The big idea: You can pay with 3 coins or 4 coins, but never 3½ of the smallest coin — electric charge works the same way: it is quantised, coming only in whole-number lumps, never a fraction of a lump.
The smallest lump is the elementary charge, e = 1.60 × 10⁻¹⁹ C. This is the charge on one proton (+e) or one electron (−e).
So any charge Q is just a whole number of these lumps: Q = N e, where N is a whole number.
| Idea | Continuous (wrong) | Quantised (real) |
|---|---|---|
| Allowed charges | any value at all | only whole multiples of e |
| Smallest amount | no smallest amount | one elementary charge, e |
| Example charges | 1.5e, 2.3e, π·e … | 1e, 2e, 3e, … (whole numbers) |
Spot it: Quantised means "comes in fixed steps" — like money in whole cents, not any amount you like.
An object is charged because it has extra electrons (negative) or is missing electrons (positive). You can only ever add or remove whole electrons — so the charge can only change in steps of e.
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Because charge comes in whole lumps of e, the charge on any object is the number of lumps N multiplied by the size of one lump:
- the total charge on the object (C, coulombs)
- a whole number — how many elementary charges (extra or missing electrons)
- the elementary charge, e = 1.60 × 10⁻¹⁹ C (given in the data booklet)
Q = N e. Cover the one you want: N and e side by side → multiply (Q = N e); Q above e → divide (N = Q ÷ e); Q above N → divide (e = Q ÷ N).
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Going the other way: To find how many extra (or missing) electrons an object has, rearrange to make N the subject:
N = Q ÷ e — divide the measured charge by e.
The answer must come out as a whole number. If it doesn't, you've made an error — charge is always a whole multiple of e.
A tiny plastic sphere carries a charge of −8.0 × 10⁻¹⁹ C. How many extra electrons does it hold? (e = 1.60 × 10⁻¹⁹ C.)
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How this is tested — quantisation links to Millikan's oil-drop experiment, the classic evidence for it:
Paper 1A
- Identify which charge values are allowed (whole multiples of e).
- Count electrons with N = Q ÷ e.
Paper 2
- Part of a longer oil-drop question — deduce a charge from the fact that it must be a whole-number multiple of e (e.g. when a drop splits).
The classic trap: Giving N as a decimal. Charge is quantised, so N is always a whole number — round only because of measurement error, never to a fraction.
Millikan's oil-drop experiment — the evidence: Millikan balanced tiny charged oil drops in an electric field and measured the charge on each one.
Every charge he found was a whole-number multiple of one smallest step — and that step was e = 1.60 × 10⁻¹⁹ C.
No drop ever had a fraction of e. That is the experimental proof that charge is quantised.
In an oil-drop experiment a single drop is found to carry a charge of 6.4 × 10⁻¹⁹ C. (a) Deduce how many elementary charges this is. (b) The drop then splits into two equal halves, sharing its charge equally; deduce the charge on each half and check it is allowed by quantisation. (e = 1.60 × 10⁻¹⁹ C.)
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