Nuclear Decay Worksheet - Fill Online, Printable, Fillable, Blank ... - Free Printable

It looks like you've uploaded an image of a worksheet on nuclear decay, where students are asked to write complete nuclear equations for various types of radioactive decay. The worksheet includes three sections:

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

You've already filled in some answers, and there are handwritten notes indicating corrections or clarifications. Let's go through each section carefully and explain the correct solutions.

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🔹 Section 1: Alpha Decay

Alpha decay involves the emission of an alpha particle, which is a helium nucleus:
\[
^4_2\text{He}
\]
So, when a nucleus undergoes alpha decay, its mass number decreases by 4, and atomic number decreases by 2.

#### Problem 1:
\[
^{210}_{84}\text{Po} \rightarrow ^{206}_{82}\text{Pb} + ^4_2\text{He}
\]
✔ Correct!

#### Problem 2:
\[
^{234}_{92}\text{U} \rightarrow ^{230}_{90}\text{Th} + ^4_2\text{He}
\]
✔ Correct!

#### Problem 3:
\[
^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}
\]
✔ Correct!

#### Problem 4:
\[
^{222}_{86}\text{Rn} \rightarrow ^{218}_{84}\text{Po} + ^4_2\text{He}
\]
✔ Correct!

> ✔ All alpha decay equations are correct.

---

🔹 Section 2: Beta Decay (β⁻)

Beta minus decay occurs when a neutron turns into a proton, emitting an electron (\( \beta^- \)) and an antineutrino. The emitted beta particle is:
\[
^0_{-1}\beta
\]
So, the mass number stays the same, but the atomic number increases by 1.

#### Problem 1:
\[
^{35}_{16}\text{S} \rightarrow ^{35}_{17}\text{Cl} + ^0_{-1}\beta
\]
✔ Correct!

#### Problem 2:
\[
^{80}_{35}\text{Br} \rightarrow ^{80}_{36}\text{Kr} + ^0_{-1}\beta
\]
✔ Correct!

#### Problem 3:
\[
^{36}_{18}\text{Ar} \rightarrow ^{36}_{19}\text{K} + ^0_{-1}\beta
\]
✘ Incorrect!
Explanation: Argon-36 is stable and does not undergo beta decay. But assuming it were to decay, this would be incorrect because potassium (K) has atomic number 19, so if Ar (Z=18) emits a β⁻, it becomes K (Z=19). So the equation *is* correct if we assume decay.

But note: Argon-36 is stable, so this is hypothetical. However, in problems like this, we often ignore stability and just follow the rules.

So technically, the equation is correct based on decay rules.

#### Problem 4:
\[
^{13}_{6}\text{C} \rightarrow ^{13}_{7}\text{N} + ^0_{-1}\beta
\]
✔ Correct! Carbon-14 is more common, but C-13 can theoretically undergo beta decay (though very rare). Still, the equation follows the rule.

> ✔ All beta decay equations are correct in terms of balancing.

---

🔹 Section 3: Electron Capture (EC)

In electron capture, an inner-shell electron is captured by the nucleus, combining with a proton to form a neutron and a neutrino. This results in:
- Mass number stays the same.
- Atomic number decreases by 1.
- Emitted particle: \( ^0_{+1}e \) (but actually, no particle is emitted — it’s an internal process).

The nuclear equation is written as:
\[
^A_Z\text{X} + ^0_{-1}e \rightarrow ^A_{Z-1}\text{Y} + \nu_e
\]
But in many textbooks, it's simplified to:
\[
^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + ^0_{+1}e
\]
Note: The \( ^0_{+1}e \) represents a positron? No — that’s positron emission (β⁺).

⚠️ Important Distinction:
- Electron Capture (EC): \( ^A_Z\text{X} + ^0_{-1}e \rightarrow ^A_{Z-1}\text{Y} + \nu_e \)
- Positron Emission (β⁺): \( ^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + ^0_{+1}e + \nu_e \)

But in many worksheets, especially at introductory levels, they simplify EC as:
\[
^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + ^0_{+1}e
\]
This is not accurate, because the \( ^0_{+1}e \) is a positron, not an electron.

However, sometimes people use \( ^0_{+1}e \) to represent the "effective" result of EC (i.e., a proton turning into a neutron), even though it's misleading.

Let’s check your answers:

#### Problem 1:
\[
^{230}_{90}\text{Th} \rightarrow ^{230}_{89}\text{Ac} + ^0_{+1}e
\]
✘ Incorrect notation
This looks like positron emission, not electron capture.

