Lesson 1 · 20 min

Inside the atom: protons, neutrons and electrons

How did Rutherford find the nucleus? How do three particle counts pin down an atom or ion? And why is chlorine’s atomic mass 35.45 — a value no chlorine atom has?

In this lesson

State the charge, mass and location of protons, neutrons and electrons
Write a nuclide symbol and charge from the particle counts — and read the counts back
Explain what isotopes are and compute a relative atomic mass from abundances
Describe what Rutherford’s scattering experiment saw and how it revealed the nucleus

The periodic table gives chlorine a relative atomic mass of 35.45. Yet if you could weigh chlorine atoms one at a time, you would never find 35.45 — every chlorine atom weighs close to 35 or to 37. Where does a number that matches no atom come from? To answer, we first have to open the atom and see what is inside.

An atom that is almost empty

In 1909 Geiger and Marsden fired α particles (helium nuclei, charge +2) from a radioactive source at very thin metal foils. In the popular “plum pudding” model, positive charge was spread through the whole atom, so α particles should pass almost undisturbed. Most did go straight through — but about 1 in 8000 bounced back, deflected by more than 90°.

In 1911 Rutherford worked out what this meant: the atom’s positive charge and nearly all of its mass must sit in a tiny nucleus, with the electrons spread through the vast space around it. A nucleus has a radius of about $10^{-15}$ m, the atom about $10^{-10}$ m — if the atom were a football stadium, the nucleus would be a pea on the centre spot.

The three particles that build atoms
Particle	Charge	Mass / u	Where
proton p	+1	1.00728	in the nucleus
neutron n	0	1.00866	in the nucleus
electron e⁻	−1	0.000549 (≈ 1/1836)	outside the nucleus, filling almost all the volume

Source: CODATA 2018 recommended values (NIST); 1 u = 1.66054 × 10⁻²⁷ kg.

Predict first

A particle has 17 protons, 18 neutrons and 18 electrons. What is it?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

An argon atom, Ar A chlorine atom, Cl A chloride ion, Cl⁻ An argon ion, Ar⁺

Three numbers pin a particle down

Atomic number Z = number of protons. It fixes the element: change one proton and you have a different element.
Mass number A = protons + neutrons. Electrons are too light to count.
Charge = protons − electrons. Losing electrons makes a cation; gaining them makes an anion.

A nuclide symbol puts the three numbers on three corners of the element symbol: mass number top left, atomic number bottom left, charge top right.

{}^{A}_{Z}\mathrm{X}^{q}\qquad A = Z + N\qquad q = Z - n_\mathrm{e}

For example

\ce{^{35}_{17}Cl-}

: 17 protons, 18 neutrons, 18 electrons.

$Z$: atomic number (protons)
$N$: number of neutrons
$A$: mass number = protons + neutrons
$n_\mathrm{e}$: number of electrons
$q$: net charge (in units of e)

Protons · neutrons · electrons

Atom builder

Protons

Neutrons

Electrons

+proton (+)
neutron (neutral)
−electron (−)

The nucleus is enlarged ten-thousandfold; to scale it would be an invisible dot.

Z = 6 ¹²C Carbon · Nonmetal

Nuclide symbol: ${}^{12}_{6}\mathrm{C}$
Mass number A = Z + N: 6 + 6 = 12
Net charge: 6 − 6 = 0 neutral atom
Neutrons / protons: 1.00

Stable nuclide · natural abundance 98.93 %

Stable isotopes of Carbon

Radioactive examples

Mass: ≈ 12 u electrons carry only 0.027 %
Size: nuclear radius ≈ 2.7 fm, atom ≈ 76 pm: the atom is ~27,700× wider

Try

Build ¹²C, then add two neutrons to make ¹⁴C: still carbon, but the nucleus is now unstable. Add or remove electrons and watch the charge; finally change the proton number — the whole element changes. Note the size row: the atom is tens of thousands of times wider than its nucleus.

