Quantisation of Charge: Why Q = ne

Physics · Electric Charges And Fields · NEET

Quantisation of charge means every charge is a whole-number multiple of the basic charge e, written as Q = ne, where n is an integer (..., -2, -1, 0, 1, 2, ...) and e = 1.6 x 10^-19 C. You can never have a charge like 1.5e or half an electron. Memory hook: charge comes in "coins" of e, so you can pay 1, 2 or 100 coins, but never one-and-a-half coins.
Charge is allowed only at whole multiples of eQ1e2e3e4e5e2.5enot allowed0
Charge can sit only on the green ticks (whole multiples of e). A value like 2.5e falls between ticks, so it can never exist for a free charge.

Your doubts, answered

Can a body ever have a charge like 4.8 x 10^-19 C but not 5 x 10^-19 C?

Yes for 4.8 x 10^-19 C, no for 5 x 10^-19 C. Charge must be Q = ne. Check: 4.8 x 10^-19 / 1.6 x 10^-19 = 3, a whole number, so it is allowed (n = 3). But 5 x 10^-19 / 1.6 x 10^-19 = 3.125, not a whole number, so that value is impossible. Always divide the given charge by e and see if you get an integer.

What does the n in Q = ne actually represent?

n is the number of extra or missing electrons on the body. If the body has 3 extra electrons, n = -3 and Q = -3e. If it lost 3 electrons, n = +3 and Q = +3e. So n just counts electrons, and it must be a whole number because you cannot add or remove half an electron.

Is charge continuous or discrete? Why does my textbook treat it as continuous?

Charge is truly discrete (it jumps in steps of e). But e = 1.6 x 10^-19 C is so tiny that in everyday charges (like 1 microcoulomb = about 6 x 10^12 electrons) the steps look smooth. So for large-scale problems we treat charge as continuous, but at the fundamental level it is quantised.

Why is the smallest free charge 1.6 x 10^-19 C and not smaller?

Experiments (Millikan's oil-drop experiment) showed all free charges are whole multiples of e = 1.6 x 10^-19 C, the charge on one electron or proton. Nothing free has ever been measured with less. This experimental fact is what quantisation of charge means for NEET.

Quarks have charge like +2e/3, so is Q = ne wrong?

No. Quarks do carry fractional charges (+2e/3 or -e/3), but quarks are never found free or alone; they always combine so the total is a whole multiple of e. Since NEET deals with free, isolated charges, the rule Q = ne with integer n holds perfectly.

⚠️ The NEET trap
Any charge value can exist, so 3.2 x 10^-19 C and 4 x 10^-19 C are both fine.
Only whole multiples of e are allowed. 3.2 x 10^-19 C = 2e (allowed, n = 2), but 4 x 10^-19 C = 2.5e (not an integer, impossible).
🧠 When a question asks which charge value is NOT possible, divide each option by 1.6 x 10^-19 C and reject any that is not a whole number.

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Frequently asked

What is quantisation of charge in one line?

It is the fact that any charge is always a whole-number multiple of the basic charge e, written Q = ne, with n an integer and e = 1.6 x 10^-19 C.

What is the value of e?

e = 1.6 x 10^-19 coulomb. It is the magnitude of charge on one electron or one proton and is the smallest free charge that exists.

Can n be zero or negative in Q = ne?

Yes. n = 0 means a neutral body (equal positive and negative charge). Negative n means excess electrons (net negative charge); positive n means missing electrons (net positive charge).

How do I find the number of electrons transferred?

Use n = Q / e. For example, a charge of 1.6 x 10^-6 C means n = 1.6 x 10^-6 / 1.6 x 10^-19 = 10^13 electrons transferred.

Why is quantisation of charge important for NEET?

NTA sets direct one-mark questions asking which charge value is possible or how many electrons were transferred. Knowing Q = ne lets you solve them in seconds by dividing by e.