IB Physics HL Topic 5 — Atomic & Nuclear Paper 1 & 2 _Z^AX ~13 min read

Nuclear Notation

Rutherford’s experiment gave the atom a tiny central nucleus. Now we need a way to say exactly what’s in it. Every nucleus is just a bundle of protons and neutrons, and physicists write it down with a neat shorthand: the element symbol carrying two little numbers. Learn to read those two numbers and you can count the protons, neutrons, and electrons in any atom or ion on the page.

📘 What you need to know

Atoms are made of three subatomic particles: protons, neutrons, and electrons
Protons and neutrons sit in the nucleus; electrons orbit around it
A nucleus is written in _Z^AX notation, where X is the chemical symbol
Nucleon number (A) = total number of protons + neutrons (the mass number)
Proton number (Z) = number of protons (the atomic number)
Number of neutrons = A − Z
A neutral atom has equal numbers of protons and electrons
The periodic table is ordered by atomic number Z
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A)

The three subatomic particles

Everything is built from protons, neutrons, and electrons. Each has a charge and a mass, and you need to know their relative values. Charge can be given in coulombs (C) or in units of the elementary charge e; mass in kilograms (kg) or in atomic mass units (u).

Particle	Charge / C	Charge / e	Mass / kg	Mass / u
Proton	+1.60 × 10⁻¹⁹	+1	1.673 × 10⁻²⁷	1.007
Neutron	0	0	1.675 × 10⁻²⁷	1.009
Electron	−1.60 × 10⁻¹⁹	−1	9.109 × 10⁻³¹	0.000549

Two patterns worth memorising. First, the proton and neutron have almost the same mass (~1 u each), while the electron is roughly 1,840× lighter — so essentially all the atom’s mass sits in the nucleus. Second, the proton and electron carry equal and opposite charges, so a neutral atom must have equal numbers of each. Those two facts answer a surprising number of exam questions.

Reading the notation

A nucleus is described by stacking two numbers to the left of the chemical symbol.

The top number A is the nucleon (mass) number; the bottom number Z is the proton (atomic) number. Subtract to get the neutrons: N = A − Z.

Proton no.
Z

A − Z
gives

Neutrons
N

Z + N
gives

Nucleon no.
A

A tiny trap that catches everyone: in Chemistry the nucleon number is usually called the mass number and the proton number the atomic number. They mean exactly the same things — just don’t mix up which is which. The bigger number on top is always protons + neutrons; the smaller one below is protons alone.

Isotopes

Change the number of neutrons and you get an isotope — the same element (same proton number, same chemical behaviour) but a different mass. Carbon-12 and carbon-14 are both carbon, both have 6 protons, but carbon-14 has two extra neutrons.

Isotopes have the same Z (same element) but different A (different neutron count)
They sit in the same place on the periodic table (same chemical properties)
They differ in mass, and some isotopes are radioactive while others are stable

WE 1

A carbon nucleus is written as ₆¹⁴C. State the number of (a) protons, (b) neutrons, and (c) electrons in a neutral atom of this isotope.

(a) protons = Z 6 protons (b) neutrons = A − Z N = 14 − 6 8 neutrons (c) electrons (neutral atom) A neutral atom has equal protons and electrons. 6 electrons The bottom number (6) is protons; subtract it from the top (14) for neutrons. Because the atom is neutral, electrons match protons exactly. Carbon-14, by the way, is the radioactive isotope used in carbon dating.

WE 2

An aluminium ion is written ₁₃²⁷Al³⁺. Determine the number of (a) protons, (b) neutrons, and (c) electrons in this ion.

(a) protons = Z 13 protons (b) neutrons = A − Z N = 27 − 13 14 neutrons (c) electrons (a 3+ ion) A 3+ charge means 3 fewer electrons than protons. electrons = 13 − 3 10 electrons The +3 is the giveaway: a positive ion has lost electrons, so it has fewer electrons than protons. The proton and neutron counts don’t change — only the electrons. Watch the sign: a negative ion would have gained electrons.

WE 3

Chlorine has two common isotopes: ₁₇³⁵Cl and ₁₇³⁷Cl. (a) State what is meant by isotopes. (b) State how the two nuclei differ. (c) State one property they share.

(a) meaning of isotopes atoms of the same element with the same proton number but different neutron numbers (b) how they differ Cl-35 has 35 − 17 = 18 neutrons; Cl-37 has 37 − 17 = 20 neutrons. Cl-37 has 2 more neutrons (and so more mass) (c) a shared property Both have 17 protons, so the same chemical behaviour. identical chemical properties (same element) Isotopes are chemically identical because chemistry is governed by the number of electrons, which matches the proton number. The neutrons change only the mass (and sometimes the stability), never the chemistry.

🔬 Reading a nuclide

Bottom number = Z = protons.
Top number = A = protons + neutrons.
Neutrons = A − Z.
Neutral atom? Electrons = protons = Z.
Ion? Adjust electrons by the charge: +n means n fewer electrons, −n means n more.
Isotopes? Same Z, different A.

💡 Top tips

Bottom = protons (Z), top = nucleons (A). Neutrons = A − Z.
Nucleon number = mass number; proton number = atomic number (same things).
Neutral atom → electrons = protons. Always check for a charge first.
Positive ion → fewer electrons; negative ion → more electrons.
Isotopes: same element, same Z, different A (different neutrons).
Almost all the mass is in the nucleus — the electron is ~1,840× lighter.

⚠ Common mistakes

Swapping A and Z — the bigger number on top is nucleons
Reading the top number as neutrons — it’s protons plus neutrons
Forgetting to subtract: neutrons = A − Z, not just A
Ignoring the ion charge when counting electrons
Thinking isotopes have different chemical properties — they’re chemically identical
Saying isotopes differ in protons — they differ in neutrons

Quick recap: A nucleus is written _Z^AX, where Z is the proton (atomic) number and A is the nucleon (mass) number. The neutrons are A − Z, and a neutral atom has electrons = protons = Z. For an ion, adjust the electrons by the charge. Isotopes are atoms of the same element (same Z) with different neutron numbers (different A) — identical chemistry, different mass. Nearly all the atom’s mass lives in the nucleus.

We can now describe any nucleus and count its particles. But the atom’s real secrets come from its electrons — and the light they give off. When atoms are heated they emit very specific colours, and cool gases absorb exactly those same colours. Those patterns are a fingerprint of the atom’s inner structure. Next page: Emission & Absorption Spectra.