Nuclear Equations worksheet with problems on alpha and beta decay, including a periodic table key.

Let's solve each part of the nuclear equations worksheet step by step, explaining the principles behind alpha and beta decay.

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## 1) a) Complete the equation:

> ²⁰⁸₉₂U → ⁴₂He + ? Th

This is an alpha decay. In alpha decay, a nucleus emits an alpha particle (⁴₂He), which consists of 2 protons and 2 neutrons.

Rules:

- Mass number (top number) decreases by 4.
- Atomic number (bottom number) decreases by 2.

So:

- Original mass: 208 → after emitting He-4 → 208 - 4 = 204
- Original atomic number: 92 → after losing 2 protons → 92 - 2 = 90

Now look up element with atomic number 90 on the periodic table → Thorium (Th)

✔ So the completed equation is:

> ²⁰⁸₉₂U → ⁴₂He + ²⁰⁴₉₀Th

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## 2) Write equations for alpha decay of these isotopes

Alpha decay: emit ⁴₂He → subtract 4 from mass number, subtract 2 from atomic number.

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a) ²²²₈₈Ra → ⁴₂He + ?

- Mass: 222 - 4 = 218
- Atomic number: 88 - 2 = 86

Element with atomic number 86 → Radon (Rn)

✔ Equation: ²²²₈₈Ra → ⁴₂He + ²¹⁸₈₆Rn

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b) ²⁰⁸₈₄Po → ⁴₂He + ?

- Mass: 208 - 4 = 204
- Atomic number: 84 - 2 = 82

Element with atomic number 82 → Lead (Pb)

✔ Equation: ²⁰⁸₈₄Po → ⁴₂He + ²⁰⁴₈₂Pb

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c) ¹⁸⁵₇₉Au → ⁴₂He + ?

- Mass: 185 - 4 = 181
- Atomic number: 79 - 2 = 77

Element with atomic number 77 → Iridium (Ir)

✔ Equation: ¹⁸⁵₇₉Au → ⁴₂He + ¹⁸¹₇₇Ir

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d) ¹⁸⁵₇₈Pt → ? He + ?

Wait — this one is written as “→ ? He + ?”, so we need to fill in both the alpha particle and the daughter.

But since it’s alpha decay, the emitted particle is always ⁴₂He.

So:

- Mass: 185 - 4 = 181
- Atomic number: 78 - 2 = 76

Element with atomic number 76 → Osmium (Os)

✔ Equation: ¹⁸⁵₇₈Pt → ⁴₂He + ¹⁸¹₇₆Os

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## 3) Write equations for beta decay of these isotopes

In beta minus decay (β⁻), a neutron turns into a proton, emitting an electron (⁰₋₁e).

Rules:

- Mass number stays the same (electron has negligible mass)
- Atomic number increases by 1 (because you gain a proton)

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a) ⁶₂He → ⁰₋₁e + ?

- Mass: 6 → stays 6
- Atomic number: 2 + 1 = 3

Element with atomic number 3 → Lithium (Li)

✔ Equation: ⁶₂He → ⁰₋₁e + ⁶₃Li

*(Note: Helium-6 is unstable and does undergo beta decay to Lithium-6)*

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b) ²⁴₁₁Na → ⁰₋₁e + ?

- Mass: 24 → stays 24
- Atomic number: 11 + 1 = 12

Element with atomic number 12 → Magnesium (Mg)

✔ Equation: ²⁴₁₁Na → ⁰₋₁e + ²⁴₁₂Mg

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c) ²⁰¹₇₉Au → ⁰₋₁e + ?

- Mass: 201 → stays 201
- Atomic number: 79 + 1 = 80

Element with atomic number 80 → Mercury (Hg)

✔ Equation: ²⁰¹₇₉Au → ⁰₋₁e + ²⁰¹₈₀Hg

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d) ⁴²₁₉K → ? e + ?

Beta decay emits ⁰₋₁e, so we fill that in.

- Mass: 42 → stays 42
- Atomic number: 19 + 1 = 20

Element with atomic number 20 → Calcium (Ca)

✔ Equation: ⁴²₁₉K → ⁰₋₁e + ⁴²₂₀Ca

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## ✔ Final Answers Summary:

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1) a)

²⁰⁸₉₂U → ⁴₂He + ²⁰⁴₉₀Th

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2) Alpha Decay Equations:

a) ²²²₈₈Ra → ⁴₂He + ²¹⁸₈₆Rn
b) ²⁰⁸₈₄Po → ⁴₂He + ²⁰⁴₈₂Pb
c) ¹⁸⁵₇₉Au → ⁴₂He + ¹⁸¹₇₇Ir
d) ¹⁸⁵₇₈Pt → ⁴₂He + ¹⁸¹₇₆Os

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3) Beta Decay Equations:

a) ⁶₂He → ⁰₋₁e + ⁶₃Li
b) ²⁴₁₁Na → ⁰₋₁e + ²⁴₁₂Mg
c) ²⁰¹₇₉Au → ⁰₋₁e + ²⁰¹₈₀Hg
d) ⁴²₁₉K → ⁰₋₁e + ⁴²₂₀Ca

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## 🧠 Key Concepts Recap:

- Alpha decay: lose 4 in mass, 2 in atomic number → new element 2 places left on periodic table.
- Beta decay (β⁻): mass unchanged, atomic number +1 → new element 1 place right on periodic table.
- Always conserve total mass number and atomic number across the reaction.

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