What method did Rutherford use to discover the nucleus of the atom?

Rutherford discovered the nucleus of the atom through his gold foil experiment, which involved bombarding a thin sheet of gold foil with alpha particles. This method was key to identifying the nucleus because it allowed him to observe the scattering patterns of the alpha particles as they interacted with the gold atoms.

In this experiment, a majority of the alpha particles passed straight through the foil, indicating that atoms are mostly empty space. However, a small fraction of the particles were deflected at large angles, and some even bounced back directly. This observation led Rutherford to propose that a dense, positively charged center—later known as the nucleus—exists within the atom. The nucleus is responsible for the deflection of the alpha particles, providing crucial evidence that contradicted the previously accepted "plum pudding" model of the atom, which did not account for a concentrated central core.

The other methods listed, such as analyzing cathode rays, using an electron gun, and measuring x-rays emitted by elements, do not directly relate to Rutherford's identification of the atomic nucleus and were utilized in different contexts or studies in atomic theory.