Robert Millikan determined the magnitude of the electron’s charge by oil-drop experiment.
He was awarded The Nobel Prize in Physics in the year 1923 for his work in the measuring of elementary charge and for work on the photoelectric effect.
Oil drop experiment:
“The oil drop experiment was first performed by Robert A. Millikan and Harvey Fletcher in the year 1909 in order to measure the elementary electric charge (the charge of the electron).”
Tiny oil drops is sprayed by the atomizer into the upper portion of the chamber, under the influence of gravity some of the oil drops fall through the small hole cut in the top charge plate.
And when the oil drops come between the charge plate it is gets ionized by the influence of the x-rays.
By setting the magnitude of voltage between the charged plates, such that electromagnetic force between the oil droplet and the charged plate becomes equal to the gravitational force of the oil droplet, then the oil droplet remains to stay in the air. Which is observed by the microscope.
And through repetition of this process, the observer gets the multiple values and the lowest integer multiple of the charge value have the magnitude of the elementary charge itself which is about 1.606 x 10^-19 coulomb (the charge of a single electron).
Reference Source:
[1] Wikipedia Contributors. Robert Andrews Millikan. Wikipedia. Published December 23, 2021. Accessed December 24, 2021. https://en.wikipedia.org/wiki/Robert_Andrews_Millikan.
[2] The Nobel Prize in Physics 1923. NobelPrize.org. Published 2021. Accessed December 24, 2021. https://www.nobelprize.org/prizes/physics/1923/millikan/facts/.
[3] Wikipedia Contributors. Oil drop experiment. Wikipedia. Published December 21, 2021. Accessed December 25, 2021. https://en.wikipedia.org/wiki/Oil_drop_experiment.
[4] Millikan oil-drop experiment | Date, Summary, & Results | Britannica. In: Encyclopædia Britannica. ; 2021. Accessed December 25, 2021. https://www.britannica.com/science/Millikan-oil-drop-experiment.
[5] How Was The Charge Of An Electron Determined? BYJU’S. Published October 23, 2019. Accessed December 25, 2021. https://byjus.com/questions/how-was-the-charge-of-an-electron-determined/.