Nuclear Decay Equations
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Alpha, Beta and Gamma Decay: Nuclear Equations
Reference: Conservation in Nuclear Equations
In a balanced nuclear equation, the mass number (A) and the atomic number (Z) are conserved on both sides.
Alpha (α): A decreases by 4 and Z decreases by 2.
Beta-minus (β⁻): A stays the same and Z increases by 1.
Gamma (γ): A and Z stay the same; the nucleus loses energy.
Worked examples
Alpha: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He (α)
A: 238 = 234 + 4; Z: 92 = 90 + 2.
Beta-minus: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e (β⁻)
A: 14 = 14 + 0; Z: 6 = 7 + (−1).
Gamma: ⁹⁹ᵐ₄₃Tc → ⁹⁹₄₃Tc + ⁰₀γ (γ)
A and Z remain unchanged because gamma radiation carries energy, not nucleons.
Instructions: Complete each nuclear equation, show your working, and state whether the radiation is alpha, beta-minus, or gamma. Use conservation of A and Z.
Complete the Nuclear Equations
²²⁶₈₈Ra → ____________________ + ⁴₂He
Radiation: ____________________
²³²₉₀Th → ²³²₉₁Pa + ____________________
Radiation: ____________________
____________________ → ²¹⁰₈₄Po + ⁴₂He
Radiation: ____________________
¹³⁷ᵐ₅₆Ba → ____________________ + ____________________
Radiation: ____________________
³⁵₁₆S → ____________________ + ____________________
Radiation: ____________________
Answer Key
1. ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He; alpha.
2. ²³²₉₀Th → ²³²₉₁Pa + ⁰₋₁e; beta-minus.
3. ²¹⁴₈₆Rn → ²¹⁰₈₄Po + ⁴₂He; alpha.
4. ¹³⁷ᵐ₅₆Ba → ¹³⁷₅₆Ba + ⁰₀γ; gamma.
5. ³⁵₁₆S → ³⁵₁₇Cl + ⁰₋₁e; beta-minus.
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