# A-level Physics (Advancing Physics)/Millikan's Experiment

Electrons have a finite charge, which is approximately 1.6 x 10−19C. This was first proven by Robert Millikan in 1909. Millikan sprayed drops of oil which were then charged (ionised) either by friction as they were sprayed, or with x-rays. They were then allowed to fall into a uniform electric field.

Once in the uniform electric field, the strength of the field was adjusted in order to keep an oil drop stationary. This was done by hand, looking through a microscope. In a stationary position, the gravitational force and the electric force were balanced - there was no net force on the oil drop. So, at this point:

${\displaystyle {\frac {qV}{d}}=mg}$

The electric field strength was adjusted by changing the voltage between the two plates. The voltage at which the drops were stationary was measured. The charge on each drop was then calculated. Millikan found that these charges were all multiples of 1.6 x 10−19C, thus showing that the charge of each drop was made up of smaller charges with a charge of 1.6 x 10−19C.

## Questions

h = 6.63 x 10−34 Js

c = 3 x 108 ms−1

g = 9.81 ms−2

1. Rearrange the formula above in terms of q.

2. The mass of an oil drop cannot be measured easily. Express the mass of an oil drop in terms of its radius r and its density ρ, and, by substitution, find a more useful formula for q.

3. An oil droplet of density 885kgm−3 and radius 1μm is held stationary in between two plates which are 10 cm apart. At what potential differences between the plates is this possible?

4. If the X-rays used to ionise the oil are of wavelength 1 nm, how much energy do they give to the electrons? Why does this mean that the oil drops are ionised?

5. In reality, the oil drops are moving when they enter the uniform electric field. How can this be compensated for?

Worked Solutions