The Electron II

The Electron II is the eleventh lecture in the Properties of Matter section of PH1011. It covers the properties of conductors, semi-conductors and insulators, Milikan's experiment, and material resistance (the Hall effect is also present in notes however as "optional reading", and therefore will not be covered here).

Previous: The Electron I

Next: X-Rays

Milikans Experiment
Milikan suspended charged oil droplets in an electric field in order to determine the charge on an electron. The energy of the field is given by E=V/d, and the drop remained stationary between the plates when qE = mg (when the electrostatic force is equal to gravitational force). The mass of the drop can be found using m=Vρ = 4/3πr3ρ. Therefore a straightforward equation for q is given - q = 4/3πr3ρgd/V.

The radius of individual drops can be measured using terminal velocity - outwith the electric field, when fgravity = fair resistance, (f=ma) : 4/3πr3ρg = 6πnrv (n being the viscocity of air). This gives r2= 9πnv/2ρg. The experiment was repeated many times, and q always results as an integer multiple of 1.6x10-19C. This is the same value as found in electrolysis, proving that the electron is present in both experiments.

Conductivity
The conductivity of materials is dependent upon their electron configurations. The resistivity (ρ; ohms per metre) of a material can aid definition of the electrical resistance R (Ω) - R = ρl/A. The opposites of these are conductivity and conductance, given by ς = 1/ρ (units: ohms-1, Ω-1 or Siemens, S) and G = 1/R (units Sm-1) respectively.

In general there are three classes of material: conductors, insulators and semiconductors. As can be expected, conductors have ρ far lower than 1, insultors far higher, and semiconductors in between. This can be described using a band model - the energy of the highest filled electron level is the Fermi energy, and sits in specific energy bands. The distance between these determines the conductance and resistance of materials; conductors have half filled bands, giving e various aavilable free states, whereas insulators and semiconductors have filled bands but a differing gap between them. Electrons must have energy input to reach the next level and therefore conduct - allowing semiconductors to conduct with only a little energy but insulators to rarely if ever conduct.

Doping in semiconductors can also allow a change in conductance; the introduction of impurities changes the number of charge carriers available and therefore changes conductance. Superconductivity also exists, as in some materials a temperature drop causes electrical resistance to cease effect entirely.

Summary
The charge on an electron is 1.6x10-19 and this can be proven through Milikan's experiment (using the terminal velocity of a droplet to find its radius -> mass -> charge). Materials conduct differently depending on their electron configurations; insulators have a high energy gap, semiconductors a low energy gap and conductors a half filled shell. Conductance is measured in Ω-1 or S and conductivity is measured in Sm-1..