The elementary charge

Q: What is the value of the elementary charge?

1.602176634 × 10⁻¹⁹ C. Since 2019 e is exactly 1.602176634 × 10⁻¹⁹ coulombs. One ampere is now about 6.24 × 10¹⁸ elementary charges passing a point every second.

Is electric charge smooth, or does it come in lumps?

e = 1.602\,176\,634 \times 10^{-19}\ \text{C}

Exact, by definition, since 2019 12 min read, with an experiment to run

Every electric charge you will ever meet is a whole number of one tiny lump. That lump, the elementary charge $e$ , is the charge of one proton, or minus the charge of one electron.

A phone charger pushes about six billion billion of them through the cable every second. Since 2019 $e$ is fixed exactly and defines the ampere.

1 · Play first

Float an oil drop with electricity

In 1909 Robert Millikan and Harvey Fletcher sprayed tiny oil drops between two metal plates. Some drops picked up a few extra electrons. With the right voltage on the plates, the electric push upward exactly balances gravity, and the drop hovers.

Catch a drop, tune the voltage until it hangs still, and log its charge. After a few drops, look at the numbers: they all sit on steps of one size.

What to notice

A drop with more charge needs less voltage to hover.
The charges are always about 1, 2, 3 or more times the same small number, never in between.
Falling speed tells you the drop's size, so you can work out its weight.

2 · The equation, piece by piece

When the drop hovers, the electric force up equals its weight down. The field between the plates is the voltage divided by the gap. Tap any piece.

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q

Charge on the drop

What we measure for each drop.

Millikan's 1913 value was $1.592\times10^{-19}$ C, about 0.6% low, because the air viscosity he used was slightly wrong.

3 · How we found it

1Charge in lumps

In the 1830s Michael Faraday found that the same current always deposits the same amount of metal in electrolysis. That hinted charge came in fixed portions tied to atoms.

In 1897 J. J. Thomson showed cathode rays were streams of tiny charged particles: electrons. He measured their charge-to-mass ratio, but not the charge alone.

2The oil drop

Millikan and his student Harvey Fletcher switched from water drops, which evaporated, to oil drops that lasted for hours. By 1913 they had watched hundreds of drops and every charge fell on steps of one size.

Millikan won the 1923 Nobel Prize, partly for this.

3Fixing the ampere

Quantum effects in electronics, the Josephson and quantum Hall effects, tie voltage and resistance to $e$ and $h$ . In 2019 $e$ was fixed exactly and the ampere is now defined as a flow of $e$ per second.

1834
Faraday's laws of electrolysis hint charge comes in portions.
1874
George Stoney estimates a smallest unit of charge.
1897
Thomson discovers the electron.
1909
Millikan and Fletcher begin the oil-drop experiment.
1913
Millikan publishes $e \approx 1.59\times10^{-19}$ C.
2019
$e$ is fixed exactly and defines the ampere.

4 · How the value is pinned down

Since 2019 $e$ is exactly 1.602176634 × 10⁻¹⁹ coulombs. One ampere is now about 6.24 × 10¹⁸ elementary charges passing a point every second.

Electrical standards labs use the quantum Hall effect, set by $h/e^2$ , to make perfectly repeatable resistances.

5 · What if it were different?

If e were bigger

Electrons would grip atoms more tightly, changing the size of atoms and the whole of chemistry.

If charge were smooth

There would be no atoms with fixed numbers of electrons, and no periodic table.

Why it matters to you

Your phone counts its battery charge in units that come straight from $e$ .

6 · Try it at home

Count charges with electrolysis

Pass a known current through salty water and measure the hydrogen gas it makes. Each hydrogen molecule needs two electrons, so counting molecules counts charges.

You need

A 9 V battery and a multimeter set to measure current
Two pencils sharpened at both ends (the graphite is the electrode)
A glass of water with a spoonful of baking soda
A small upside-down test tube or narrow glass full of water, to catch gas

Do this

Put both pencil tips in the water and connect them to the battery, with the meter in series to read the current.
Catch the bubbles from the pencil on the negative side under the upside-down tube.
Run for 10 minutes, keeping note of the current, then measure the volume of gas collected.

The maths

Charge passed $Q = It$ . At room temperature one mole of gas fills about 24 litres, so moles of hydrogen are volume / 24 L. Electrons $= 2 \times$ moles $\times N_A$ , so $e = Q/(2 \times \text{moles} \times N_A)$ .

Stay safe: Use only baking soda, not table salt, which can make chlorine. Work somewhere airy and keep the small amount of hydrogen away from flames.

7 · Common mix-ups

MythQuarks break the rule, because they have a third of a charge.

ActuallyQuarks are never found alone. Every free particle still carries a whole number of $e$ .

MythMillikan's drops showed a perfect value.

ActuallyHis number was slightly off because of a wrong value for air's stickiness.

MythElectrons are tiny balls of charge.

ActuallyAs far as we can tell, an electron has no size at all. Only its charge and mass are measurable.

8 · References

CODATA value: elementary charge, NIST, 2018
On the elementary electrical charge and the Avogadro constant, R. A. Millikan, Physical Review 2, 1913
The International System of Units (SI Brochure, 9th edition), BIPM, 2019
Cathode rays, J. J. Thomson, Philosophical Magazine 44, 1897

Next constantThe Boltzmann constant: What is temperature, really, and how hot is one molecule?