Worksheet for practicing nuclear decay reactions and balancing nuclear equations.

Let’s solve this step by step.

We are given 10 nuclear decay problems in Table A, and we need to identify each as alpha (α), beta (β⁻), positron (β⁺), or gamma (γ) decay.

Here’s how to tell them apart:

- Alpha decay: nucleus emits an alpha particle → that’s a helium nucleus: ⁴₂He. So mass number decreases by 4, atomic number decreases by 2.
- Beta-minus decay (β⁻): neutron turns into proton + electron + antineutrino. Electron is emitted → so atomic number increases by 1, mass number stays same. Written as ⁰₋₁e or β⁻.
- Positron emission (β⁺): proton turns into neutron + positron + neutrino. Positron is emitted → atomic number decreases by 1, mass number stays same. Written as ⁰₊₁e or β⁺.
- Gamma decay: no change in protons or neutrons — just energy released. No particles with mass or charge emitted. Just γ ray. Mass and atomic numbers unchanged.

Now let’s go one by one.

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1. ²³⁸₉₂U → ²³⁴₉₀Th + ?

Mass: 238 → 234 → difference of 4
Atomic #: 92 → 90 → difference of 2
→ That’s alpha decay! Emitted particle is ⁴₂He.

✔ Answer: Alpha decay

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2. ¹⁴₆C → ¹⁴₇N + ?

Mass: 14 → 14 → same
Atomic #: 6 → 7 → increased by 1
→ Beta-minus decay! Emitted particle is ⁰₋₁e (electron)

✔ Answer: Beta-minus decay

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3. ⁶₂₇Co* → ⁶⁰₂₇Co + ?

Same element, same mass, same atomic number → only energy released
→ Gamma decay! The * means excited state.

✔ Answer: Gamma decay

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4. Decay emitting an electron

Electron = beta-minus particle → ⁰₋₁e

✔ Answer: Beta-minus decay

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5. Nuclear decay giving off a helium nucleus

Helium nucleus = ⁴₂He → that’s alpha particle

✔ Answer: Alpha decay

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6. Least penetrating nuclear decay

Alpha particles are heavy and slow → stopped by paper → least penetrating

✔ Answer: Alpha decay

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7. Most damaging nuclear decay to the human body

This is tricky — but if inside the body, alpha emitters are very dangerous because they dump all their energy in small area. But externally, gamma is worse. However, standard answer for “most damaging” when ingested/inhaled is alpha.

But wait — sometimes questions mean “most penetrating” vs “most damaging”. Let’s think: Alpha can’t penetrate skin, but if inside you, it’s very damaging. Beta can penetrate a bit. Gamma goes through.

In many textbooks, alpha is considered most damaging *if internal*, which is often implied.

But let’s check context — question says “to the human body” — doesn’t specify internal/external. Hmm.

Actually, looking at common curriculum answers: Alpha decay is often listed as most damaging *when inside the body*, which is typical scenario for harm.

I’ll go with alpha.

✔ Answer: Alpha decay

*(Note: Some might argue gamma, but based on biological impact per unit energy deposited, alpha has high LET — linear energy transfer — so more damage locally.)*

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8. Nuclear decay that can be stopped by skin or paper

That’s alpha decay — yes, even a sheet of paper stops it.

✔ Answer: Alpha decay

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9. Nuclear decay that can be stopped by aluminum

Beta particles can be stopped by a few mm of aluminum. Alpha is stopped by paper, gamma needs lead or thick concrete.

So beta decay → stopped by aluminum.

✔ Answer: Beta-minus decay

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10. Write symbols for alpha, beta, positron, gamma rays

Standard notation:

- Alpha: ⁴₂He or α
- Beta-minus: ⁰₋₁e or β⁻
- Positron: ⁰₊₁e or β⁺
- Gamma: γ or ⁰₀γ

Usually written as:

Alpha: ⁴₂He
Beta: ⁰₋₁e
Positron: ⁰₊₁e
Gamma: γ

✔ Answers:
- Alpha: ⁴₂He
- Beta: ⁰₋₁e
- Positron: ⁰₊₁e
- Gamma: γ

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Now Table B: Balance the equations.

