Sub-atomic Particles

Dalton's atom was a solid, indivisible ball. Two families of experiments with glass discharge tubes shattered that picture. When scientists passed a high-voltage current through a gas at low pressure, mysterious rays streamed out from the cathode, bent toward a positive plate, and turned out to be identical no matter which gas or metal was used — the first sign that every atom contains a common negative particle, the electron. A second stream, escaping through holes in a perforated cathode, bent the other way and changed with the gas used, revealing a positive particle, the proton, that belongs to the specific atom. Decades later James Chadwick found a third, uncharged particle of similar mass, the neutron, hiding in the nucleus alongside the proton. This article builds up the relative charge, relative mass, and location of all three sub-atomic particles, then shows how to use them to find the number of electrons and the approximate mass of any neutral atom.

The core insight

Every atom is built from three sub-atomic particles — the negatively charged, near-massless electron outside the nucleus, and the positively charged proton and neutral neutron of nearly equal mass packed inside the nucleus — with a neutral atom always having equal numbers of protons and electrons.

The core idea

How the electron was found. A discharge tube is a sealed glass tube with two metal plates (electrodes) at very low gas pressure, connected to a high-voltage source. The rays that stream from the cathode (the negative electrode) toward the anode are called cathode rays. Two observations mattered: the rays bent toward the positively charged plate when passed between charged plates, showing they carry negative charge, and the same rays appeared for every gas and every electrode material tried. A property that never changes with the material must belong to every atom — so cathode rays are a fundamental particle common to all matter, the electron, discovered by J. J. Thomson.

How the proton was found. Using a cathode with holes punched through it (a perforated cathode), a second stream of rays was found travelling in the opposite direction, from anode to cathode, escaping through the holes. These canal rays (or anode rays) bent toward the negative plate, showing positive charge, but — unlike cathode rays — their mass and charge changed depending on which gas filled the tube. That gas-dependence showed canal rays are not a single universal particle but the leftover positively charged residues of whichever gas atoms were used. The lightest such particle, obtained using hydrogen gas, was named the proton.

How the neutron was found. Adding up the charges of protons and electrons could explain why an atom is neutral, but not why an atom's mass was roughly double what its proton count alone predicted. In 1932 James Chadwick identified a third particle in the nucleus with almost the same mass as a proton but carrying no charge at all — the neutron. Its existence closed the gap between the number of protons and the total mass of the atom. The three particles compare as follows:

Particle	Relative charge	Relative mass	Location
Electron ( $e^-$ )	$-1$	negligible ( $\approx \tfrac{1}{2000}$ of a proton)	outside the nucleus
Proton ( $p^+$ )	$+1$	$\approx 1\ \text{u}$	inside the nucleus
Neutron ( $n$ )	$0$	$\approx 1\ \text{u}$	inside the nucleus

Because an atom as a whole carries no net charge, the total positive charge from the protons must exactly cancel the total negative charge from the electrons:

\text{number of electrons} = \text{number of protons} \qquad \text{(neutral atom only)}.

where: this equality holds for a neutral atom; if the atom loses or gains electrons to become an ion, the two counts differ. The protons and neutrons sit together in a tiny, dense central nucleus that carries almost the entire mass of the atom, while the far lighter electrons occupy the much larger space surrounding it — which is why an atom is mostly empty space by volume but almost entirely nucleus by mass.

Figure

A simple atom diagram showing a dense central nucleus made of protons and neutrons surrounded by orbiting electrons at a much larger distance

Why the atomic mass adds up the way it does

An atom's approximate mass, in atomic mass units (u), equals the number of protons plus the number of neutrons, and this article now shows why that simple sum is justified rather than just asserted, using nothing but the three relative masses already listed.

Step 1. Write the total mass of a neutral atom as the sum of the masses of everything inside it: $Z$ protons, $N$ neutrons, and (for a neutral atom) $Z$ electrons, where $Z$ is the number of protons and $N$ is the number of neutrons. Using the relative mass values from the table, this total is $Z(1\ \text{u}) + N(1\ \text{u}) + Z\left(\tfrac{1}{2000}\ \text{u}\right)$ .

Step 2. Compare the size of the electron term with the proton and neutron terms. Even for a fairly heavy atom with, say, $Z = 20$ electrons, the electron contribution is $20 \times \tfrac{1}{2000}\ \text{u} = 0.01\ \text{u}$ — about a hundredth of a single proton's mass. Against a total mass in the range of tens of atomic mass units, this term changes the answer by less than half a per cent.

