Nuclear decay worksheet featuring problems on alpha and beta particle emissions with blank spaces for writing nuclear equations.

You’ve uploaded a worksheet titled “Nuclear Decay” that asks you to complete nuclear equations for three types of radioactive decay:

1. Alpha particle emission (α-decay)
2. Beta particle emission (β⁻-decay)
3. Electron capture (EC)

I’ll solve each section step-by-step and explain the reasoning.

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## 🔹 SECTION 1: ALPHA PARTICLE EMISSION (α-decay)

In alpha decay, an atom emits an alpha particle, which is a helium nucleus:
→ ⁴₂He (mass number = 4, atomic number = 2)

So, when a nucleus emits an alpha particle:
- Its mass number decreases by 4
- Its atomic number decreases by 2

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1. ²³⁰₉₀Th → ___ + ___

- Mass: 230 – 4 = 226
- Atomic number: 90 – 2 = 88
- Element with Z=88 is Radium (Ra)

✔ Answer:
²³⁰₉₀Th → ²²⁶₈₈Ra + ⁴₂He

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2. ²³⁸₉₂U → ___ + ___

- Mass: 238 – 4 = 234
- Atomic number: 92 – 2 = 90
- Element with Z=90 is Thorium (Th)

✔ Answer:
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

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3. ²³⁸₉₈U? Wait — typo? Probably meant ²³⁸₉₂U again? But written as ²³⁸₉₈U? That doesn’t make sense — Uranium is always Z=92.

Wait — looking at your image, it says:

> ²³⁸₉₈U → ___ + ___

That’s likely a typo — uranium is Z=92, not 98. Element 98 is Cf (Californium).

But let’s assume it's ²³⁸₉₂U (common isotope), since ²³⁸₉₈U doesn’t exist naturally.

If it’s really ²³⁸₉₈Cf (Californium-238), then:

- Mass: 238 – 4 = 234
- Atomic number: 98 – 2 = 96
- Element 96 is Curium (Cm)

✔ So if it’s Cf:
²³⁸₉₈Cf → ²³⁴₉₆Cm + ⁴₂He

BUT — given context, this is probably a typo and should be ²³⁸₉₂U → same as #2.

However, since you wrote “²³⁸₉₈U”, I’ll go with Cf to match the subscript.

✔ Final answer (assuming typo corrected to Cf):
²³⁸₉₈Cf → ²³⁴₉₆Cm + ⁴₂He

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4. ²²²₈₆Rn → ___ + ___

- Mass: 222 – 4 = 218
- Atomic number: 86 – 2 = 84
- Element 84 is Polonium (Po)

✔ Answer:
²²²₈₆Rn → ²¹⁸₈₄Po + ⁴₂He

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## 🔹 SECTION 2: BETA PARTICLE EMISSION (β⁻-decay)

In beta-minus decay, a neutron turns into a proton, emitting an electron (beta particle):
→ ⁰₋₁e or ⁰₋₁β

So:
- Mass number stays the same
- Atomic number increases by 1

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1. ¹⁴₆C → ___ + ___

- Mass: 14 (unchanged)
- Atomic number: 6 + 1 = 7
- Element 7 is Nitrogen (N)

✔ Answer:
¹⁴₆C → ¹⁴₇N + ⁰₋₁e

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2. ⁹⁰₃₈Sr → ___ + ___

- Mass: 90
- Atomic number: 38 + 1 = 39
- Element 39 is Yttrium (Y)

✔ Answer:
⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e

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3. ⁴⁰₁₉K → ___ + ___

- Mass: 40
- Atomic number: 19 + 1 = 20
- Element 20 is Calcium (Ca)

✔ Answer:
⁴⁰₁₉K → ⁴⁰₂₀Ca + ⁰₋₁e

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4. ¹³₇N → ___ + ___

- Mass: 13
- Atomic number: 7 + 1 = 8
- Element 8 is Oxygen (O)

✔ Answer:
¹³₇N → ¹³₈O + ⁰₋₁e

*(Note: Nitrogen-13 actually decays via positron emission, but per instructions, we’re doing beta-minus decay — so this is hypothetical.)*

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## 🔹 SECTION 3: ELECTRON CAPTURE (EC)

In electron capture, the nucleus captures an inner-shell electron:
→ ⁰₋₁e is absorbed

So:
- Mass number stays the same
- Atomic number decreases by 1

It’s like the reverse of beta-minus decay.

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1. ¹⁹⁶₇₈Pt + ___ → ___

- Mass: 196 (unchanged)
- Atomic number: 78 – 1 = 77
- Element 77 is Iridium (Ir)

✔ Answer:
¹⁹⁶₇₈Pt + ⁰₋₁e → ¹⁹⁶₇₇Ir

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2. ¹¹⁰₄₉In + ___ → ___

- Mass: 110
- Atomic number: 49 – 1 = 48
- Element 48 is Cadmium (Cd)

✔ Answer:
¹¹⁰₄₉In + ⁰₋₁e → ¹¹⁰₄₈Cd

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3. ¹⁹⁶₇₈Pt + ___ → ___

Same as #1? Typo? Or maybe different isotope?

Wait — in your image, it says:

> ¹⁹⁶₇₈Pt + ___ → ___
> ¹⁹⁶₇₈Pt + ___ → ___

Probably duplicate? Or maybe second one is different?

Looking at your image again — it seems like the third one is:

> ¹⁹⁶₇₈Pt + ___ → ___
> ¹⁹⁶₇₈Pt + ___ → ___

Actually, looking closely — the last one is:

> ¹²³₅₃I + ___ → ___

Ah! The last one is Iodine-123

So:

4. ¹²³₅₃I + ___ → ___

- Mass: 123
- Atomic number: 53 – 1 = 52
- Element 52 is Tellurium (Te)

✔ Answer:
¹²³₅₃I + ⁰₋₁e → ¹²³₅₂Te

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## ✔ FINAL ANSWERS SUMMARY

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Alpha Decay:

1. ²³⁰₉₀Th → ²²⁶₈₈Ra + ⁴₂He
2. ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
3. ²³⁸₉₈Cf → ²³⁴₉₆Cm + ⁴₂He *(assuming typo — U should be Cf)*
4. ²²²₈₆Rn → ²¹⁸₈₄Po + ⁴₂He

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Beta Decay:

1. ¹⁴₆C → ¹⁴₇N + ⁰₋₁e
2. ⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e
3. ⁴⁰₁₉K → ⁴⁰₂₀Ca + ⁰₋₁e
4. ¹³₇N → ¹³₈O + ⁰₋₁e

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Electron Capture:

1. ¹⁹⁶₇₈Pt + ⁰₋₁e → ¹⁹⁶₇₇Ir
2. ¹¹⁰₄₉In + ⁰₋₁e → ¹¹⁰₄₈Cd
3. ¹²³₅₃I + ⁰₋₁e → ¹²³₅₂Te

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## 🧠 KEY CONCEPTS REMEMBERED:

- Alpha decay: loses He nucleus → mass -4, atomic # -2
- Beta decay: neutron → proton + e⁻ → mass same, atomic # +1
- Electron capture: absorbs e⁻ → mass same, atomic # -1

Let me know if you’d like these explained with diagrams or real-world examples!