Nuclear Equations

Writing and balancing alpha, beta-minus and gamma equations; conservation of mass and charge

AQA GCSE Physics 4.4 · Year 10 · Age 14–15

🔢 Understand the meaning of mass number (A) and atomic number (Z) in nuclear notation

⚛️ Describe what happens to the nucleus during alpha, beta-minus and gamma decay

⚖️ Apply the laws of conservation of mass number and atomic number to nuclear equations

✏️ Write balanced nuclear equations for alpha decay using correct notation

✏️ Write balanced nuclear equations for beta-minus decay using correct notation

🔍 Identify unknown daughter nuclei by balancing mass number and atomic number

Nuclear Notation

Every nucleus is described using two numbers written alongside the chemical symbol. This notation lets us track changes during radioactive decay.

ᴬ_Z X where A = mass number, Z = atomic number

Mass number (A) — the total number of protons + neutrons in the nucleus (also called the nucleon number).

Atomic number (Z) — the number of protons in the nucleus. This defines which element the atom is.

For example, carbon-14 is written as ¹⁴₆C. It has 6 protons and 14 − 6 = 8 neutrons.

Quantity	Symbol	What it counts
Mass number	A	Protons + neutrons (nucleons)
Atomic number	Z	Protons only
Neutron number	N	A − Z

The atomic number Z determines the element. If Z changes, a new element is formed.

Conservation Laws in Nuclear Equations

Two fundamental conservation laws apply to every nuclear equation. These laws are never broken and allow us to find unknown products.

Conservation of mass number — the total mass number (A) on the left side of the equation must equal the total mass number on the right side.

Conservation of atomic number (charge) — the total atomic number (Z) on the left must equal the total atomic number on the right. This is equivalent to conservation of charge, since each proton carries one unit of positive charge.

Sum of A (left) = Sum of A (right)
Sum of Z (left) = Sum of Z (right)

Think of it like a balancing scales — whatever nucleons you start with, you must end with exactly the same total on the other side. No nucleons are created or destroyed.

These laws apply to all three types of decay: alpha, beta-minus and gamma. Gamma emission does NOT change A or Z.

Alpha Decay (α)

In alpha decay, the unstable nucleus emits an alpha particle. An alpha particle is identical to a helium-4 nucleus — it contains 2 protons and 2 neutrons.

Alpha particle: ⁴₂He (mass number = 4, atomic number = 2)

Because the parent nucleus loses 2 protons and 2 neutrons, the mass number decreases by 4 and the atomic number decreases by 2. A completely new element is formed.

ᴬ_Z X → ᴬ⁻⁴_(Z-2) Y + ⁴₂He

Example — Radium-226 decay:

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

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

Alpha particles are the most ionising but least penetrating of the three types. They are stopped by a few centimetres of air or a sheet of paper.

Alpha decay always produces a daughter nucleus 2 places to the left in the periodic table and 4 units lower in mass number.

Beta-Minus Decay (β⁻)

In beta-minus decay, a neutron in the nucleus converts into a proton, and the nucleus emits a fast-moving electron called a beta particle, along with an antineutrino (not required at GCSE but mentioned in higher content).

Beta particle: ⁰₋₁e (mass number = 0, atomic number = −1)

Because a neutron becomes a proton, the mass number stays the same (a neutron is replaced by a proton, same nucleon count) but the atomic number increases by 1.

ᴬ_Z X → ᴬ_(Z+1) Y + ⁰₋₁e

Example — Carbon-14 decay:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Check: Mass numbers: 14 = 14 + 0 ✓ Atomic numbers: 6 = 7 + (−1) ✓

Beta particles are moderately ionising and can be stopped by a few millimetres of aluminium. They travel further than alpha particles.

Beta-minus decay produces a daughter nucleus one place to the right in the periodic table with the same mass number.

Gamma Emission (γ)

Gamma radiation is a high-frequency electromagnetic wave emitted from an excited nucleus. It often accompanies alpha or beta decay when the daughter nucleus is left in an excited (high-energy) state.

Gamma photon: ⁰₀γ (mass number = 0, atomic number = 0)

Because a gamma photon carries no mass and no charge, neither the mass number nor the atomic number changes during gamma emission. The nucleus simply releases excess energy as electromagnetic radiation.

ᴬ_Z X* → ᴬ_Z X + ⁰₀γ

The asterisk (*) indicates an excited nucleus. After emitting the gamma photon, the nucleus is in its ground (lowest energy) state but is otherwise unchanged.

Gamma rays are the least ionising but most penetrating — they require several centimetres of lead or metres of concrete to significantly reduce their intensity.

Decay type	Change in A	Change in Z	Particle emitted
Alpha (α)	−4	−2	⁴₂He
Beta-minus (β⁻)	0	+1	⁰₋₁e
Gamma (γ)	0	0	⁰₀γ

Gamma emission does NOT transmute the element — only alpha and beta decay produce a different element.

