Answer to Question #13361 in Mechanics | Relativity for Shetal Varghese

Question

Explain how the alpha particle scattering experiment provides an estimate of the dimensions of an atomic nucleus

Answer 1

In order to estimate the size of the nucleus, Rutherford used his analysis of the results to devise a model of what was happening. This model assumes that the nucleus is a point charge. However, the nucleus has some size (albeit tiny) and he could estimate this size by looking for readings that started to deviate from those predicted by his model. Let's look at this in more detail.

The nucleus has a positive charge. This means that it will repel the positively charged alpha particles. Picture 1.9 shows the paths of alpha particle as they pass close to (or towards) the nucleus. The electrostatic repulsion makes them vere off course. Some of them are deflected straight back.
Rutherford assumed that the charge of the nucleus was concentrated at its centre and devised a formula for how many particles would be deflected in each direction. The results matched this formula extremely well – lending support to Rutherford's model.

He then reasoned that if an alpha particle were to penetrate the nucleus, then the alpha particle would be exposed to less charge. The effective charge acting on an alpha particle that penetrated the nucleus would be less than the total charge of the nucleus. This would mean that the alpha particle would be deflected less than expected. So, he hypothesised that if the alpha particles were penetrating the nucleus, the number being deflected by large angles would be less than predicted. However, the experiment revealed no such deviation, meaning that the alpha particles were not penetrating the nucleus. And therefore, he concluded that the nucleus must be smaller than the distance of closest approach of any of the alpha particles.