IB Physics SLTopic 5 — The Atomic & Nuclear WorldPaper 1 & 2same Z, different A~7 min read
Isotopes & Decay
Every carbon atom in the universe has exactly 6 protons — that’s what makes it carbon. But it can carry a different number of neutrons, giving heavier or lighter versions of the same element. Some of those versions are perfectly happy; others are lopsided and unstable, and they fix themselves by firing out radiation at moments nobody can predict. This page is where atomic structure meets radioactivity.
📘 What you need to know
Isotopes are nuclei of the same element: same number of protons (same Z) but different numbers of neutrons (different A)
The proton number Z is fixed for an element; the nucleon number A changes between isotopes
Isotopic data (the relative abundance of each isotope) is used to work out an element’s relative atomic mass
An imbalance of protons and neutrons can make a nucleus unstable
Unstable nuclei undergo radioactive decay: they spontaneously disintegrate and emit an alpha, beta, or gamma particle to become more stable
Radioactive decay is both spontaneous (unaffected by temperature, pressure, or chemistry) and random (you can’t predict which nucleus decays when)
A Geiger–Müller tube shows this randomness as an irregular, fluctuating count rate
What Is an Isotope?
Picture the nucleus as a bag of protons and neutrons. The number of protons is the atom’s identity badge: 1 proton is always hydrogen, 6 is always carbon, 92 is always uranium. Change the protons and you’ve changed the element entirely. But the number of neutrons is more flexible — you can add or remove a few without changing which element it is. Those different-neutron versions are called isotopes.
The classic example is hydrogen. Ordinary hydrogen has 1 proton and no neutrons. Add one neutron and you get deuterium; add two and you get tritium. All three are hydrogen (still just 1 proton), but they get steadily heavier.
All three are hydrogen because each has one proton (fixed Z). They differ only in neutron count, so the nucleon number A climbs from 1 to 3.
We write a nucleus using the notation AZX, where A is the nucleon (mass) number on top and Z is the proton number below. For isotopes of the same element, the bottom number (Z) stays put while the top number (A) changes.
same element
→ same Z, different A →
isotopes
Isotopic Data & Relative Atomic Mass
Most elements turn up in nature as a mixture of isotopes, in fixed proportions. The percentage of each is called isotopic data (or relative abundance), and it’s measured with a mass spectrometer. The relative atomic mass you see on the periodic table isn’t the mass of any single atom — it’s the weighted average across all the naturally occurring isotopes, taking their abundances into account.
To find it, multiply each isotope’s mass by its fractional abundance and add the results together:
Relative atomic massAr = Σ (isotope mass × fractional abundance)
🧭 Finding the relative atomic mass
List each isotope with its mass number and its % abundance
Turn percentages into fractions — divide each by 100 (they should add to 1)
Multiply each isotope’s mass by its fraction
Add all the products together — that’s the relative atomic mass
Sanity-check: the answer must sit between the lightest and heaviest isotope, closer to the most abundant one
When a Nucleus Becomes Unstable
Not every isotope is content. If a nucleus has an imbalance of protons and neutrons — too many of one, or simply too many nucleons overall — it becomes unstable. An unstable nucleus can’t stay as it is, so it decays: it spontaneously reshuffles itself into a more stable arrangement, flinging out radiation in the process. This is radioactive decay, defined as the spontaneous disintegration of a nucleus to form a more stable one, emitting an alpha, beta, or gamma particle.
How long this takes varies enormously — some unstable nuclei decay within nanoseconds, others hang around for tens of thousands of years before they go.
unstable nucleus
→ emits radiation →
more stable nucleus
Spontaneous and Random
Radioactive decay has two defining features, and examiners love to test that you know both precisely.
Spontaneous means the decay can’t be influenced by outside conditions. Heating the sample, squeezing it, freezing it, or reacting it chemically makes no difference at all — the nucleus decays entirely on its own schedule. This is very different from ordinary chemical reactions, which speed up when you heat them.
Random means you can’t predict exactly when any particular nucleus will decay. Every unstable nucleus has the same fixed probability of decaying in the next second, but which one actually goes, and when, is down to chance. The upside: with a huge number of nuclei, the average behaviour of the whole group becomes very predictable, even though each individual is unpredictable.
A Geiger–Müller tube’s count rate jumps about unpredictably from moment to moment (teal) even though the overall trend (dashed grey) falls smoothly. The jaggedness is direct evidence that decay is random.
Quick recap: isotopes share the same proton number Z but differ in nucleon number A; isotopic abundances give the periodic table’s relative atomic mass; and unstable nuclei decay spontaneously (no outside influence) and randomly (unpredictable timing) to become more stable.
WE 1
A sample of an element contains just two isotopes: one of mass number 63 (abundance 69.0%) and one of mass number 65 (abundance 31.0%). Calculate the relative atomic mass of the sample to 2 decimal places.
Set up the weighted average
turn each % into a fraction: 0.690 and 0.310 (they add to 1)
Ar = (63 × 0.690) + (65 × 0.310)
Ar = 43.47 + 20.15 = 63.62Ar = 63.62The answer sits between 63 and 65, nearer 63 because that isotope is more abundant — a good sanity check.
WE 2
Two nuclei have the following details: nucleus 1 has nucleon number 40 and 22 neutrons; nucleus 2 has nucleon number 38 and 20 neutrons. State, with reasoning, whether they are isotopes of the same element.
Find the proton number of each (protons = nucleons − neutrons)
nucleus 1: Z = 40 − 22 = 18
nucleus 2: Z = 38 − 20 = 18
Compare
both have Z = 18, so both are the same element
their nucleon numbers differ (40 vs 38), so their neutron counts differ
Yes — they are isotopes of the same elementThe test is always the proton number: same Z means same element; different A means different isotope.
💡 Top tips
Protons define the element, neutrons define the isotope. To spot isotopes, always work out and compare the proton number (Z = A − neutrons)
Relative atomic mass is a weighted average, so it lands between the isotope masses — not a whole number, and nearer the most abundant isotope
Learn both decay words exactly:spontaneous = not affected by temperature, pressure, or chemistry; random = the exact time of decay can’t be predicted
Randomness is the evidence. If asked how a GM tube shows decay is random, say the count rate fluctuates irregularly from one interval to the next
⚠ Common mistakes
Saying isotopes have different numbers of protons — they have different neutrons; the proton number is what stays the same
Confusing random with spontaneous: random is about unpredictable timing; spontaneous is about being unaffected by outside conditions
Thinking you can speed up decay by heating or compressing the sample — you can’t; decay ignores all environmental factors
Rounding the relative atomic mass to a whole number, or getting a value outside the range of the isotope masses
Up next: Alpha, Beta & Gamma Decay. Now that you know why nuclei become unstable, we’ll look at the three things they actually throw out — what each particle is, how it changes the nucleus, and how far each one can travel.
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