Nuclear Equations

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 7.7 — The effect of alpha, beta, gamma and neutron emission on atomic and mass number
• 7.8 — Balancing nuclear equations in terms of mass and charge

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

A decay changes the nucleus, so it changes the two numbers that describe it. Working out how is mostly bookkeeping, and the bookkeeping obeys one rule: the totals on each side of the equation must match. The mass numbers must balance, and the atomic numbers must balance, because charge and nucleons are both conserved.

ALPHA DECAY is the easy one. An alpha particle is two protons and two neutrons, so when a nucleus emits one it loses four nucleons in total and two of them are protons. The MASS NUMBER FALLS BY 4 and the ATOMIC NUMBER FALLS BY 2. Losing two protons means it is now a different element, two places back in the periodic table. Uranium-238 emitting an alpha particle becomes thorium-234.

BETA DECAY is the one that catches everybody, and it does so because the usual short description of it is misleading. A beta particle is an electron — but there are no electrons in a nucleus, so it cannot simply be leaving. What actually happens is that a NEUTRON TURNS INTO A PROTON, and the electron is created and ejected at that instant.

Follow the particles through a beta decay and the numbers fall out

1. Start with a nucleus that has too many neutrons for stability.
2. One NEUTRON changes into a PROTON, and an electron is created and thrown out.
3. Count the nucleons: there was one neutron, and now there is one proton. The TOTAL number of nucleons is unchanged, so the MASS NUMBER STAYS THE SAME.
4. Count the protons: there is now one more than there was. So the ATOMIC NUMBER GOES UP BY 1.
5. The element therefore moves one place FORWARD in the periodic table. Carbon-14 becomes nitrogen-14.
6. The charge still balances: the nucleus gained +1 and a −1 electron left, so the total change is zero.

Think of it like a member of a committee changing sides

A committee of fourteen has six who vote yes and eight who vote no. One of the eight changes their mind and votes yes instead, and to mark it they hand in a card saying 'one vote transferred'. Afterwards there are still fourteen people in the room — nobody left — but now seven vote yes. The membership is unchanged and the count of yes votes has gone up by one. That is beta decay. The mass number is the committee size and the atomic number is the yes votes, and the electron flying out is the card: it is evidence of the change rather than a member departing. This is why the mass number holds steady while the atomic number climbs, which looks contradictory only if you imagine someone walking out.

GAMMA EMISSION changes NEITHER number. A gamma ray carries no mass and no charge; it is energy leaving a nucleus that has too much of it, usually just after an alpha or beta decay has left the nucleus in an excited arrangement. The element is unchanged and the isotope is unchanged — the nucleus simply settles down. This is why gamma never appears on its own in these equations: it accompanies another decay rather than replacing one.

NEUTRON EMISSION, which happens in fission, is the fourth case. A neutron has a mass number of 1 and no charge, so the MASS NUMBER FALLS BY 1 and the ATOMIC NUMBER IS UNCHANGED. The element stays the same and the nucleus becomes a lighter isotope of it.

Balancing an equation, and then finding an unknown from the balance

(a) Radium-226 (atomic number 88) emits an alpha particle. What is the daughter nucleus? (b) A nucleus of mass number 214 and atomic number 82 decays to one of mass number 214 and atomic number 83. What was emitted?

1. (a) Alpha decay: mass number falls by 4, so 226 − 4 = 222.
2. Atomic number falls by 2, so 88 − 2 = 86. The daughter is radon-222.
3. Check the balance: 226 = 222 + 4 for mass, and 88 = 86 + 2 for charge. Both sides agree.
4. (b) The mass number has not changed at all, so whatever left has a mass number of 0.
5. The atomic number has risen by 1, so whatever left has a charge of −1.
6. Mass number 0 and charge −1 is a beta particle. The emission was beta decay.

Answer: (a) Radon-222. (b) A beta particle — the mass number held and the atomic number rose by one.

That second part is the skill worth practising, because exam questions frequently give both nuclei and ask what was emitted. Work backwards from the two differences: mass down 4 and charge down 2 is alpha; mass unchanged and charge up 1 is beta; mass down 1 and charge unchanged is a neutron; nothing changed at all is gamma. The differences identify the emission uniquely, so you never have to remember which decay a particular element undergoes.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

What each emission does to the two numbers

Learn this definition · Beta decay

A neutron in the nucleus changes into a proton, and an electron is created and emitted at that instant. The mass number is unchanged because a nucleon has been converted rather than lost, and the atomic number rises by one because there is now an extra proton.

The rule that balances every nuclear equation

• The MASS NUMBERS on each side must add to the same total
• The ATOMIC NUMBERS on each side must add to the same total
• An alpha particle counts as mass 4, charge +2
• A beta particle counts as mass 0, charge −1
• A gamma ray counts as mass 0, charge 0
• A neutron counts as mass 1, charge 0

Identifying an unknown emission from the two nuclei

1. Subtract the daughter's mass number from the parent's.
2. Subtract the daughter's atomic number from the parent's.
3. Mass down 4 and charge down 2: an ALPHA particle.
4. Mass unchanged and charge UP 1: a BETA particle.
5. Mass down 1 and charge unchanged: a NEUTRON.
6. Both unchanged: GAMMA emission.

uranium-238 → thorium-234 + alpha particle

Conditions: Alpha decay. Mass: 238 = 234 + 4. Charge: 92 = 90 + 2. The element moves two places back.

carbon-14 → nitrogen-14 + beta particle

Conditions: Beta decay. Mass: 14 = 14 + 0. Charge: 6 = 7 + (−1). The element moves one place forward.

