Radioactive Decay
Section: Nuclear Physics | Syllabus: Cambridge IGCSE Physics (0625)
What is Radioactive Decay?
Radioactive decay is a change in an unstable nucleus that can result in the emission of α-particles, β-particles and/or γ-radiation. These changes are spontaneous (they happen by themselves, without any external trigger) and random (it is impossible to predict when any particular nucleus will decay).
- During α-decay or β-decay, the nucleus changes to that of a different element, because the number of protons changes
Why Isotopes Are Radioactive
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Isotopes of an element may be radioactive due to:
- An excess of neutrons in the nucleus - too many neutrons compared to protons makes the nucleus unstable, e.g. carbon-14 has 6 protons but 8 neutrons
- The nucleus being too heavy - very large nuclei (high nucleon number) are generally unstable, e.g. all isotopes of uranium are radioactive
- Carbon-12 (126C, 6 protons, 6 neutrons) is stable, but carbon-14 (146C, 6 protons, 8 neutrons) is radioactive due to its excess neutrons - it decays to become more stable
Alpha Decay
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In alpha decay, an unstable nucleus emits an alpha particle, becoming more stable.
- The nucleon number, A, decreases by 4 (2 protons + 2 neutrons are lost)
- The proton number, Z, decreases by 2
- The element changes to one that is 2 places lower in the periodic table
- The number of excess neutrons in the nucleus is reduced, increasing its stability
AZX → A−4Z−2Y + 42He
Worked Example: Alpha Decay of Radium-226
Muchindu is asked to write the equation for the alpha decay of radium-226.
22688Ra → 22286Rn + 42He
- Mass numbers balance: 226 = 222 + 4
- Proton numbers balance: 88 = 86 + 2
- Radium (Z = 88) changes to radon (Z = 86)
Beta Decay
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In beta decay, a neutron in the nucleus changes into a proton, and an electron (the beta particle) is emitted from the nucleus:
neutron → proton + electron
- The nucleon number, A, stays the same
- The proton number, Z, increases by 1
- The element changes to the next element in the periodic table
- The number of excess neutrons in the nucleus is reduced, increasing its stability
AZX → AZ+1Y + 0−1e
Worked Example: Beta Decay of Carbon-14
Muumbe is asked to write the equation for the beta decay of carbon-14.
146C → 147N + 0−1e
- Mass numbers balance: 14 = 14 + 0
- Proton numbers balance: 6 = 7 + (−1)
- Carbon (Z = 6) changes to nitrogen (Z = 7), as one neutron has converted to a proton
Gamma Emission
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Gamma radiation is often emitted after alpha or beta decay, when the nucleus still has excess energy.
- The nucleus releases its excess energy as a gamma ray photon
- No change in nucleon number (A) or proton number (Z) - the element stays the same
- The nucleus becomes more stable (drops to a lower energy state)
Worked Example: Combined Decay (Alpha then Gamma)
Museli writes the two-step decay of radium-226, which first undergoes alpha decay to an excited radon nucleus, which then emits a gamma ray:
22688Ra → 22286Rn* + 42He
22286Rn* → 22286Rn + γ
The asterisk (*) shows that the radon nucleus is in an excited (high-energy) state immediately after the alpha decay, before it releases a gamma ray.
Comparison: Alpha, Beta and Gamma Decay
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| Property | Alpha Decay | Beta Decay | Gamma Emission |
|---|---|---|---|
| Particle/radiation emitted | 42He | 0−1e | γ (photon) |
| Change in A | Decreases by 4 | No change | No change |
| Change in Z | Decreases by 2 | Increases by 1 | No change |
| Element changes? | Yes (2 places back) | Yes (1 place forward) | No |
| Effect on excess neutrons | Reduces | Reduces | No change |
| Effect on stability | Increases | Increases | Increases |
Writing and Balancing Decay Equations
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In a nuclear equation, the total mass number (A) and the total proton number (Z) must be the same on both sides.
Worked Example: Completing an Alpha Decay Equation
Muchindu is given the start of the equation for the alpha decay of uranium-238 and asked to complete it:
23892U → ? + 42He
- Mass number of the daughter nucleus: 238 = A + 4, so A = 234
- Proton number of the daughter nucleus: 92 = Z + 2, so Z = 90 (thorium, Th)
- Answer: 23892U → 23490Th + 42He
Worked Example: Identifying the Type of Decay
Muumbe is given the equation 24195Am → 23793Np + ? and asked to identify the missing particle.
- Mass number decreased by 4 (241 → 237) and proton number decreased by 2 (95 → 93), so this is alpha decay
- Answer: 24195Am → 23793Np + 42He
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