# Calculating electron charge in lab

1. Mar 9, 2013

### bfusco

1. The problem statement, all variables and given/known data
The purpose of this experiment is to measure the smallest unit into which electric charge can be divided, that is, the charge of an electron e. The method is the one proposed by R.A. Millikan in 1910. A small sphere of mass m having a charge q can be suspended in air by applying an electric field of field strength E to balance the gravitational force on it. We then have:

m g =q E .

We neglect here the (very) small buoyant force.

The charge q will in general not be the electron charge but rather an integral multiple of it:

q = n e, with n = 1, 2, 3, ...

When the measurement is repeated several times, e can be found as the largest common denominator of the measured charges q.

In the absence of an electric field, the electrons will reach a constant terminal velocity vT after a short time. The viscous force balances the gravitational force, so that the net force acting on the droplet is zero and we have:

mg=KvT

where according to Stoke's law:

K = 6π η r ,

with η the viscosity of air (1.83×10-5Nsm-2 at 18°C), r the radius of the spheres (≅ 0.50μm). From measuring the terminal velocity vT of free fall, the mass of the spheres can be determined.

3. The attempt at a solution
alright i have most of the work done, i calculate the terminal velocities, and the electric fields based on the data i collected. now i have all this data and i dont know how to use it to get the value of "e".

what i have: voltages, distances, times, terminal velocities, masses, E-fields, charges

considering there was a lot of data i used excel to calculate the values, now with the known values how do i figure out the values of n, n being from q=ne?

an example of some of the date i have for charge: 5.4364E-10, 1.022E-9.

2. Mar 9, 2013

### bfusco

the lab tells me to guess for the values of n, but how am i suppose to have an idea of what to guess without using the known value of e?

3. Mar 9, 2013

### haruspex

The charge data should form clusters of values roughly equally spaced. Some clusters may be absent, so some gaps may be two or three times the size of others. If you can partition the data that way, you then assume that each cluster corresponds to a different integer multiple of e.