# Speed Of Electrons

From the "Hopper" entry in WhimsicalUnitsOfMeasurement:

Some have mischaracterized this unit as the distance an electron will travel in 1 nanosecond. In fact, electrons in conductive media do not travel at c, they travel at incredibly slow velocities, on the order of a fraction of a millimeter per second. The rate can vary, and the amount of current in the conductor is a function of the average speed of the electrons in it.

Not true. Electrons travel at about c/3, but the speed of the electrons is not the same thing as the speed of the signal.

Rebuttal: Answer: Electrons can have a wide range of speeds. A slow case: we know that electrons move when there is a current flow in a wire, but the speed at which the electrons themselves move in the wire - the so-called electron drift velocity - surprises most people. For example, for a copper wire of radius 1 mm carrying a steady current of 10 Amps, the drift velocity is only about 0.024 cm/sec! On the fast side: the Bohr model of the hydrogen atom has the (bound) electron zipping around the nucleus at about 2 million meters/sec. And on the very fast side, some examples are: beta particles, which are emitted by some radioactive materials; and the innermost electrons of atoms of elements having large atomic number, such as Uranium. In these cases, the electrons are traveling at very nearly the speed of light. (about 300 million meters/sec). [from http://newton.dep.anl.gov/askasci/phy99/phy99092.htm ]

Although the drift velocity in a wire is small, the thermal velocity of the electrons tends to be quite large. Something of the order of 100,000 meters/sec. So they are buzzing about at random at high speeds, with a small superimposed drift velocity caused by the electric field.

Electric current is essentially a measure of how many charge carriers you can move through a given cross-section of conductor in a given amount of time. This will depend on the size of the cross section, the number of charge carriers, and their velocity. A current of 1 A corresponds to a transfer of 1 Coulomb of charge per second. An electron carries 1.6*10-19C so you need to move 6.3*10^18 electrons/sec. Divide by the density of electrons in a copper wire (about 8.45*10^22 electrons/cm^3) and the cross section of the wire (for AWG 18 this is pi*(1.02mm/2)^2 or 0.008 cm^2) and you get 0.0093 cm/s.

If the drift velocity of electrons in the wire were c/3, the current would be roughly 1 tera-ampere. Given a nominal 10.5 Ohms/1000 feet for AWG 18 copper, you can calculate a power dissipation on the order of 10^26 watts in a one-foot length, enough to instantly vaporize the wire and anyone foolish enough to try this experiment. ;-)

It is interesting to note: Several creative people have surmised that it might be possible to extract endless amounts of energy from a dipole if one understands how electrons and current travel through resistive mediums.

Yes, but most (I've seen) rely on Maxwell's demon style effects, trying to switch potential from one circuit to another without loss. And a lot of zero-point handwaving. Quantum effects are odd, however. It may work one day. TTBrown found that rocks could continuously drive a few microamps through a load. So all we need to do is wire a lot of rocks together.

...and for the rest of you, bang... the... rocks... together...

Wondering how electrons can be so slow and still have electricity go so fast? Imagine a long plastic tube filled with ping-pong balls. You gently press on the ball at one end so that a different ball falls out the other. Both the information that you had pressed, and the energy to dislodge the ball, travel much faster than the ball you pressed. At the local speed of sound for the Ping-Pong Ball medium

From ComputerHardwareOfTheFuture

Re: the maximum speed of an electron in copper

In a 10 kV TravellingWaveTube, the axial speeds of the charge-carriers (electrons) and the field (signal) are both about two-tenths of the speed of light. TravellingWaveTubes are vacuum tubes. The walls of the vacuum tube are usually made of iron and copper.

However, in a copper IC track, lets say 0.5 mm wide, by 0.1 mm thick, with about 30 mA current passing through it:

```			Current	        3.00E- 2 A
Electron charge	1.60E-19 C
I/e	        1.87E+17 electrons/second

Width	5.00E-4 m gives X-section Area	5.00E- 8 m^2
Height	1.00E-4 m

(# Electrons / Time) / Area  3.74E+24 electrons / second / m^2

Copper	has 		8.45E+28 conduction electrons/m^3
giving drift velocity	4.43E- 5 m/s

```
further, suppose this track is inside a fairly fast machine

```	clock speed	5.00E+08 Hz
clock period	2.00E-09 s
drift velocity	4.43E-05 m/s lets take the value above for the sake of argument
distance moved	8.86E-14 m/clock cycle

```
The motion of the charge carriers just isn't significant.

DeleteMe:

anyone to check my arithmetic?
• The value for conduction electrons / m^3 matched the number of atoms / m^3, within the error of the copper's density.
• But the width was off by 10x (0.5 mm vs. 0.5 cm), so an AnonymousDonor fixed it.
• and the division of (I/e) / Area / (# conduction electrons / volume) was off by another 20x, so the AnonymousDonor fixed that too.
• and the division of drift velocity by frequency was off by another 10x, so the AnonymousDonor fixed that too.
• The final answer is absurdly precise.
• Even so, the motion of the charge carriers isn't significant.

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