Radioactive Decay — Alpha and Beta Reactions
An unstable nucleus cannot fix itself by chemistry. To reach stability it must change what it is made of — and when it does, one element turns into another.
Q1 · In Lesson 1 you learned that mass is conserved in chemical reactions. In a nuclear reaction, what quantities do you think must still "balance" on both sides of the equation?
Q2 · If an unstable nucleus has too many protons, what could it throw out to reduce that number and become more stable?
● Know
- That radioactive decay is the spontaneous breakdown of an unstable nucleus, emitting radiation
- What alpha ($\alpha$) and beta ($\beta^-$) particles are
- That nuclear equations conserve mass number and atomic number
● Understand
- How emitting an alpha particle changes the atomic number by 2 and mass number by 4
- How beta-minus decay turns a neutron into a proton, raising the atomic number by 1
- Why decay changes one element into a different element (transmutation)
● Can do
- Write and balance alpha-decay nuclear equations
- Write and balance beta-decay nuclear equations
- Identify the daughter nuclide produced in a given decay
When a nucleus is unstable because it is too large, one way it can become more stable is to eject an alpha particle. An alpha particle is a clump of 2 protons and 2 neutrons — exactly a helium nucleus, written $^{4}_{2}\text{He}$ (or $^{4}_{2}\alpha$).
Losing an alpha particle means the nucleus loses 2 protons and 2 neutrons, so:
- the mass number $A$ drops by 4
- the atomic number $Z$ drops by 2 — so the atom becomes a different element (this is transmutation).
A nuclear equation must balance like a see-saw: the mass numbers (top) must add up the same on both sides, and so must the atomic numbers (bottom). For example, uranium-238 undergoes alpha decay:
$^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}$
Check: mass numbers $234 + 4 = 238$ ✓ and atomic numbers $90 + 2 = 92$ ✓. The parent (uranium) has become a daughter nuclide (thorium) plus an alpha particle.
Radium-226 undergoes alpha decay. To find the daughter, subtract 4 from the mass number and 2 from the atomic number. Radium is $^{226}_{88}\text{Ra}$, so the daughter has mass $226 - 4 = 222$ and atomic number $88 - 2 = 86$, which is radon: $^{226}_{88}\text{Ra} \rightarrow {}^{222}_{86}\text{Rn} + {}^{4}_{2}\text{He}$. Check: $222 + 4 = 226$ ✓, $86 + 2 = 88$ ✓.
Radon in Australian homes and mines: The radon gas produced by radium's alpha decay is itself radioactive. Because Australia has uranium-rich rocks, radon monitoring matters in some mines and buildings. Smoke detectors in many older Australian homes also relied on the alpha emitter americium-241 to detect smoke particles — a direct everyday use of alpha decay.
Do not forget to balance both numbers. A common mistake is to subtract 4 from the mass number but forget to subtract 2 from the atomic number (or vice versa). Always check: the tops add up equal, and the bottoms add up equal.
If a nucleus is unstable because it has too many neutrons, it can undergo beta-minus ($\beta^-$) decay. Inside the nucleus, a neutron turns into a proton, and in the process a high-speed electron — the beta particle — is created and fired out. We write the beta particle as $^{0}_{-1}\text{e}$ (mass number 0, "charge" −1).
The effect on the nucleus:
- the mass number $A$ stays the same (a neutron became a proton, so the total nucleon count is unchanged)
- the atomic number $Z$ increases by 1 (one more proton) — again the atom becomes a different element.
For example, carbon-14 (which you met in Lesson 21) undergoes beta decay to become nitrogen-14:
$^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e}$
Check: mass numbers $14 + 0 = 14$ ✓ and atomic numbers $7 + (-1) = 6$ ✓. The beta particle's "−1" is essential to balancing the bottom row.
Strontium-90, a beta emitter, decays to yttrium. The mass number stays 90; the atomic number rises from 38 to 39: $^{90}_{38}\text{Sr} \rightarrow {}^{90}_{39}\text{Y} + {}^{0}_{-1}\text{e}$. Check: $90 + 0 = 90$ ✓, $39 + (-1) = 38$ ✓.
