IB MYP 4-5 Chemistry -Balancing nuclear equations- Study Notes - New Syllabus
IB MYP 4-5 Chemistry -Balancing nuclear equations- Study Notes
Key Concepts
- Balancing Nuclear Equations
Balancing Nuclear Equations
Balancing Nuclear Equations
A nuclear equation shows how the nucleus of an atom changes during a radioactive decay or nuclear reaction. Balancing nuclear equations means ensuring that the total mass number and atomic number are the same on both sides of the equation — just like the conservation of mass and charge in chemical reactions.
In any nuclear reaction, the sum of mass numbers (A) and atomic numbers (Z) is always conserved.
Basic Structure of a Nuclear Equation
The general form is:
\( \mathrm{^{A}_{Z}X \rightarrow ^{A’}_{Z’}Y + ^{a}_{z}p} \)
- \( \mathrm{^{A}_{Z}X} \): parent nucleus (original atom)
- \( \mathrm{^{A’}_{Z’}Y} \): daughter nucleus (new atom formed)
- \( \mathrm{^{a}_{z}p} \): emitted particle (α, β, γ, or neutron)
Rules for Balancing:
- Sum of mass numbers (A) must be equal on both sides.
- Sum of atomic numbers (Z) must be equal on both sides.
- Energy and emitted particles must be accounted for (α, β, γ, etc.).
Step-by-Step Process to Balance Nuclear Equations
- Identify the radiation emitted (α, β⁻, β⁺, or γ).
- Write the symbol for the emitted particle:
- Alpha: \( \mathrm{^4_2He} \)
- Beta minus (β⁻): \( \mathrm{^0_{-1}e} \)
- Beta plus (β⁺): \( \mathrm{^0_{+1}e} \)
- Gamma: \( \mathrm{\gamma} \)
- Ensure mass number balance: Add/subtract to make total A equal on both sides.
- Ensure atomic number balance: Add/subtract to make total Z equal on both sides.
- Verify the resulting element using the periodic table (atomic number determines the element’s symbol).
Common Types of Nuclear Reactions
| Type of Reaction | General Equation | Change in Nucleus |
|---|---|---|
| Alpha Decay | \( \mathrm{^{A}_{Z}X \rightarrow ^{A-4}_{Z-2}Y + ^4_2He} \) | Mass −4, Atomic no. −2 |
| Beta Minus Decay (β⁻) | \( \mathrm{^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y + ^0_{-1}e} \) | Atomic no. increases by 1 |
| Beta Plus Decay (β⁺) | \( \mathrm{^{A}_{Z}X \rightarrow ^{A}_{Z-1}Y + ^0_{+1}e} \) | Atomic no. decreases by 1 |
| Gamma Emission | \( \mathrm{^{A}_{Z}X^* \rightarrow ^{A}_{Z}X + \gamma} \) | No change in A or Z |
Example
Balance the equation for alpha decay of uranium-238.
▶️ Answer / Explanation
Step 1: Alpha particle = \( \mathrm{^4_2He} \).
Step 2: Subtract 4 from mass number and 2 from atomic number of uranium.
\( \mathrm{^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2He} \)
Final Answer: Thorium-234 is produced with emission of an alpha particle.
Example
Balance the nuclear equation for beta decay of carbon-14.
▶️ Answer / Explanation
Step 1: In β⁻ decay, a neutron changes into a proton, emitting an electron \( \mathrm{^0_{-1}e} \).
Step 2: Atomic number increases by 1; mass number stays the same.
\( \mathrm{^{14}_{6}C \rightarrow ^{14}_{7}N + ^0_{-1}e} \)
Final Answer: Carbon-14 decays into nitrogen-14 and emits a beta particle.
Example
Balance the nuclear equation for beta-plus (positron) emission from sodium-22.
▶️ Answer / Explanation
Step 1: In β⁺ decay, a proton changes into a neutron, emitting a positron \( \mathrm{^0_{+1}e} \).
Step 2: Atomic number decreases by 1; mass number remains constant.
\( \mathrm{^{22}_{11}Na \rightarrow ^{22}_{10}Ne + ^0_{+1}e} \)
Final Answer: Sodium-22 decays into neon-22 by emitting a positron.
Checking Conservation in Nuclear Equations
For every nuclear reaction:
- Total mass number (A) on the left = total mass number on the right.
- Total atomic number (Z) on the left = total atomic number on the right.
Example Check:
\( \mathrm{^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2He} \)
- Mass: 238 = 234 + 4
- Atomic number: 92 = 90 + 2
Applications of Balanced Nuclear Equations
- Radiocarbon dating: Uses \( \mathrm{^{14}_6C} \) decay equations.
- Nuclear medicine: Tracks radioactive isotopes in the body.
- Nuclear power: Describes fission of uranium and plutonium isotopes.
Nuclear Equation Balancing Overview
| Type | Particle Emitted | Effect on Mass Number | Effect on Atomic Number |
|---|---|---|---|
| Alpha Decay | \( \mathrm{^4_2He} \) | −4 | −2 |
| Beta Minus (β⁻) | \( \mathrm{^0_{-1}e} \) | 0 | +1 |
| Beta Plus (β⁺) | \( \mathrm{^0_{+1}e} \) | 0 | −1 |
| Gamma Emission | \( \mathrm{\gamma} \) | 0 | 0 |