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

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

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

⚽ 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