Protons, Neutrons and Electrons

"How many neutrons does copper have?" is a question with no honest single answer, and the way most courses teach you to answer it produces a copper atom that does not exist.

The counting itself is subtraction. What makes it go wrong is that the periodic table gives you two numbers, neither of which is a neutron count, and one of which is an average over a mixture. Getting this right is worth doing carefully, because every isotope, ion and nuclear question downstream depends on it.

Three quantities, and which of them the table shows

• Atomic number, Z — the number of protons. It is a whole number, it is printed on the periodic table, and it defines the element absolutely. An atom with six protons is carbon; give it a seventh and it is nitrogen, whatever else you do to it.

• Mass number, A — protons plus neutrons, counted together as nucleons. Always a whole number, because you cannot have a fraction of a particle. It is not printed on the periodic table.

• Neutron number, N — found by subtraction, never given directly:

  N = A − Z
  

• Electrons — equal to Z in a neutral atom, and only then. In an ion:

  electrons = Z − charge
  

  where the charge carries its sign. That formula catches out more people than any other on this page, so read the sign carefully: a 2+ charge means two fewer electrons than protons, because the positive charge arose from removing them.

The other number on the periodic table — the decimal one, 63.546 for copper — is the standard atomic weight. It is an average across the isotopes as they occur in nature, weighted by abundance, and it is not the mass number of anything.

Rounding the atomic weight: right for chlorine, wrong for copper

The usual shortcut is to round the atomic weight to the nearest whole number and treat that as the mass number. Sometimes this works and sometimes it invents a nuclide.

Chlorine. 35.45 rounds to 35. Chlorine-35 is real, it makes up about three quarters of natural chlorine, and it has 17 protons and 18 neutrons. The shortcut succeeds.

Copper. 63.546 rounds to 64 — and copper-64 does not occur naturally at all. It is a radioactive nuclide with a half-life of about thirteen hours. Natural copper is a mixture of copper-63 (69.15%) and copper-65 (30.85%), and the average lands between them at a value that belongs to neither.

Bromine fails in the same way and more starkly. Its atomic weight of 79.904 rounds to 80, but bromine's two stable isotopes are bromine-79 and bromine-81 in an almost even split, and bromine-80 has a half-life of under eighteen minutes.

So the shortcut is not a rule, it is a guess that happens to be right when one isotope strongly dominates. Use it if a question gives you nothing else, and understand that what you have produced is "the most likely mass number", not a fact about a particular atom. When a question means a specific isotope it will always say so, and then you use the mass number you were given and ignore the table's decimal entirely.

Reading the notation

The full form writes both numbers on the left of the symbol, mass number above and atomic number below:

³⁵₁₇Cl

Top left is always the larger number, which is the quickest way to remember which is which. The bottom-left 17 is strictly redundant — the symbol Cl already fixes the proton count — which is why the shorter forms ³⁵Cl and "chlorine-35" mean exactly the same thing and are more common in practice.

An ion adds a charge to the top right: ³⁵Cl⁻. Do not confuse a superscript charge with a subscript count; ³⁵Cl⁻ is one chloride ion, while Cl₂ is a molecule of two chlorine atoms and carries no charge.

Four counts, worked

Iron-56. Iron's atomic number is 26, so there are 26 protons. The mass number is 56, so N = 56 − 26 = 30 neutrons. The atom is neutral, so 26 electrons.

Fe³⁺, from the same isotope. The nucleus is untouched by ionisation: still 26 protons and 30 neutrons. Electrons = 26 − 3 = 23. Notice that the mass barely changes — three electrons weigh about one part in thirty thousand of the atom — which is why an ion and its parent atom have effectively the same molar mass.

Sulfide, ³²S²⁻. Sulfur is element 16, so 16 protons and 32 − 16 = 16 neutrons. The 2− charge means two extra electrons: 16 + 2 = 18 electrons. Those eighteen electrons are the same number argon has, which is the point of the ion existing — the reasoning behind that is on the ions guide.

Hydrogen-1. One proton, one electron, and zero neutrons. It is the only common nuclide with no neutrons at all, and a reminder that N = A − Z is arithmetic rather than a claim that neutrons must be present.

Working backwards from particles to identity

Exam questions often run in reverse: here are the counts, name the species.

A particle has 18 electrons, 20 neutrons and a charge of 2+.

The charge tells you the proton count, and this is the only route to it — electron count alone never identifies an element. Rearranging electrons = Z − charge:

Z = electrons + charge = 18 + 2 = 20

Element 20 is calcium. The mass number is A = Z + N = 20 + 20 = 40. The species is ⁴⁰Ca²⁺.

The habit that makes this reliable: find Z first, always, and only then look anything up. Searching the periodic table for an element with 18 electrons will land you on argon and every subsequent answer will be wrong.

Where the simple addition breaks down

Mass number is a count, not a mass, and treating it as one hides some real physics.

Add up the masses of two free protons and two free neutrons and you get 4.0319 u. A helium-4 nucleus actually weighs 4.0015 u. The missing 0.0304 u — about three quarters of one per cent — was released as binding energy when the nucleus formed, and it is why nuclear reactions liberate so much more energy than chemical ones. It is also why the exact mass of an isotope is never quite its mass number, except for carbon-12, where the agreement is exact by definition because carbon-12 is what defines the unit.

Two further edges are worth knowing:

• Free neutrons are unstable. A neutron outside a nucleus decays to a proton, an electron and an antineutrino, with a mean lifetime of about 879 seconds. Inside most nuclei it is stable indefinitely, because the decay is energetically blocked.
• The neutron's lifetime is genuinely disputed. Two experimental approaches disagree. Trapping neutrons and counting the survivors gives about 878 seconds; measuring a beam and counting the protons produced gives about 888 seconds. The gap is several times the stated uncertainties, it has persisted for two decades, and nobody has established whether it points to an unknown decay channel or an unrecognised systematic error in one method.

Checking a set of counts

Four quick tests, in the order they catch things:

1. Does the proton count match the element? If not, nothing else matters — you have the wrong element.
2. Is A a whole number? If you have written 63.5 as a mass number, you have used the atomic weight where the mass number belonged.
3. Does electrons versus protons agree with the sign of the charge? More electrons than protons must mean a negative ion.
4. Is N sensible? Below calcium, neutrons and protons are roughly equal. Above it, stable nuclei need progressively more neutrons than protons — lead has 82 protons and around 125 neutrons — so a heavy atom with N smaller than Z should make you look again.