Isotopes

Atoms with the same number of protons but different numbers of neutrons are isotopes of one element. They have the same electrons, so their chemistry is almost identical; only the mass differs, and whether the nucleus is stable. Hydrogen has three: protium $\ce{^{1}H}$ (no neutron), deuterium $\ce{^{2}H}$ (one) and radioactive tritium $\ce{^{3}H}$ . Carbon-12 and carbon-13 are stable, carbon-14 decays — archaeologists date objects with its half-life of about 5700 years.

Most elements occur as a mixture of isotopes, in proportions that are nearly the same all over the Earth. That is where 35.45 comes from.

The average a mass spectrometer weighs

A mass spectrometer turns atoms into singly charged ions, accelerates them in an electric field and bends them in a magnetic field. Light ions bend more than heavy ones, so each isotope lands in its own place, and the height of each peak is proportional to how many there are. An element’s relative atomic mass is the abundance-weighted mean of its isotope masses.

A_\mathrm{r} = \sum_i m_i\,x_i

Use abundances as fractions (all the

x_i

add up to 1).

$A_\mathrm{r}$: relative atomic mass
$m_i$: mass of isotope i (u)
$x_i$: natural abundance of isotope i (fraction)

Mass-to-charge · abundance · atomic weight

Isotope mass spectrometer

Log scale (see trace isotopes)

Atomic weight from the spectrum

Isotope	Mass m / u	Abundance x / %	m·x / u
³⁵Cl	34.96885	75.76	26.4924
³⁷Cl	36.96590	24.24	8.9605
Sum		100.00	35.4529

\begin{aligned}A_\mathrm{r}(\mathrm{Cl}) &= \sum_i m_i x_i \\ &= 34.969\times0.7576 + 36.966\times0.2424 \\ &= 35.453\end{aligned}

Standard atomic weight in the element table: 35.45 · difference 0.0029 (within natural variation and the table’s last digit)

Start with chlorine: two peaks, about 3 : 1. Switch to Cl₂⁺ — why three peaks now, roughly 9 : 6 : 1? Then look at bromine (two almost equal peaks) and tin (ten isotopes), and switch on the log scale to find the deuterium in hydrogen.

Worked example

Compute chlorine’s relative atomic mass

The mass spectrum of natural chlorine shows 75.76 % ³⁵Cl (34.969 u) and 24.24 % ³⁷Cl (36.966 u). Find chlorine’s relative atomic mass.

Concept check

What do ¹⁴C and ¹⁴N have in common?

The number of protons The number of neutrons The mass number Their chemistry

Try the calculation

Boron has two stable isotopes: ¹⁰B (10.013 u, 19.9 %) and ¹¹B (11.009 u, 80.1 %). What is boron’s relative atomic mass?

Key takeaways

An atom is a tiny, dense nucleus (protons + neutrons) surrounded by electrons; Rutherford’s α-scattering experiment revealed the nucleus.
Proton number Z fixes the element, mass number A = Z + N, and charge = protons − electrons; ions come from gaining or losing electrons.
Isotopes share Z but differ in N: nearly identical chemistry, possibly different nuclear stability.
Relative atomic mass is the abundance-weighted mean $A_\mathrm{r} = \sum m_i x_i$ — which is why it is rarely a whole number.

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Data and references

H. Geiger & E. Marsden, “On a Diffuse Reflection of the α-Particles”, Proc. R. Soc. Lond. A 82, 495 (1909).
E. Rutherford, “The Scattering of α and β Particles by Matter and the Structure of the Atom”, Phil. Mag. 21, 669 (1911).
E. Tiesinga et al., CODATA Recommended Values of the Fundamental Physical Constants: 2018, Rev. Mod. Phys. 93, 025010 (2021).
M. Berglund & M. E. Wieser, “Isotopic compositions of the elements 2009 (IUPAC Technical Report)”, Pure Appl. Chem. 83, 397 (2011); J. Meija et al., “Isotopic compositions of the elements 2013”, Pure Appl. Chem. 88, 293 (2016).
M. Wang et al., “The AME 2020 atomic mass evaluation (II)”, Chinese Phys. C 45, 030003 (2021); F. G. Kondev et al., “The NUBASE2020 evaluation of nuclear physics properties”, Chinese Phys. C 45, 030001 (2021).
K. S. Krane, Introductory Nuclear Physics, Wiley (1988), ch. 3 (nuclear radius).