rutherford's atom copies the sun–planet system, but the forces differ: planets are held by gravity, while the nucleus and electron are charged and interact by Coulomb's law.

An electron moving in a circle is always accelerating (centripetally). Classical electromagnetic theory says an accelerating charge radiates electromagnetic waves, so the electron should keep losing energy.

Losing energy, it would spiral inwards and fall into the nucleus (Fig. 12.6). Such an atom cannot be stable, yet real atoms are.

Classically, the frequency of the emitted wave equals the frequency of revolution. As the electron spirals in, its angular velocity keeps changing, so the emitted frequency changes continuously: the atom would give a continuous spectrum, not the observed line spectrum.

Example 12.4: with r = 5.3 × 10⁻¹¹ m and v = 2.2 × 10⁶ m/s, the revolution frequency is ν = v/2πr ≈ 6.6 × 10¹⁵ Hz; classically this would be the initial frequency of the emitted light. (NCERT prints the speed as 2.2 × 10⁻⁶ m/s in this example; the value from Example 12.3 is 2.2 × 10⁶ m/s.)

Both earlier models are unstable: Thomson's electrostatically, Rutherford's because its orbiting electrons radiate.