← The Nuclear Atom

# The Thomson Model and Thomson Scattering

Saturday, February 5, 2022

## The Thomson Model (or Plum Pudding Model) of the Atom

For an atom with $Z$ electrons, there is a sphere of $Ze$ positive charge encapsulating those electrons.

### Scattering experiments

Scattering experiments are when atoms are bombarded by charged particles to observe the deflection they experience.

In scattering experiments, the particles are deflected by the electric charges within the atom (the positive charge in the atom repels a positively charged particle while the electrons attract it). The positive charges have a much greater effect than the electrons, since the mass of the electrons is so much less than the particle.

Since experiments on a single atom are nearly impossible, scattering experiments are typically done to metal foils. The average scattering angle is $\theta_{av}$, and the atomic radius is denoted $R$. The total scattering angle, $\theta$, is the angle of deflection the particle experiences through the foil as a whole, can be approximated as such:

$\theta \simeq \sqrt{N}\theta_{av}$

The Thomson model is accurate when predicting the average scattering angle for a single atom through a foil about $10^4$ atoms thick, but fails completely for the probability of scattering at large angles.

### Rutherford's experiment

Ernest Rutherford conducted an experiment which showed that alpha-particles scattered at angles greater than $90\degree$ with a probability of $10^{-4}$, which is significantly more likely than Thomson's model predicts (his model predicts $10^{-3000}$). This led Rutherford to propose a model of the atom where the positive charge is not equally distributed but rather concentrated in a very small region.