Carbon dating Australia's past: The beta decay of carbon-14 is the basis of radiocarbon dating. Australian researchers have used it to date charcoal from ancient Aboriginal occupation sites, helping to show that First Nations Peoples have lived on this continent for at least 65,000 years — among the oldest continuous cultures on Earth. You will see how the timing works when you study half-life in Lesson 24.
The beta particle is not an electron from the atom's shells. It is created in the nucleus at the moment a neutron changes into a proton. Its mass number is written as 0 because it is far lighter than a nucleon, and its charge is written as −1 so the equation balances.
Quick-fire true or false on alpha and beta decay.
An alpha particle is a helium nucleus (2 protons, 2 neutrons).
Alpha decay decreases the atomic number by 2.
In beta decay, the mass number changes.
In beta-minus decay, a neutron becomes a proton.
Nuclear equations must balance mass number and atomic number.
A chemical reaction can turn one element into another.
Beta decay increases the atomic number by 1.
Decay that changes the element is called transmutation.
Writing nuclear equations is just careful bookkeeping. Use these two golden rules every time:
- Top row (mass numbers) must be equal on the left and right.
- Bottom row (atomic numbers) must be equal on the left and right.
Remember the particles:
- Alpha: $^{4}_{2}\text{He}$ → subtract 4 from $A$, subtract 2 from $Z$.
- Beta-minus: $^{0}_{-1}\text{e}$ → $A$ unchanged, add 1 to $Z$.
- Gamma ($\gamma$): pure energy, $^{0}_{0}\gamma$ → changes neither $A$ nor $Z$ (it just carries away excess energy).
Finding a missing piece: if you are given the parent and one product, work out the other by making both rows balance. Sometimes you identify the decay type by seeing how the numbers changed: $A$ down by 4 and $Z$ down by 2 means alpha; $A$ unchanged and $Z$ up by 1 means beta-minus.
What type of decay turns $^{234}_{90}\text{Th}$ into $^{234}_{91}\text{Pa}$? The mass number is unchanged (234 → 234) and the atomic number rose by 1 (90 → 91). That is the signature of beta-minus decay: $^{234}_{90}\text{Th} \rightarrow {}^{234}_{91}\text{Pa} + {}^{0}_{-1}\text{e}$.
Decay chains in the ground: Uranium-238 does not turn into stable lead in one jump — it takes a long chain of alpha and beta decays through thorium, radium, radon and more, balancing at every step. Geologists, including those mapping Australia's uranium provinces, use these chains and their timings (half-lives) to date rocks billions of years old.
Gamma radiation is not a separate "type of decay" that changes the element. Gamma rays carry away leftover energy and have $A = 0$, $Z = 0$, so they never change the mass number or atomic number. Only alpha and beta emission change which element you have.
Connect the key ideas about radioactive decay. Click two connected ideas to explain the link.
Wrong: "Alpha decay reduces the mass number by 2." No — an alpha particle has a mass number of 4, so it reduces the mass number by 4 and the atomic number by 2.
Right: In alpha decay the mass number drops by 4 (2 protons + 2 neutrons leave) and the atomic number drops by 2.
Wrong: "In beta decay the nucleus loses a proton." No — beta-minus decay gains a proton, because a neutron is converted into a proton (and an electron is emitted).
Right: In beta-minus decay a neutron becomes a proton, so the atomic number increases by 1 while the mass number stays the same.
Wrong: "A chemical reaction could change uranium into lead if you found the right catalyst." No — chemical reactions only rearrange electrons and atoms; they never change the number of protons in a nucleus, so they cannot transmute elements. Only nuclear reactions can.
Right: Only nuclear reactions, which change the nucleus itself, can transmute one element into another. Chemistry rearranges atoms; it cannot change what an atom is.
Producing Radioisotopes at Lucas Heights
At ANSTO's Lucas Heights facility, scientists deliberately create radioisotopes that decay by beta and gamma emission for use in medicine. Technetium-99m, used in millions of diagnostic scans worldwide, is produced from the decay of molybdenum-99 made in Australian reactors. Writing and balancing the nuclear equations for these decays — exactly the skill in this lesson — is essential to predicting which daughter products form and what radiation they release.
