Nuclear Equations [H]

This lesson covers nuclear equations as required by the AQA GCSE Physics specification (4.4.2). This is Higher Tier only content, indicated by [H]. You need to be able to write and balance nuclear equations for alpha decay, beta decay, and gamma emission, and to use these equations to identify unknown products.

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What Are Nuclear Equations?

A nuclear equation represents a radioactive decay process. It shows the parent nucleus (the original unstable nucleus), the daughter nucleus (the new nucleus formed after decay), and the radiation emitted.

In nuclear equations, each nuclide is written with its:

• Mass number (A) as a superscript (top number)
• Atomic number (Z) as a subscript (bottom number)

The key rule for balancing nuclear equations is:

The total mass number (A) on the left must equal the total mass number on the right. The total atomic number (Z) on the left must equal the total atomic number on the right.

Exam Tip: Nuclear equations are balanced when the sum of the mass numbers is the same on both sides AND the sum of the atomic numbers is the same on both sides. Always check both numbers. If either does not balance, your equation is wrong.

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Alpha Decay Equations

In alpha decay, the nucleus emits an alpha particle, which has:

• Mass number A = 4
• Atomic number Z = 2

This means:

• The daughter nucleus has a mass number that is 4 less than the parent.
• The daughter nucleus has an atomic number that is 2 less than the parent.

General Form

Parent (A, Z) --> Daughter (A-4, Z-2) + Alpha particle (4, 2)

Examples

Uranium-238 decays by alpha emission:

U (238, 92) --> Th (234, 90) + He (4, 2)

Check: Mass numbers: 238 = 234 + 4. Correct. Check: Atomic numbers: 92 = 90 + 2. Correct.

Radium-226 decays by alpha emission:

Ra (226, 88) --> Rn (222, 86) + He (4, 2)

Check: Mass numbers: 226 = 222 + 4. Correct. Check: Atomic numbers: 88 = 86 + 2. Correct.

Polonium-210 decays by alpha emission:

Po (210, 84) --> Pb (206, 82) + He (4, 2)

Check: Mass numbers: 210 = 206 + 4. Correct. Check: Atomic numbers: 84 = 82 + 2. Correct.

graph LR
    A["Parent Nucleus<br>Mass: A<br>Atomic: Z"] --> B["Daughter Nucleus<br>Mass: A-4<br>Atomic: Z-2"]
    A --> C["Alpha Particle<br>Mass: 4<br>Atomic: 2"]

    style A fill:#e74c3c,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#e67e22,color:#fff

Exam Tip: To find the daughter element in alpha decay, subtract 2 from the atomic number and look up the new element on the periodic table. For example, uranium (Z=92) minus 2 gives Z=90, which is thorium.

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Beta Decay Equations

In beta decay, a neutron in the nucleus converts into a proton and an electron. The electron is emitted as a beta particle. The beta particle has:

• Mass number A = 0 (negligible mass)
• Atomic number Z = -1 (negative charge equivalent to -1 proton)

This means:

• The daughter nucleus has the same mass number as the parent (A stays the same).
• The daughter nucleus has an atomic number that is 1 more than the parent (Z increases by 1).

General Form

Parent (A, Z) --> Daughter (A, Z+1) + Beta particle (0, -1)

Examples

Carbon-14 decays by beta emission:

C (14, 6) --> N (14, 7) + e (0, -1)

Check: Mass numbers: 14 = 14 + 0. Correct. Check: Atomic numbers: 6 = 7 + (-1) = 6. Correct.

Strontium-90 decays by beta emission:

Sr (90, 38) --> Y (90, 39) + e (0, -1)

Check: Mass numbers: 90 = 90 + 0. Correct. Check: Atomic numbers: 38 = 39 + (-1) = 38. Correct.

Iodine-131 decays by beta emission:

I (131, 53) --> Xe (131, 54) + e (0, -1)

Check: Mass numbers: 131 = 131 + 0. Correct. Check: Atomic numbers: 53 = 54 + (-1) = 53. Correct.

graph LR
    A["Parent Nucleus<br>Mass: A<br>Atomic: Z"] --> B["Daughter Nucleus<br>Mass: A<br>Atomic: Z+1"]
    A --> C["Beta Particle<br>Mass: 0<br>Atomic: -1"]

    style A fill:#e74c3c,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#f39c12,color:#fff

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Gamma Emission

In gamma emission, the nucleus emits a gamma ray (a high-energy photon). The gamma ray has:

• Mass number A = 0
• Atomic number Z = 0

This means:

• The mass number and atomic number of the nucleus do not change.
• The element does not change.
• Gamma emission simply releases excess energy from the nucleus.

Gamma emission usually accompanies alpha or beta decay — after emitting an alpha or beta particle, the daughter nucleus may be in an excited state and releases the extra energy as a gamma ray.

Example

After alpha decay, the daughter nucleus may emit gamma radiation:

Nucleus (A, Z) in excited state --> Nucleus (A, Z) in ground state + gamma (0, 0)

Exam Tip: In the exam, gamma emission is sometimes shown alongside alpha or beta decay in the same equation. The gamma ray does not change the mass number or atomic number, so it does not affect the balancing of the equation.

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Worked Examples: Finding Unknown Nuclides

A common exam question gives you an incomplete nuclear equation and asks you to find the missing nuclide.

Example 1: Alpha Decay

Th (232, 90) --> ? (?, ?) + He (4, 2)

Mass number of daughter = 232 - 4 = 228 Atomic number of daughter = 90 - 2 = 88

Element with Z = 88 is Radium (Ra). Answer: Ra (228, 88)

Example 2: Beta Decay

? (40, ?) --> Ca (40, 20) + e (0, -1)

Atomic number of parent = 20 + (-1) = 20... Wait, let us redo this. The total atomic number on the right = 20 + (-1) = 19. So the parent has Z = 19. Element with Z = 19 is Potassium (K). Answer: K (40, 19)

Example 3: Identifying the Type of Decay

Bi (214, 83) --> Po (214, 84) + ? (?, ?)

Mass number of particle = 214 - 214 = 0 Atomic number of particle = 83 - 84 = -1

A particle with A = 0 and Z = -1 is a beta particle. Answer: Beta decay; the emitted particle is e (0, -1).

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Balancing Practice Table