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This lesson covers how to write and balance nuclear decay equations for alpha, beta and gamma decay — as required by the Edexcel GCSE Physics specification (1PH0), Topic 6: Radioactivity. You need to understand how the atomic number and mass number change during each type of decay, and be able to write balanced nuclear equations.
Before writing decay equations, you need to understand nuclear notation. An atom or particle is written as:
ᴬ_Z X
Where:
For example, uranium-238 is written as: ²³⁸₉₂U (mass number 238, atomic number 92).
In alpha decay, the nucleus emits an alpha particle — a helium-4 nucleus containing 2 protons and 2 neutrons.
| Number | Change |
|---|---|
| Mass number (A) | Decreases by 4 (2 protons + 2 neutrons are lost) |
| Atomic number (Z) | Decreases by 2 (2 protons are lost) |
Because the atomic number changes, the atom becomes a different element.
The alpha particle is a helium-4 nucleus: ⁴₂He
ᴬ_Z X → ᴬ⁻⁴_(Z−2) Y + ⁴₂He
Example 1: Uranium-238 undergoes alpha decay
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Example 2: Radium-226 undergoes alpha decay
²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He
Example 3: Polonium-210 undergoes alpha decay
²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He
Exam Tip: In alpha decay, always subtract 4 from the mass number and 2 from the atomic number. Then use the periodic table to identify the new element from its atomic number.
In beta decay, a neutron in the nucleus transforms into a proton and an electron. The electron is ejected at high speed as a beta particle.
| Number | Change |
|---|---|
| Mass number (A) | Stays the same (a neutron becomes a proton — total nucleons unchanged) |
| Atomic number (Z) | Increases by 1 (one extra proton is formed) |
Because the atomic number changes, the atom becomes a different element.
The beta particle (electron) is written as: ⁰₋₁e or ⁰₋₁β
ᴬ_Z X → ᴬ_(Z+1) Y + ⁰₋₁e
Example 1: Carbon-14 undergoes beta decay
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Example 2: Strontium-90 undergoes beta decay
⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e
Example 3: Iodine-131 undergoes beta decay
¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e
Exam Tip: In beta decay, the mass number does NOT change. The atomic number increases by 1. Remember: a neutron turns into a proton (atomic number goes up) and an electron (which is emitted). Always check your equation balances on both sides.
Gamma emission occurs when a nucleus in an excited state (high energy) releases excess energy as a gamma ray — a high-frequency electromagnetic wave.
| Number | Change |
|---|---|
| Mass number (A) | No change |
| Atomic number (Z) | No change |
Gamma emission does not change the atom into a different element. The nucleus simply loses energy. Gamma emission often accompanies alpha or beta decay — the daughter nucleus is left in an excited state and then emits gamma to release the excess energy.
The gamma ray is written as: ⁰₀γ
When writing nuclear equations, both sides must balance:
A nucleus of americium-241 decays to neptunium-237. What particle is emitted?
²⁴¹₉₅Am → ²³⁷₉₃Np + ?
Answer: ²⁴¹₉₅Am → ²³⁷₉₃Np + ⁴₂He ✓
Thorium-234 undergoes beta decay. What is the daughter nucleus?
²³⁴₉₀Th → ? + ⁰₋₁e
Answer: ²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e ✓
Some unstable nuclei undergo a series of decays before reaching a stable state. This is called a decay chain or decay series.
graph LR
A["²³⁸₉₂U<br/>Uranium-238"] -->|"α decay"| B["²³⁴₉₀Th<br/>Thorium-234"]
B -->|"β decay"| C["²³⁴₉₁Pa<br/>Protactinium-234"]
C -->|"β decay"| D["²³⁴₉₂U<br/>Uranium-234"]
D -->|"α decay"| E["²³⁰₉₀Th<br/>Thorium-230"]
E -->|"..."| F["²⁰⁶₈₂Pb<br/>Lead-206<br/>(stable)"]
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