What experiment was used to discover the charge to mass ratio of the electron as well as the electron itself?

J. J. Thomson's experiment

Explanation:

The physicist J.J. Thomson began experimenting with cathode ray tubes and found out that atoms contain small subatomic particles with a negative charge at the end of 19th century. He called these particles corpuscles, but now are known as electrons.

Thomson devised an experiment that consisted of using a cathode ray tube, which was nothing more than a glass tube in which the air had mostly been extracted (to generate a vacuum) with wires inserted at both ends, and then pass an electrical charge through the tube to create a fluorescent glow.  

Then, with the results of the experiments carried out, Thomson discovered the electron and showed that the atom was not indivisible. So, Thomson developed in 1904 a new atomic model that was called the plum pudding atomic model.