General rule: In nuclear reactions, total mass number (top) and total atomic number (bottom) must balance on both sides.

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a. ²³⁸₉₂U → ⁴₂α + _____

Left: mass=238, atomic=92
Right: alpha has mass=4, atomic=2 → so missing part must have:

Mass: 238 - 4 = 234
Atomic: 92 - 2 = 90 → Thorium (Th)

✔ Answer: ²³⁴₉₀Th

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b. ²³⁵₉₂U → ⁹₃₈Sr + _____

Left: mass=235, atomic=92
Right: Sr has mass=90, atomic=38 → missing part:

Mass: 235 - 90 = 145
Atomic: 92 - 38 = 54 → Xenon (Xe)

Wait — actually, uranium fission usually gives two medium nuclei + neutrons. But here only one product shown? Probably missing another fragment.

Looking again: equation is ²³⁵₉₂U → ⁹₃₈Sr + _____

It should be balanced with another nucleus. Maybe it's implying one other product? Or perhaps it's incomplete?

Wait — maybe it's supposed to be:

²³⁵₉₂U → ⁹₃₈Sr + ¹⁴³₅₄Xe + ? neutrons?

But the blank is only one space. Perhaps it's expecting the other main fragment.

Standard fission: U-235 + n → Sr-90 + Xe-143 + 3n

But here no neutron on left. Equation starts with U-235 alone? That doesn't make sense for fission.

Perhaps typo? Or maybe it's decay? U-235 doesn't decay to Sr-90 directly.

Wait — looking back at original image description — user wrote:

"b. ²³⁵₉₂U → ⁹₃₈Sr + _________"

Probably expects the complementary fission fragment.

Assume it's fission: so mass balance: 235 = 90 + x → x=145
Atomic: 92 = 38 + y → y=54 → Xe-145? But Xe-145 isn't stable.

Common pair is Sr-90 and Xe-143, but 90+143=233, so need 2 neutrons? But not shown.

Perhaps the blank is for the other nucleus, and we ignore neutrons? Not accurate.

Another possibility: maybe it's ²³⁵₂U → ⁰₃Sr + ¹⁴³₅₄Xe + 2¹₀n — but only one blank.

Looking at the format, probably they want the other nucleus, assuming neutrons are implied or not counted? But that’s bad practice.

Wait — in some simplified versions, they might write just the two fragments.

But 90 + 145 = 235, 38 + 54 = 92 → so ¹⁴⁵₅₄Xe

Yes, that balances.

✔ Answer: ¹⁴⁵₅₄Xe

*(Note: In reality, fission produces neutrons too, but for balancing purposes here, we'll go with this.)*

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c. ¹⁴₆C → ⁰₋₁β + _____

Beta decay: carbon-14 to nitrogen-14

Mass: 14 = 0 + x → x=14
Atomic: 6 = -1 + y → y=7 → Nitrogen

✔ Answer: ¹⁴₇N

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d. ²¹⁸₈₄Po → ⁴₂α + _____

Alpha decay: polonium-218

Mass: 218 - 4 = 214
Atomic: 84 - 2 = 82 → Lead (Pb)

✔ Answer: ²¹⁴₈₂Pb

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e. ¹⁴²₅₆Ba → ⁰₋₁β + _____

Beta decay: barium-142

Mass: 142 = 0 + x → x=142
Atomic: 56 = -1 + y → y=57 → Lanthanum (La)

✔ Answer: ¹⁴²₅₇La

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f. ²¹⁰₈₃Bi → ⁴₂α + _____

Alpha decay: bismuth-210

Mass: 210 - 4 = 206
Atomic: 83 - 2 = 81 → Thallium (Tl)

✔ Answer: ²⁰⁶₈₁Tl

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g. ²³⁵₉₂U → ¹⁴¹₅₆Ba + _____ + 3¹₀n

Fission reaction.

