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

## Content

### Milikan*s 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 =* ρ*l/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**..