Correct EC equation should be:
\[
^{230}_{90}\text{Th} + ^0_{-1}e \rightarrow ^{230}_{89}\text{Ac} + \nu_e
\]
But since the worksheet says “write the complete nuclear equation” and uses \( ^0_{+1}e \), it might expect:
\[
^{230}_{90}\text{Th} \rightarrow ^{230}_{89}\text{Ac} + ^0_{+1}e
\]
Even though this is technically wrong — it's confusing EC with β⁺.

But in many high school curricula, they use \( ^0_{+1}e \) to represent both EC and β⁺, which is a simplification.

So, depending on context, this may be accepted.

But strictly speaking: No, this is not correct.

Let’s look at the next ones.

#### Problem 2:
\[
^{116}_{50}\text{Sn} \rightarrow ^{116}_{49}\text{In} + ^0_{+1}e
\]
Same issue. Should be:
\[
^{116}_{50}\text{Sn} + ^0_{-1}e \rightarrow ^{116}_{49}\text{In} + \nu_e
\]

Again, if the worksheet expects \( ^0_{+1}e \), it might be acceptable, but it's misleading.

#### Problem 3:
\[
^{190}_{76}\text{Os} \rightarrow ^{190}_{75}\text{Re} + ^0_{+1}e
\]
Same issue.

#### Problem 4:
\[
^{123}_{53}\text{I} \rightarrow ^{123}_{52}\text{Te} + ^0_{+1}e
\]
Again, same.

---

✔ Summary of Corrections

| Section | Type | Equation | Status |
|--------|------|---------|--------|
| 1 | α decay | All correct | ✔ |
| 2 | β⁻ decay | All correct | ✔ |
| 3 | EC | All show \( ^0_{+1}e \) → incorrect notation | ✘ |

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🔧 Corrected Electron Capture Equations

For electron capture, the proper way to write it is:

\[
^A_Z\text{X} + ^0_{-1}e \rightarrow ^A_{Z-1}\text{Y} + \nu_e
\]

But if the worksheet wants only one side (like in beta decay), then perhaps they want:

\[
^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + ^0_{+1}e
\]

But this is only acceptable if they're using \( ^0_{+1}e \) as a placeholder for EC, even though it's not accurate.

Many teachers accept this simplification.

So, if your teacher uses this convention, then your answers are fine.

But scientifically, electron capture is not the same as positron emission.

---

📝 Final Answer (with corrections):

#### Alpha Decay:
1. \( ^{210}_{84}\text{Po} \rightarrow ^{206}_{82}\text{Pb} + ^4_2\text{He} \) ✔
2. \( ^{234}_{92}\text{U} \rightarrow ^{230}_{90}\text{Th} + ^4_2\text{He} \) ✔
3. \( ^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He} \) ✔
4. \( ^{222}_{86}\text{Rn} \rightarrow ^{218}_{84}\text{Po} + ^4_2\text{He} \) ✔

#### Beta Decay:
1. \( ^{35}_{16}\text{S} \rightarrow ^{35}_{17}\text{Cl} + ^0_{-1}\beta \) ✔
2. \( ^{80}_{35}\text{Br} \rightarrow ^{80}_{36}\text{Kr} + ^0_{-1}\beta \) ✔
3. \( ^{36}_{18}\text{Ar} \rightarrow ^{36}_{19}\text{K} + ^0_{-1}\beta \) ✔ *(hypothetical)*
4. \( ^{13}_{6}\text{C} \rightarrow ^{13}_{7}\text{N} + ^0_{-1}\beta \) ✔

#### Electron Capture (Corrected):
1. \( ^{230}_{90}\text{Th} + ^0_{-1}e \rightarrow ^{230}_{89}\text{Ac} + \nu_e \)
OR (if simplified): \( ^{230}_{90}\text{Th} \rightarrow ^{230}_{89}\text{Ac} + ^0_{+1}e \) ✘ (misleading)
2. \( ^{116}_{50}\text{Sn} + ^0_{-1}e \rightarrow ^{116}_{49}\text{In} + \nu_e \)
3. \( ^{190}_{76}\text{Os} + ^0_{-1}e \rightarrow ^{190}_{75}\text{Re} + \nu_e \)
4. \( ^{123}_{53}\text{I} + ^0_{-1}e \rightarrow ^{123}_{52}\text{Te} + \nu_e \)

> ⚠️ Note: The neutrino (\( \nu_e \)) is often omitted in basic worksheets.

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💡 Key Takeaway:

- Alpha decay: \( ^4_2\text{He} \) emitted → A↓4, Z↓2
- Beta decay: \( ^0_{-1}\beta \) emitted → A unchanged, Z+1
- Electron capture: Electron absorbed → A unchanged, Z−1, but do not write \( ^0_{+1}e \) unless specified as a simplification.

If your teacher accepts \( ^0_{+1}e \) for EC, then your answers are acceptable. But ideally, electron capture should include the electron on the left.

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