Nuclear Equations | Physics

📖 In-Depth Theory

Writing Nuclear Equations

Nuclear equations show radioactive decay using nuclear notation.

Rules for BALANCING nuclear equations:

MASS NUMBERS must balance — top numbers sum the same on both sides.

ATOMIC NUMBERS must balance — bottom numbers sum the same on both sides.

ALPHA PARTICLE symbol: ⁴₂He (or ⁴₂α)

BETA PARTICLE symbol: ⁰₋₁e (or ⁰₋₁β)

GAMMA RAY: represented by γ — no change to mass or atomic number

Alpha decay:

Parent nucleus → daughter nucleus + alpha particle

Mass number decreases by 4. Atomic number decreases by 2.

Beta decay:

Parent nucleus → daughter nucleus + beta particle

A neutron becomes a proton + electron: ¹₀n → ¹₁p + ⁰₋₁e

Mass number unchanged. Atomic number increases by 1.

Alpha and Beta Decay Examples

ALPHA DECAY EXAMPLE:

Radium-226 decays by alpha emission:

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

Check: mass numbers: 226 = 222 + 4 ✓

Atomic numbers: 88 = 86 + 2 ✓

Radium (88) → Radon (86) — atomic number decreases by 2, so element changes.

BETA DECAY EXAMPLE:

Carbon-14 decays by beta emission:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Check: mass numbers: 14 = 14 + 0 ✓

Atomic numbers: 6 = 7 + (−1) ✓

Carbon (6) → Nitrogen (7) — atomic number increases by 1.

GAMMA EMISSION:

Often follows alpha or beta decay — nucleus releases excess energy as gamma ray.

No change to mass number or atomic number.

No separate nuclear equation needed — just add + γ.

Effect on the Nucleus

ALPHA DECAY:

Mass number: decreases by 4

Atomic number: decreases by 2

Result: new element (two places lower in periodic table)

BETA DECAY:

Mass number: unchanged (a neutron converts to a proton + electron)

Atomic number: increases by 1

Result: new element (one place higher in periodic table)

GAMMA EMISSION:

Mass number: unchanged

Atomic number: unchanged

Result: same element, just releases energy

PATTERN TO REMEMBER:

Alpha → lose 4 mass, lose 2 charge

Beta → same mass, gain 1 charge

Gamma → no change to nucleus

EXAM STRATEGY:

Always check both mass AND atomic numbers balance.

Use the periodic table to identify the daughter element from its new atomic number.

⚠️ Common Mistake

In beta decay, the MASS NUMBER stays the same — a neutron turns into a proton plus an electron. The atomic number INCREASES by 1 (one more proton). Students often think beta decay is like alpha and reduces mass number.

📐 Key Equations

Alpha decay: A decreases by 4, Z decreases by 2

Beta decay: A unchanged, Z increases by 1

Gamma: no change to A or Z

📌 Key Note

Nuclear equations: mass numbers and atomic numbers must balance on both sides. Alpha (⁴₂He): A−4, Z−2. Beta (⁰₋₁e): A same, Z+1. Gamma (γ): no change. New element formed in alpha and beta (different Z). Always verify balance.

🎯 Matching Activity — Nuclear Equation Changes

Match each decay type to the change in mass number and atomic number. — drag the symbols on the right to match the component names on the left.

Alpha decay

Drop here

Beta decay

Drop here

Gamma emission

Drop here

Beta particle

Drop here

Mass number −4, atomic number −2 — new element two places lower

⁰₋₁e — electron emitted from nucleus when neutron converts to proton

No change to mass number or atomic number — same element, energy released

Mass number unchanged, atomic number +1 — new element one place higher

⚽ FIFA Worked Examples

Alpha Decay Equation

Write the nuclear equation for alpha decay of ²²⁶₈₈Ra (radium).

F

Alpha decay: A decreases by 4, Z decreases by 2. Product + ⁴₂He

I

A = 226 − 4 = 222; Z = 88 − 2 = 86. Z=86 is radon (Rn)

F

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

A

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He (check: 226 = 222+4 ✓; 88 = 86+2 ✓)

🎯 Test Yourself

Question 1 of 2

1. Thorium-234 (²³⁴₉₀Th) undergoes beta decay. What is the daughter nucleus?

2. In a nuclear equation, the mass numbers on both sides must balance. A nucleus of ²³⁸₉₂U emits an alpha particle. What is the mass number of the daughter nucleus?

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⚡ Nuclear Equations

Writing Nuclear Equations

Alpha and Beta Decay Examples

Effect on the Nucleus

Mr. Badmus AI