Left: mass=235, atomic=92
Right: Ba-141: mass=141, atomic=56; 3 neutrons: mass=3, atomic=0; so missing part:

Mass: 235 - 141 - 3 = 91
Atomic: 92 - 56 - 0 = 36 → Krypton (Kr)

✔ Answer: ⁹¹₃₆Kr

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h. ²³⁸₉₂U → ⁴₂α + _____

Same as part a!

Mass: 238 - 4 = 234
Atomic: 92 - 2 = 90 → Thorium

✔ Answer: ²³⁴₉₀Th

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i. ²³⁸₉₂U → ²³⁴₉₀Th + _____

Again, same as above — alpha decay

Missing: ⁴₂α

✔ Answer: ⁴₂α

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j. ²³⁹₉₄Pu → ⁴₂α + _____

Plutonium-239 alpha decay

Mass: 239 - 4 = 235
Atomic: 94 - 2 = 92 → Uranium

✔ Answer: ²³⁵₉₂U

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Now Table C: Write balanced equations.

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1) Alpha decay of iridium-174

Iridium: Ir, atomic number 77

Alpha decay: emit ⁴₂He

So: ¹⁷⁴₇Ir → ⁴₂He + ?

Mass: 174 - 4 = 170
Atomic: 77 - 2 = 75 → Rhenium (Re)

✔ Equation: ¹⁷⁴₇Ir → ⁴₂He + ¹⁷⁰₅Re

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2) Beta decay of platinum-199

Platinum: Pt, atomic number 78

Beta-minus decay: emit ⁰₋₁e

So: ¹⁹⁹₇₈Pt → ⁰₋₁e + ?

Mass: 199 = 0 + x → x=199
Atomic: 78 = -1 + y → y=79 → Gold (Au)

✔ Equation: ¹⁹⁹₇₈Pt → ⁰₋₁e + ¹⁹⁹₇₉Au

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3) Beta decay of iodine-184

Iodine: I, atomic number 53

Beta decay: ¹⁸⁴₃I → ₋₁e + ?

Mass: 184
Atomic: 53 → becomes 54 → Xenon (Xe)

✔ Equation: ¹⁸⁴₅₃I → ⁰₋₁e + ¹⁸⁴₅₄Xe

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4) Beta decay of uranium-237

Uranium: U, atomic number 92

Beta decay: ²³⁷₉₂U → ⁰₋₁e + ?

Mass: 237
Atomic: 92 → 93 → Neptunium (Np)

✔ Equation: ²³⁷₉₂U → ⁰₋₁e + ²³⁷₉Np

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Now compiling all answers.

Final Answer:

Table A:
1. Alpha decay
2. Beta-minus decay
3. Gamma decay
4. Beta-minus decay
5. Alpha decay
6. Alpha decay
7. Alpha decay
8. Alpha decay
9. Beta-minus decay
10. Alpha: ⁴₂He, Beta: ⁰₋₁e, Positron: ⁰₊₁e, Gamma: γ

Table B:
a. ²³⁴₉₀Th
b. ¹⁴⁵₅₄Xe
c. ¹⁴₇N
d. ²¹⁴₈₂Pb
e. ¹⁴²₅₇La
f. ²⁰⁶₈₁Tl
g. ⁹¹₃₆Kr
h. ²³⁴₉₀Th
i. ⁴₂α
j. ²³⁵₉₂U

Table C:
1. ¹⁷⁴₇₇Ir → ⁴₂He + ¹⁷⁰₇₅Re
2. ¹⁹⁹₇₈Pt → ⁰₋₁e + ¹⁹⁹₉Au
3. ¹⁸⁴₅₃I → ⁰₋₁e + ¹⁸⁴₅₄Xe
4. ²³⁷₉₂U → ⁰₋₁e + ²³⁷₉₃Np