Question

How did Rutherford know that the nucleus was positively charged?

Answer 1

Rutherford carried an experiment using alpha particles. Alpha particles consist of two protons and two neutrons so they are positively charged. Some of the alpha particles deflected since the like charges repel. Some of the alpha particles went straight through the foil undeflected; it means the atom has some large empty space.

Complete step by step answer:
In $1911$ . Rutherford carried out a series of experiments using $\alpha -$ particles. The $\alpha -$ particles were directed against a thin foil. The foil was surrounded by a circular fluorescent rise sulphide screen. Whenever an $\alpha -$ particle struck the screen, it produced a flash of light.
Rutherford made following observations:
most of $\alpha -$ particular went straight without deflection
A few of them get deflected through small angles.
A very few did not pass through the foil at all but suffered large deflections. It even came back in more or less the direction from which they had come, i.e. a deflection of $180{}^\circ .$ Since charges repel.
Rurhterford made the conclusion that the cause of the deflections of the positively charged alpha particles had to be something within the atom that was also positively charged. He further concluded in his metal foil experiments that most of the atom is empty space with a tiny, dense, positively charged nucleus at the center that contains most of the mass of the atom. He also concluded that the electrons orbit the nucleus like the planets orbit the sun. Through this experiment Rutherford discovered the positively charged nucleus.

Note: Alpha particles are actually helium atoms from which electrons have been removed. Each alpha particle consists of a mass equal to about four times that of a hydrogen atom and carries a positive charge.
This model was similar to the solar system, the nucleus representing the sun and revolving electrons as planets. The electrons are, therefore, generally referred to as planetary electrons.