Understanding decay equations also underpins safe handling of radioactive materials in Australian hospitals, mines and research labs, and is the basis for the radioactive dating that has revealed both the deep age of Australian rocks and the long history of Aboriginal occupation.
✍ Copy Into Your Books
▾Alpha decay (α)
- Emits a helium nucleus: He-4 (2p, 2n)
- Mass number A decreases by 4
- Atomic number Z decreases by 2
- e.g. U-238 → Th-234 + He-4
Beta-minus decay (β⁻)
- A neutron turns into a proton; an electron is emitted
- Mass number A stays the same
- Atomic number Z increases by 1
- e.g. C-14 → N-14 + e⁻ (0, −1)
Golden rules
- Top numbers (mass) balance both sides
- Bottom numbers (atomic) balance both sides
- Decay changes the element = transmutation
- Gamma (γ) changes neither A nor Z
Complete the Nuclear Equation
Identify the Decay Type
At the start, the hook asked how an atom can change into a completely different element, and why ordinary chemistry can't do it.
Now write a clear answer using the words nucleus, proton number and transmutation. Then give one balanced example of alpha or beta decay from this lesson.
Q1. Thorium-232 ($^{232}_{90}\text{Th}$) undergoes alpha decay. Write the balanced nuclear equation, identifying the daughter nuclide, and show how you checked that it balances. (3 marks)
Q2. Compare alpha decay and beta-minus decay. In your answer, describe the particle emitted in each and state how each affects the mass number and atomic number of the nucleus. (4 marks)
Q3. A student writes the decay $^{14}_{6}\text{C} \rightarrow {}^{13}_{7}\text{N} + {}^{0}_{-1}\text{e}$. Identify the error in this equation, correct it, and explain the rule the student broke. (3 marks)
Revisit Your Thinking
Go back to your Think First answers. Has your understanding changed?
- Can you now state the two quantities that must balance in a nuclear equation?
- Can you explain how a nucleus changes its proton number to become more stable?
Model answers (click to reveal)
Answers
▾MCQ 1
B — An alpha particle is a helium nucleus, $^{4}_{2}\text{He}$, made of 2 protons and 2 neutrons.
MCQ 2
C — Emitting an alpha particle removes 2 protons and 2 neutrons, so the atomic number drops by 2 and the mass number drops by 4.
MCQ 3
A — In beta-minus decay a neutron is converted into a proton, and a fast electron (the beta particle) is created and emitted.
MCQ 4
D — Alpha decay: mass 222 − 4 = 218, atomic number 86 − 2 = 84 (polonium). So $^{222}_{86}\text{Rn} \rightarrow {}^{218}_{84}\text{Po} + {}^{4}_{2}\text{He}$, which balances on both rows.
MCQ 5
C — Transmutation requires changing the number of protons in the nucleus. Chemical reactions only rearrange electrons and atoms and never alter the nucleus, so they cannot change one element into another.
Short Answer 1
Model answer: Alpha decay removes 4 from the mass number and 2 from the atomic number: $232 - 4 = 228$ and $90 - 2 = 88$, which is radium. Equation: $^{232}_{90}\text{Th} \rightarrow {}^{228}_{88}\text{Ra} + {}^{4}_{2}\text{He}$. Check: mass numbers $228 + 4 = 232$ ✓; atomic numbers $88 + 2 = 90$ ✓. The equation balances.
Short Answer 2
Model answer: Alpha decay emits an alpha particle (a helium nucleus, $^{4}_{2}\text{He}$); this decreases the mass number by 4 and the atomic number by 2. Beta-minus decay emits a beta particle (a fast electron, $^{0}_{-1}\text{e}$) when a neutron turns into a proton; this leaves the mass number unchanged but increases the atomic number by 1. Both produce a daughter nuclide of a different element and both must balance for mass number and atomic number.
Short Answer 3
Model answer: The error is the daughter's mass number: it is written as 13 but should be 14, because beta decay does not change the mass number. The corrected equation is $^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e}$. The student broke the rule that the mass numbers (top row) must balance on both sides: with mass 13 the tops would be $13 + 0 = 13 \neq 14$.