Final answer:
The Oil Drop Experiment by Robert A. Millikan determined the charge of an electron to be -1.6 x 10^-19 coulombs through detailed measurement and calculation of electrically charged oil droplets in an electric field.
Step-by-step explanation:
The experiment that discovered the charge of an electron is Millikan's Oil Drop Experiment. In this experiment conducted between 1908 and 1917, American physicist Robert A. Millikan was able to measure the electron charge directly. He did this by creating microscopic oil droplets that became electrically charged either by friction or X-ray exposure. These charged droplets were suspended between two metal plates with an electric field. By meticulously observing and measuring their behavior in the electric field and performing calculations, the balance of gravitational and electric forces on the droplets allowed Millikan to deduce that the charge on them was quantized. This charge was calculated to be -1.6 x 10^-19 coulombs, which is recognized as the charge of a single electron.