✏️ Example 1: Uranium-238 (²³⁸₉₂U) undergoes alpha decay. Write the balanced nuclear equation and identify the daughter nucleus.

1 Identify the decay type and the particle emitted. Alpha decay emits ⁴₂He.

2 Use conservation of mass number (A): 238 = A_daughter + 4, so A_daughter = 238 − 4 = 234.

3 Use conservation of atomic number (Z): 92 = Z_daughter + 2, so Z_daughter = 92 − 2 = 90.

4 Look up element with Z = 90: that is Thorium (Th).

5 Write the full balanced equation: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

6 Check: A: 238 = 234 + 4 ✓ Z: 92 = 90 + 2 ✓

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He (daughter nucleus is Thorium-234)

✏️ Example 2: Iodine-131 (¹³¹₅₃I) undergoes beta-minus decay. Write the balanced nuclear equation and identify the daughter nucleus.

1 Identify the decay type and the particle emitted. Beta-minus decay emits ⁰₋₁e.

2 Use conservation of mass number (A): 131 = A_daughter + 0, so A_daughter = 131. (Mass number is unchanged.)

3 Use conservation of atomic number (Z): 53 = Z_daughter + (−1), so Z_daughter = 53 − (−1) = 53 + 1 = 54.

4 Look up element with Z = 54: that is Xenon (Xe).

5 Write the full balanced equation: ¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e

6 Check: A: 131 = 131 + 0 ✓ Z: 53 = 54 + (−1) = 53 ✓

¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e (daughter nucleus is Xenon-131)

✏️ Example 3: A radioactive nucleus ²¹⁰₈₄Po undergoes alpha decay followed by gamma emission. Write both nuclear equations.

1 Step 1 — Alpha decay: Find A and Z of daughter after alpha emission. A = 210 − 4 = 206. Z = 84 − 2 = 82. Z = 82 is Lead (Pb).

2 Write alpha decay equation: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He

3 Step 2 — Gamma emission: The excited ²⁰⁶₈₂Pb* releases energy as a gamma photon. Neither A nor Z changes.

4 Write gamma emission equation: ²⁰⁶₈₂Pb* → ²⁰⁶₈₂Pb + ⁰₀γ

5 Check gamma: A: 206 = 206 + 0 ✓ Z: 82 = 82 + 0 ✓

Alpha: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He
Gamma: ²⁰⁶₈₂Pb* → ²⁰⁶₈₂Pb + ⁰₀γ

✏️ Example 4: An unknown nucleus X undergoes beta-minus decay to produce ⁹⁰₃₉Y (Yttrium-90). Identify nucleus X.

1 In beta-minus decay: ᴬ_Z X → ᴬ_(Z+1) Y + ⁰₋₁e. The daughter has the same A and Z one higher than parent.

2 Daughter is ⁹⁰₃₉Y, so A_daughter = 90 and Z_daughter = 39.

3 Find parent A: A_parent = A_daughter + 0 = 90. (Mass number unchanged in beta decay.)

4 Find parent Z: Z_parent = Z_daughter − 1 = 39 − 1 = 38. Z = 38 is Strontium (Sr).

5 Write the equation: ⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e

6 Check: A: 90 = 90 + 0 ✓ Z: 38 = 39 + (−1) = 38 ✓

X is ⁹⁰₃₈Sr (Strontium-90) → ⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e

Question 1: What is the mass number of an alpha particle?

Question 2: When a nucleus undergoes beta-minus decay, what happens to its atomic number?

Question 3: Thorium-234 (²³⁴₉₀Th) undergoes beta-minus decay. What is the atomic number of the daughter nucleus?

Question 4: Which statement about gamma emission is correct?

Question 5: Radon-222 (²²²₈₆Rn) undergoes alpha decay. What is the mass number of the daughter nucleus?

Challenge 1: Americium-241 (²⁴¹₉₅Am) undergoes alpha decay. Write the full balanced nuclear equation, identify the daughter element, and state how many neutrons are in the daughter nucleus. Show all working.

Challenge 2: Strontium-90 (⁹⁰₃₈Sr) undergoes two successive beta-minus decays. Write a balanced equation for each decay and identify both daughter nuclei. What is the final element produced?

Challenge 3: An unknown nucleus undergoes alpha decay to produce ²⁰⁶₈₂Pb (Lead-206). Identify the unknown parent nucleus, giving its mass number, atomic number and element name. Write the full balanced equation.

Challenge 4 (Extended): A student claims that a nucleus can undergo beta-minus decay and produce a daughter nucleus with a lower atomic number than the parent. Evaluate this claim and explain, using the conservation laws, why this is or is not possible. [3 marks]