Worksheet on balancing nuclear equations, including decay types and practice problems.

Let’s solve each nuclear equation step by step. We’ll use the rules from the table and examples given:

- In beta-minus decay (β⁻): A neutron turns into a proton + electron → atomic number increases by 1, mass stays same.
- In alpha decay: Nucleus emits He nucleus (⁴₂He) → atomic number ↓2, mass ↓4.
- In positron emission (β⁺) or electron capture: Proton turns into neutron → atomic number ↓1, mass unchanged.
- Always conserve: total atomic number (bottom numbers) and total mass number (top numbers).

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Problem 1:
³₁H → ______ + ⁰₋₁e

This is beta-minus decay (emitting an electron, ⁰₋₁e).
Mass number: 3 = ? + 0 → missing mass = 3
Atomic number: 1 = ? + (-1) → missing atomic number = 2
Element with atomic number 2 is Helium (He).
So: ³₁H → ³₂He + ⁰₋₁e
Reaction type: Beta decay (β⁻)

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Problem 2:
²³²₉₂U → ²²⁸₉₀Th + ______

Mass: 232 = 228 + ? → ? = 4
Atomic number: 92 = 90 + ? → ? = 2
That’s an alpha particle: ⁴₂He
Reaction type: Alpha decay

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Problem 3:
¹⁴⁴₅₈Ce → ¹⁴⁴₅₉Pr + ______

Mass: 144 = 144 + ? → ? = 0
Atomic number: 58 = 59 + ? → ? = -1
That’s a beta particle (electron): ⁰₁e
Reaction type: Beta decay (β⁻)

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Problem 4:
⁶⁵₃₀Zn → ______ + ⁰₊₁e

This is positron emission (β⁺).
Mass: 65 = ? + 0 → ? = 65
Atomic number: 30 = ? + 1 → ? = 29
Element with atomic number 29 is Copper (Cu)
So: ⁶⁵₃₀Zn → ⁶⁵₂₉Cu + ⁰₁e
Reaction type: Positron emission (β⁺)

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Problem 5:
⁴⁰₁K → ⁴⁰₁₈Ar + ______

Mass: 40 = 40 + ? → ? = 0
Atomic number: 19 = 18 + ? → ? = +1
That’s a positron: ⁰₊₁e
Reaction type: Positron emission (β⁺)

*(Note: This could also be electron capture — but since it shows Ar as product and no incoming electron, and we’re to fill the emitted particle, positron fits.)*

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Final Answer:

1. ³₂He ; Beta decay
2. ⁴₂He ; Alpha decay
3. ⁰₁e ; Beta decay
4. ⁶⁵₂₉Cu ; Positron emission
5. ⁰₁e ; Positron emission