## Episode 104: Drift velocity

Lesson for 16-19

- Activity time 75 minutes
- Level Advanced

In this episode, you can show that charge carriers in good conductors usually move very slowly. You can also derive and use the equation *I* = n*A**q**v*.

If this episode is not required by your specification, the demonstration could be added to those of

Lesson Summary

- Demonstration: Ions moving (15 minutes)
- Discussion: Deriving
*I*= n*A**q**v*(15 minutes) - Worked example: Using
*I*= n*A**q**v*(10 minutes) - Discussion: Interpreting
*I*= n*A**q**v*(5 minutes) - Student questions: Practice with the equation (30 minutes)

#### Demonstration: Ions moving

Show the movement of ions when a current flows through a solution. The permanganate ions (negative) carry the distinctive purple colour toward the positive electrode. An estimate of drift velocity (of the order of mm/minute) shows the extremely slow progress of the ions.

Ask whether electrons might move faster in a metal wire. (Students may point out that, for example, a light comes on as soon as the switch is closed. Leave this in the air for now; they will be able to see whether this is a correct interpretation shortly – see the Discussion at the end of this episode.)

Episode 104-1: Conduction by coloured ions (Word, 63 KB)

#### Discussion: Deriving *I* = n*A**q**v*

You can now derive the equation *I* = n*A**q**v*.

It is worth exploring the meaning of this equation before trying numerical examples.

If a material has a large density of charge carriers, (large n), then v will be relatively low (for a given current).

The thinner the wire (for the same current) the faster the charge carriers must move.

If current is increased the only term that can increase is *v*.

Episode 104-2: Derivation of nAvq (Word, 25 KB)

#### Worked examples: Using *I* = n*A**q**v*

Now make an estimate of drift velocity in a metal by estimating the value of n.

Consider a current of 1 A in a copper wire of cross-sectional area 1 mm^{2}.

Assume one free electron per atom. (This is a good estimate.) So we need to find the number of atoms present.

For copper (density 8900 kg m^{-3} and atomic mass number 63.5):

In 1 m^{3} there are 89000.0635 moles of Cu atoms , so 8.4 × 10^{28} atoms m^{-3}.

This gives a value of n of order 10 29^{m -3}.

Rearrange the equation to give:

*v* = *I*n *A**q*

and substitute values to get;

*v* = 1 A10 29^{m -3} × 1 × 10^{-6} m × 1.6 × 10^{-19} C

*v* = 6 × 10^{-5} m s^{-1}

(i.e. less than 0.1 mm s^{-1}.)

This is consistent with the observed drift of ions in the experiment.

#### Discussion: Interpreting *I* = n*A**q**v*

They should be surprised by this result. Remind them that this is the drift velocity of the electrons inside the metal and is much lower than the actual individual velocities of electrons. This is because of the random motion of the electrons. It is useful to think of a gas of electrons with large random velocities whose nominal centre of mass drifts slowly along the metal tube.

Drift velocities in semiconductors are much larger because they have much smaller values of n (by a factor of at least 10^{6}).

#### Student questions: Practice with the equation

Episode 104-3: Electrons in copper (Word, 22 KB)