Step 3. Drop the electron term as negligible compared to the proton and neutron terms, since it is thousands of times smaller than either. What remains is the working rule used throughout this topic:

\text{approximate atomic mass (in u)} = (\text{number of protons} \times 1\ \text{u}) + (\text{number of neutrons} \times 1\ \text{u}).

where: the number of protons and the number of neutrons are both whole numbers found from the atom's composition, and the answer is expressed in atomic mass units (u), the unit in which a proton or neutron has mass close to $1$ . This is exactly the rule already used for sodium in Worked example 1 of the shorter Pass-1 article: $11$ protons and $12$ neutrons gave a mass of $23\ \text{u}$ , and the reasoning above is why that shortcut of simply adding protons and neutrons — while ignoring the electrons entirely — is a safe approximation and not a coincidence.

Worked example

Question: An atom of an element has 17 protons and 18 neutrons in its nucleus, and it is electrically neutral. Find (a) the number of electrons it has, and (b) its approximate mass in atomic mass units. (c) If this atom were to lose one electron to form an ion, would its approximate mass calculated above change?

Step 1. For a neutral atom, number of electrons = number of protons, so the number of electrons is $17$ .

Step 2. Using the rule derived above, approximate mass $= (17 \times 1\ \text{u}) + (18 \times 1\ \text{u}) = 35\ \text{u}$ . This is, in fact, the chlorine atom, $^{35}_{17}\text{Cl}$ .

Step 3. Removing one electron to form an ion changes the charge of the particle (it becomes $\text{Cl}^{+}$ , with $16$ electrons but still $17$ protons and $18$ neutrons) but leaves the mass essentially unchanged, because the mass formula only ever counted protons and neutrons — the electron's contribution was already judged negligible. Answer: 17 electrons, approximate mass 35 u, and losing an electron to form the ion does not measurably change this mass.

Competitive stretch

A slightly harder version of this question gives only the mass number ( $A = 35$ ) and the number of neutrons ( $18$ ), and asks for the number of protons and electrons. Since mass number is protons plus neutrons, protons $= A - N = 35 - 18 = 17$ , and electrons $= 17$ for the neutral atom — the same answer reached by working backward through the identical rule.

Common traps

Treating the electron's mass as "small but definite" and including it in mass calculations — at this level it is negligible, so only protons and neutrons are added.
Mixing up cathode rays (electrons, same for every gas) with canal rays (protons or positive ions, different for every gas) — remember canal rays need a perforated cathode and travel in the opposite direction.
Assuming all three particles were discovered together — the neutron came decades later (Chadwick, 1932), specifically to explain mass that protons alone could not account for.
Applying "number of electrons = number of protons" to an ion — that equality holds only for a neutral atom; an ion has unequal proton and electron counts by design.

Ask the tutor: if you want to practise going from mass number and neutron count back to protons and electrons, or want the cathode-ray and canal-ray experiments explained step by step, ask the AI tutor to walk through more examples with you.

Why do cathode rays always turn out to be electrons no matter what gas is in the tube, but canal rays change with the gas?

Cathode rays come from the atoms of the electrode and the residual gas losing electrons, and every atom of every element contains electrons that behave identically — so the rays measured are always the same particle, the electron. Canal rays, in contrast, are what remains of gas atoms after they lose electrons: positively charged fragments of whatever specific gas is filling the tube. Since different gases leave behind different positive residues, canal rays are gas-dependent, while cathode rays are not.

If the neutron has no charge, how did Chadwick know it existed at all?

Chadwick could not detect the neutron by its deflection in an electric or magnetic field, since a chargeless particle is not pushed by either. Instead he inferred its existence indirectly: the total mass of atoms was consistently about double what the proton count alone predicted, and a certain type of radiation produced when beryllium was bombarded with alpha particles behaved as if it were made of neutral particles with almost a proton's mass. Careful analysis of that radiation's behaviour confirmed a new, uncharged, massive particle — the neutron.

Does every atom of the same element always have the same number of neutrons?

Not necessarily. Two atoms of the same element always have the same number of protons (that is what defines the element), but they can have different numbers of neutrons — such atoms are called isotopes. This topic only asks you to add whatever proton and neutron counts you are given to find the approximate mass; the existence of isotopes is why different samples of the same element can show slightly different average atomic masses, a detail explored further once isotopes are formally introduced.