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

h = 6.63 x 10^{−34} Js

c = 3 x 10^{8} 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.**

Assuming that the oil drop is spherical:

**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?**

q must be a multiple of e, the charge on an electron:

, where n is an integer.

Then, to find some actual values, take n = 1,2,3 ... , so V = 25.7V, 12.8V, 8.6V ...

**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?**

This provides the energy required for an electron to escape from its energy level, becoming unbound.

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

Either:

- Use a slightly stronger potential difference to slow the oil drop down, and then reduce the potential difference to keep the oil drop stationary.
- Measure the voltage required to keep the oil drop moving at a constant (terminal) velocity, using more sophisticated equipment.