IB Physics HLTopic 7 — Atomic, Nuclear & Particle PhysicsPaper 1 & 2same Z, different N~15 min read
Isotopes & Radioactive Decay
Every atom of a given element carries the same number of protons — that’s what makes it that element. But the number of neutrons can vary, and those different versions are called isotopes. Most isotopes sit happily forever, but some have an awkward mix of protons and neutrons that makes them unstable, so they fire off radiation to settle down. That restlessness is radioactive decay, and it’s the starting point for the whole of nuclear physics.
📚 What you need to know
Isotopes are nuclei with the same number of protons but different numbers of neutrons
An isotope has a fixed proton numberZ and a different nucleon numberA
The nucleon number A = protons + neutrons, so neutrons = A − Z
Isotopic data is the relative amounts (abundances) of each isotope of an element in a sample
Relative atomic mass is a weighted average of the isotope masses using their abundances
Some isotopes are unstable — they have an imbalance of protons and neutrons, or too much energy
Radioactive decay is the spontaneous disintegration of a nucleus into a more stable one, emitting an alpha, beta or gamma particle
Decay is both spontaneous (unaffected by temperature, pressure, or chemistry) and random (you can’t predict when any one nucleus decays)
With large numbers of nuclei, the overall decay can still be predicted statistically
What is an isotope?
An element is defined by its proton numberZ — every hydrogen atom has 1 proton, every carbon atom has 6. Change the proton number and you change the element entirely. But you can change the number of neutrons without changing what the element is. Those different-neutron versions are the isotopes.
Hydrogen is the classic example. It comes in three flavours, all with 1 proton but with 0, 1, and 2 neutrons:
All three atoms are hydrogen because they each have one proton. They differ only in neutron count — that’s what makes them isotopes of one another.
Here’s the trick to never getting confused: the proton number is the element’s ID badge — change it and you’ve changed elements. Neutrons are more like extra luggage; you can add or remove some and you’re still the same element, just a heavier or lighter isotope. So whenever you see two nuclei, check the protons first: same protons means same element, and different neutrons means they’re isotopes.
Notation: reading the numbers
Every nuclide is written with two numbers stacked before its chemical symbol. The top one is the nucleon number (protons + neutrons), and the bottom one is the proton number.
Nuclide notationAZXA = nucleon number (protons + neutrons) • Z = proton number • neutrons = A − Z
So for tritium, 31H, the proton number is 1 and the nucleon number is 3, which means it has 3 − 1 = 2 neutrons. Every isotope of an element keeps the same bottom number and changes the top number.
WE 1
Which of the following pairs of nuclei are isotopes of one another? Nucleus P: nucleon number 37, 20 neutrons. Nucleus Q: nucleon number 35, 18 neutrons.
Step 1 — find the protons in each nucleus
protons = nucleon number − neutrons
Nucleus P: 37 − 20 = 17 protonsNucleus Q: 35 − 18 = 17 protonsStep 2 — compare
Both have 17 protons but different neutron counts.
Yes — P and Q are isotopesSame protons = same element (this is chlorine, Z = 17). Different neutrons = different isotope. Always work out the protons first — that’s the deciding factor.
Isotopic data & relative atomic mass
Isotopic data just means the relative amounts of each isotope of an element found in a real sample. Most elements are a mixture of isotopes, and the mass shown on the periodic table — the relative atomic mass — is a weighted average that takes each isotope’s mass and how common it is into account.
Think of it like averaging exam marks across a class, but where some students count more than others. A rare isotope only nudges the average a little; a really common one pulls it strongly towards its own mass. That’s why the relative atomic mass usually sits close to the most abundant isotope, not exactly halfway between them.
To calculate it, multiply each isotope’s mass by its abundance (as a decimal), then add the results together.
Relative atomic mass from isotopic dataRAM = Σ (isotope mass × fractional abundance)
WE 2
A sample of oxygen contains three isotopes: 16O (99.76%), 17O (0.04%) and 18O (0.20%). Calculate the relative atomic mass of this oxygen sample, to two decimal places.
Step 1 — turn percentages into decimals99.76% → 0.9976, 0.04% → 0.0004, 0.20% → 0.0020Step 2 — weighted averageRAM = (16 × 0.9976) + (17 × 0.0004) + (18 × 0.0020)RAM = 15.9616 + 0.0068 + 0.0360 = 16.0044RAM = 16.00 (2 d.p.)Notice the answer sits right next to 16 — because 16O makes up over 99% of the sample. The rare heavier isotopes barely shift it. That’s the weighted average at work.
Stable vs unstable nuclei
Most isotopes are perfectly stable — they’ll sit there forever. But some have an awkward balance of protons and neutrons, and that makes them unstable. An unstable nucleus can’t stay as it is, so it will eventually break down into a more stable arrangement, releasing radiation as it does. This is where isotopes connect to radioactivity.