Model answer [4 marks]

Explain why the atomic number of a nucleus increases during beta decay, even though a negatively charged particle is emitted. [4]

In beta decay a neutron inside the nucleus changes into a proton, and an electron is created and emitted at that moment. The nucleus therefore has one more proton than before, and since the atomic number is the number of protons, the atomic number rises by one. The total number of nucleons is unchanged, because a neutron has been converted into a proton rather than lost, so the mass number stays the same. Charge is still conserved overall: the nucleus has gained a charge of +1 and a particle of charge −1 has left it.

Model answer [3 marks]

A nucleus of mass number 218 and atomic number 84 decays to a nucleus of mass number 214 and atomic number 82. Identify the emission and justify your answer. [3]

The mass number has fallen by 4, from 218 to 214, and the atomic number has fallen by 2, from 84 to 82. An emitted particle must therefore have a mass number of 4 and a charge of +2. That is an alpha particle, which consists of two protons and two neutrons, so the decay is alpha decay.

Not this: In beta decay an electron that was orbiting the atom is thrown out of the nucleus.

This: The electron is CREATED at the moment a NEUTRON TURNS INTO A PROTON inside the nucleus. There are no electrons in a nucleus to eject, and this is why the atomic number rises rather than falls.

Mark-losing trap. Beta decay: mass number UNCHANGED, atomic number UP by one. A nucleon is converted, not lost.

Mark-losing trap. Gamma changes NEITHER number — it is energy leaving, so the isotope is unaltered.

Mark-losing trap. Balance BOTH lines every time: mass numbers must total the same, and so must atomic numbers.

Mark-losing trap. Given two nuclei, work backwards from the DIFFERENCES — they identify the emission uniquely.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · State [1 mark] — A nucleus emits an alpha particle. By how much does its mass number change?
2. Grade 7 · Calculate [2 marks] — Thorium-234 has an atomic number of 90. It undergoes beta decay. What is the atomic number of the nucleus produced?
3. Grade 8 · Deduce [2 marks] — A nucleus of mass number 210 and atomic number 82 decays to a nucleus of mass number 210 and atomic number 83. Which type of decay has occurred?
4. Grade 9 · Explain [6 marks] — Select every statement that belongs in a full-mark explanation of why beta decay leaves the mass number unchanged while raising the atomic number by one.
5. 9+ · Analyse [6 marks] — Uranium-238 (atomic number 92) decays through a chain of alpha and beta emissions and ends as lead-206 (atomic number 82). A student says the chain must contain exactly 8 alpha decays, since the mass number falls by 32 and each alpha removes 4. Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who proved that an element really does turn into another, and the one who worked out what holds a nucleus together and what makes it let go. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Ernest Rutherford — the one who proved that an element really does turn into another

Every equation on this page says an element becomes a different element, and that claim was genuinely shocking when Rutherford and Frederick Soddy made it at McGill in 1902. Elements were supposed to be the fixed, unchangeable foundations of chemistry, and turning one into another was the discredited goal of the alchemists. Soddy's reaction on realising what their data meant was to say 'Rutherford, this is transmutation', and Rutherford's reply was that for heaven's sake they should not call it that, or they would be thrown out as alchemists. He is the right person to ask what it takes to publish a result that sounds like a discredited idea.

• “Why was it so alarming to say one element becomes another?”
• “How did you know the new substance was a different element?”
• “What did Soddy contribute to the work?”
• “Why could chemists not do what a decay does?”
• “How did you persuade people this was not alchemy?”

Niels Bohr — the one who worked out what holds a nucleus together and what makes it let go

This page says which nuclei decay and how, but not why any nucleus should be unstable in the first place, and Bohr supplied the model that answers it. He treated the nucleus as a drop of liquid held together by short-range attraction and pushed apart by the repulsion of its protons — a balance that works for small nuclei and becomes precarious as the proton count rises, which is why heavy elements are the radioactive ones. He is the right second figure here because he is honest about how much of it was analogy, and because the same liquid-drop picture reappears in fission later in this topic.

• “Why does a nucleus hold together at all when the protons repel?”
• “Why are the heavy elements the unstable ones?”
• “What does it mean to picture a nucleus as a liquid drop?”
• “Why do some nuclei have too many neutrons?”
• “How much of your model did you believe literally?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against Ernest Rutherford in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course

• Previous lesson: Alpha, Beta and Gamma
• Next lesson: Detecting Radiation and Background
• Atomic Structure and Isotopes — A nucleus ten thousand times smaller than the atom around it, and why two atoms of the same element can weigh different amounts.
• Alpha, Beta and Gamma — Three emissions from unstable nuclei, arriving at random — and why the one that is easiest to stop is the one to be most careful with.
• Detecting Radiation and Background — How you measure something invisible, and why the counter clicks even with no source in the room.
• Half-Life — Half of what is left, every time — which is why a radioactive sample never quite runs out.
• Uses and Dangers of Radiation — Choosing a source by its half-life and its penetration — and the difference between being irradiated and being contaminated.
• All of Physics · Incandio Science