Rutherford's experiment and the nature of the atomic nucleus

The nature of the atomic nucleus was first elucidated experimentally by Ernest Rutherford in 1911. He observed the scattering of $\alpha$-particles (helium nuclei) from a thin gold foil (see schematic below):

Figure 4: Schematic of Rutherford's experiment.

As he had assumed a relatively uniform mass distribution throughout the gold foil, he was surprised to observe that most of the $\alpha$-particles passed through the foil essentially undeflected, as if through empty space. Occaisionally, an $\alpha$-particle would be scattered strongly, as if it had collided with a dense concentration of mass. He, thus, concluded that most of the mass of the gold atoms was concentrated in a tiny, dense kernel that he called the nucleus.

Rutherford estimated the ``diameter'' of an atom to be approximately 10$^{-8}$ cm and that of the nucleus to be approximately 10$^{-13}$ cm. He proposed a model of the atom as consisting of a small, dense nucleus surrounded by enough electrons to yield an overall charge-neutral aggregate. That is, if the nuclear charge is $+Ze$, then the atom must possess $Z$ electrons. The model later introduced by Bohr, and even the current quantum mechanical picture of the atom (which you will see next semester), were built upon Rutherford's original model.

As mentioned in the first lecture, we know today that the atomic nucleus is composed of protons and neutrons. If a nucleus has $Z$ protons and $N$ neutrons, it is said to have a mass number $A$ equal to $Z+N$. Thus, if $X$ represents the chemical symbol of some element, then its nucleus is represented by

$$\stackrel{A}{Z}{\rm X}$$

Nuclei of the same chemical species having different mass numbers, hence different numbers of neutrons, are called isotopes of that species. Thus,

$$\stackrel{A}{Z}{\rm X}\;\;\;\;\;{\rm and}\;\;\;\;\;\stackrel{A'}{Z}{\rm X}$$

are isotopes of the element $X$. For example,

$$\stackrel{1}{1}{\rm H},\;\;\stackrel{2}{1}{\rm H},\;\;\;\;\;{\rm and}\;\;\;\;\; \stackrel{3}{1}{\rm H}$$

are isotopes in the hydrogen family, called ``hydrogen,'' ``deuterium,'' and ``tritium,'' respectively.