Carbon-12 and carbon-14 are both carbon (6 protons each), but carbon-14’s extra neutrons make it unstable, so it decays. Instability comes from the proton-to-neutron balance, not from which element it is.
An unstable isotope may take anywhere from a few nanoseconds to over 100,000 years to decay, depending on how unstable it is. The urge to reach stability is what drives it to constantly emit radiation.
Radioactive decay
When an unstable nucleus finally breaks down, we call it radioactive decay. Formally:
Radioactive decayThe spontaneous disintegration of a nucleus to form a more stable nucleus, releasing an alpha, beta or gamma particle
Two words in that definition carry a lot of weight in exams: decay is both spontaneous and random. They mean different things, and examiners love to test whether you can tell them apart.
Unstable nucleus
decays spontaneously
More stable nucleus
+
Radiation (α, β or γ)
Spontaneous — nothing outside can change it
A spontaneous process is one that cannot be influenced by external factors. You can heat a radioactive source, cool it, squeeze it, or react it chemically — none of it changes the decay. That’s because decay happens deep in the nucleus, which is untouched by the temperature, pressure, and chemical bonding that only affect the outer electrons.
This is a favourite exam trap. If a question asks “how could you speed up the decay by heating the sample?” the answer is: you can’t. Temperature, pressure, and chemical conditions have zero effect. The nucleus simply doesn’t care what’s going on outside it.
Random — you can’t predict a single decay
A random process is one where you cannot predict when any particular nucleus will decay. Each unstable nucleus has a fixed probability of decaying in a given time, but which one goes next, and exactly when, is impossible to know.
You can see this randomness directly with a Geiger-Muller (GM) tube placed near a source: the counts come in irregularly and jump around unpredictably. Each click is one nucleus decaying, and the erratic, jumpy rhythm is the visible fingerprint of randomness.
The overall count rate falls with time, but the moment-to-moment jumps are unpredictable — the direct evidence that individual decays are random.
Random, yet predictable in bulk
Here’s the clever part. Although you can never say when one nucleus will decay, once you have a huge number of them, the statistics become reliable. Each nucleus has the same fixed chance of decaying per second, so across millions of nuclei the overall behaviour is smooth and predictable — even though any single one is a total mystery.
It’s exactly like rolling dice. You can’t predict a single roll, but roll ten thousand dice and you can confidently say about one-sixth will land on a six. Radioactive decay works the same way: unpredictable one at a time, but rock-solid predictable in large numbers. That’s what lets us define quantities like half-life later on.
⚛ Working an isotopes question
Which element? Look at the proton numberZ (the bottom number) — that alone fixes the element.
How many neutrons? neutrons = A − Z (nucleon number minus proton number).
Are two nuclei isotopes? Same protons, different neutrons → yes.
Relative atomic mass? Multiply each isotope mass by its fractional abundance, then add.
Stable or not? An awkward proton-to-neutron balance (or excess energy) means unstable → it will decay.
Spontaneous vs random? Spontaneous = external factors can’t change it. Random = can’t predict a single nucleus.
💡 Top tips
The proton number is the element’s identity — isotopes share it and only differ in neutrons.
Neutrons = A − Z (top number minus bottom number).
Relative atomic mass is a weighted average, so it sits nearest the most abundant isotope.
Decay is spontaneous: temperature, pressure and chemistry have no effect.
Decay is random: unpredictable for one nucleus, but predictable for very large numbers.
The jumpy count rate on a GM tube is the standard evidence for randomness.
⚠ Common mistakes
Thinking isotopes differ in protons — they differ in neutrons (protons stay the same)
Using A as the neutron count — neutrons are A − Z, not A
Averaging isotope masses without weighting by abundance
Claiming decay can be sped up by heating or a chemical reaction — it can’t
Confusing spontaneous (unaffected by surroundings) with random (unpredictable timing)
Saying we can predict exactly when a single nucleus decays — we can only do bulk statistics
Quick recap:Isotopes are nuclei with the same protons but different neutrons, so they share a proton number Z and differ in nucleon number A (neutrons = A − Z). Relative atomic mass is the abundance-weighted average of the isotope masses. Some isotopes are unstable and undergo radioactive decay — the spontaneous change into a more stable nucleus, emitting α, β or γ. Decay is spontaneous (external factors can’t change it) and random (unpredictable for one nucleus, but statistically predictable for many).
Now you know why some nuclei are radioactive and what “spontaneous and random” really mean. The obvious next question is: when an unstable nucleus decays, what exactly comes out? There are three kinds of radiation, each with its own personality — how far it travels, what stops it, and how it changes the nucleus. Next page: Alpha, Beta & Gamma Particles.
Isotopes and decay not sticking yet?
Book a free meeting and we’ll nail down proton vs neutron counting, relative atomic mass, and the spontaneous-vs-random distinction examiners love.
