Radioactive Decay and Nuclear Equations
Radioactivity describes the spontaneous breakdown of unstable atomic nuclei, which release energy and particles to become more stable. For the ESAT, this involves understanding the different types of decay and being able to balance nuclear equations to track changes in elements.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Radioactive decay is a random process originating from an unstable nucleus; it is impossible to predict when a specific nucleus will decay.
- Alpha (α) particles are helium nuclei (42 He), beta (β⁻) particles are high-speed electrons (0_-1 e), and gamma (γ) rays are high-energy electromagnetic radiation.
- In nuclear equations, both the total mass number (top number) and the total atomic number (bottom number) must be conserved on both sides of the equation.
- Alpha decay reduces the mass number by 4 and the atomic number by 2.
- Beta decay occurs when a neutron turns into a proton and an electron. The mass number is unchanged, but the atomic number increases by 1.
- Gamma decay releases excess energy from a nucleus without changing its mass number or atomic number.
Diagram
› Why does this happen?
Why are some nuclei unstable?
Inside the nucleus, there's a constant tug-of-war. Protons, being positively charged, repel each other due to the electrostatic force, trying to push the nucleus apart. At the same time, a much stronger force, the strong nuclear force, pulls all the protons and neutrons together. However, this strong force only acts over extremely short distances, essentially between neighbouring particles. In large nuclei, the electrostatic repulsion between protons can add up across the whole nucleus. This combined repulsion can become strong enough to overcome the short-range strong force holding the nucleus together, making it unstable. To become more stable, it may then decay by emitting a particle, like an alpha particle.
Why does a neutron turn into a proton during beta decay?
Stability isn't just about size; it's also about having the right balance of neutrons to protons. Neutrons add to the attractive strong force without adding any electrostatic repulsion, so they act like 'glue'. If a nucleus has too many neutrons for its number of protons (it is 'neutron-rich'), it is unstable. To fix this imbalance, a neutron can transform into a proton and an electron. The new proton stays in the nucleus (increasing the atomic number by 1), while the electron is ejected at very high speed as a beta particle. This process moves the nucleus closer to a stable neutron-to-proton ratio.
Why is gamma radiation emitted?
Think of it like an atom emitting light. An electron can move to a lower energy level, releasing the extra energy as light. The nucleus can do something similar. After an alpha or beta decay, the new nucleus can be left with too much energy, making it 'excited'. To become more stable, it needs to get rid of this excess energy. It does this by emitting a very high-energy burst of electromagnetic radiation, which we call a gamma ray. This process doesn't change the number of protons or neutrons, it just allows the nucleus to settle into a more stable state.
Formulae
^AZ X → ^(A-4)_(Z-2) Y + 42 He To represent the alpha decay of a parent nuclide X into a daughter nuclide Y.
^AZ X → ^A_(Z+1) Y + 0_-1 e To represent the beta decay of a parent nuclide X into a daughter nuclide Y.
Definitions
- Unstable Nucleus
- An atomic nucleus that has an excess of energy or an imbalanced ratio of neutrons to protons, causing it to undergo radioactive decay.
- Alpha Particle (α)
- A particle consisting of two protons and two neutrons, identical to a helium nucleus. It has a charge of +2.
- Beta Particle (β⁻)
- A fast-moving electron emitted from the nucleus during the conversion of a neutron into a proton. It has a charge of -1.
- Nuclide
- A specific type of atomic nucleus characterized by its unique number of protons (atomic number) and neutrons (which determines its mass number).
Worked example
An unstable isotope of Uranium, 23892 U, undergoes a decay chain consisting of one alpha decay followed by two consecutive beta decays. Determine the chemical symbol, mass number, and atomic number of the final resulting nuclide. You are given that Thorium (Th) has Z=90, Protactinium (Pa) has Z=91, and Neptunium (Np) has Z=93.
- 1
Step 1:
Write the equation for the first alpha decay.
The parent is 23892 U.
An alpha particle is 42 He.
- 2
A changes:
238 - 4 = 234Z changes:
92 - 2 = 90The intermediate nuclide is 23490 Th.
- 3
Equation 1:
23892 U → 23490 Th + 42 He.
- 4
Step 2:
Write the equation for the first beta decay.
The parent is now 23490 Th.
A beta particle is 0_-1 e.
- 5
A is unchanged:
234.
Z changes:
90 + 1 = 91The second intermediate is 23491 Pa.
- 6
Equation 2:
23490 Th → 23491 Pa + 0_-1 e.
- 7
Step 3:
Write the equation for the second beta decay.
The parent is 23491 Pa.
- 8
A is unchanged:
234.
Z changes:
91 + 1 = 92The final nuclide is 23492 U, an isotope of the original element.
- 9
Equation 3:
23491 Pa → 23492 U + 0_-1 e.
- 10
Step 4:
State the final properties.
The final nuclide is an isotope of Uranium.
Answer: The final nuclide is 23492 U. Mass number = 234, Atomic number = 92, Symbol = U.
Common mistakes
- ×Mixing up the effect of beta decay on the atomic number. Remember a neutron becomes a proton, so the atomic number must INCREASE by 1. A common mistake is to subtract 1.
- ×Forgetting to conserve both mass number (top) and atomic number (bottom) separately. Always check that the sums on the left and right of the arrow are equal for both.
- ×Making simple arithmetic errors in multi-step decay problems. Keep a running tally of A and Z as you go through the chain to avoid calculation mistakes.
No-calculator tips
- ✓Treat the top and bottom numbers in nuclear equations as separate, simple sums. For a decay chain, calculate the total change in A and Z first, rather than finding each intermediate nucleus. E.g., two alphas and one beta means A changes by 2*(-4) = -8 and Z changes by 2*(-2) + 1*(-1) = -3.
- ✓Always do a quick sanity check after writing an equation: (Top Left) = (Sum of Top Right)? (Bottom Left) = (Sum of Bottom Right)? This takes two seconds and catches most errors.
- ✓Remember the nature of the particles to deduce their effect. Alpha is 'heavy' so it changes mass number. Beta is 'light' but changes a neutron to a proton, so it only affects the atomic number.