Physics 001.002.009 Nuclear Equations

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

• Explain that nuclear equations must conserve nucleon number and charge.
• Use notation to represent reactants and products in nuclear equations.
• Solve for missing particles or nuclides in alpha, beta positive, beta negative and gamma decay equations.
• Check whether a nuclear equation is balanced by comparing total mass number and atomic number on both sides.

Success Criteria

By the end of the lesson, students have successfully:

• Identified as mass number and as atomic number in notation.
• Applied conservation of nucleon number: total before total after.
• Applied conservation of charge: total before total after.
• Determined missing values of , or in nuclear equations.
• Written balanced decay equations for alpha, beta positive, beta negative and gamma radiation.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Science Understanding: Solve problems involving balancing nuclear equations.

Phenomenon

Smoke detectors, nuclear medicine and radioactive dating all rely on unstable nuclei changing into more stable nuclei. These changes are represented using nuclear equations.

For example, americium-241 in some smoke detectors undergoes alpha decay:

This equation is balanced because the total mass number and total atomic number are the same before and after the decay ( and ).

Key Idea

A nuclear equation is balanced when both mass number and atomic number are conserved.

Concept

The concept and thought that best describes the cause of the phenomenon is below.

Nuclear reactions involve changes inside the nucleus. When a nucleus decays or reacts, the particles before and after the reaction must obey conservation laws.

The two main rules used in Year 11 nuclear equation balancing are:

1. Conservation of nucleon number The total mass number, , must be the same on both sides.

2. Conservation of charge The total atomic number, , must be the same on both sides.

For a general nuclear equation:

The equation is balanced if:

and

Convention

The key conventions associated with the concept and in the branch of established knowledge is below.

Nuclides are written using notation:

• is the chemical symbol.
• is the mass number, equal to protons plus neutrons.
• is the atomic number, equal to the number of protons.
• The element identity is determined by , not by .
• The mass number is written as the upper-left number.
• The atomic number is written as the lower-left number.

Common radiation particles are written as:

Radiation type	Nuclear symbol	Change to nucleus
Alpha,	or	decreases by , decreases by
Beta negative,	or	unchanged, increases by
Beta positive,	or	unchanged, decreases by
Gamma,		unchanged, unchanged

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.

• Students may think the chemical symbol determines the atomic number, rather than recognising that the atomic number determines the chemical symbol.
• Students may add or subtract only the mass numbers and forget to balance atomic numbers.
• Students may think beta particles have mass number because they are particles, but beta particles are written with mass number .
• Students may confuse beta positive and beta negative decay, especially the sign of the beta particle’s atomic number.
• Students may think gamma decay changes the element, but gamma radiation has and , so the nucleus remains the same nuclide.

Further Reading

• QCAA Physics Unit 1: Ionising Radiation and Nuclear Reactions
• Periodic table for identifying elements using atomic number
• Nuclear radiation properties: alpha, beta positive, beta negative and gamma radiation
• Natural radioactive decay and nuclear stability

Explicit Instruction

To balance a nuclear equation:

1. Write the known equation using notation.
2. Add the mass numbers on each side.
3. Add the atomic numbers on each side.
4. Use conservation of mass number to find missing .
5. Use conservation of atomic number to find missing .
6. Use the periodic table to identify the element with that atomic number.
7. Check that both sides are balanced.

Important rule:

Worked Examples

Worked Example 1

Balance the alpha decay equation:

Step 1: Let the missing nuclide be .

Step 2: Balance mass number.

Step 3: Balance atomic number.

Step 4: Identify the element.

The element with atomic number is thorium, .

Final balanced equation:

Check:

Mass number:

Atomic number:

Worked Example 2

Balance the beta negative decay equation:

Step 1: Let the missing nuclide be .

Step 2: Balance mass number.

Step 3: Balance atomic number.

Step 4: Identify the element.

The element with atomic number is nitrogen, .

Final balanced equation:

Check:

Mass number:

Atomic number:

Worked Example 3

Balance the beta positive decay equation:

Step 1: Let the missing nuclide be .

Step 2: Balance mass number.

Step 3: Balance atomic number.

Step 4: Identify the element.

The element with atomic number is neon, .

Final balanced equation:

Check:

Mass number:

Atomic number:

Check for Understanding

Check 1

Is the following equation balanced?

Mass number check:

Atomic number check:

Answer: Yes, the equation is balanced.

Check 2

Find the missing particle:

Mass number:

Atomic number:

The missing particle is , a beta negative particle.

Balanced equation:

Check 3

Find the missing nuclide:

Mass number:

Atomic number:

The element with atomic number is oxygen, .

Balanced equation:

Investigation (Alternative to Explicit)

Hypothesis

If nuclear equations obey conservation of nucleon number and charge, then unknown nuclides and emitted particles can be identified by balancing total and total on both sides of the equation.

Data Collection

Students are given a set of incomplete nuclear equations involving alpha, beta positive, beta negative and gamma emissions.

Example data table:

Equation	Missing item	Total left	Total right	Total left	Total right

Students complete the table, identify the missing item and classify the type of radiation.

Analysis

Students compare the total and total values before and after each reaction.

Guiding questions:

1. Which quantity is conserved by balancing mass numbers?
2. Which quantity is conserved by balancing atomic numbers?
3. Why does alpha decay change both and ?
4. Why does beta decay change but not ?
5. Why does gamma emission not change the nuclide?

Evaluation

Students evaluate their balancing process by checking:

• Did both sides have the same total ?
• Did both sides have the same total ?
• Was the element symbol consistent with the atomic number?
• Was the emitted particle consistent with the type of decay?
• Were beta positive and beta negative particles given the correct sign for ?

Problems

The following problems are designed to build fluency in balancing nuclear equations.

Problem 1

Balance the alpha decay equation:

Problem 2

Balance the beta negative decay equation:

Problem 3

Balance the beta positive decay equation:

Problem 4

Find the missing particle:

Problem 5

Find the missing particle:

Problem 6

Balance the gamma emission equation:

Problem 7

A nucleus of uranium-235 absorbs a neutron and undergoes fission:

Find .

Mass number:

Atomic number:

Balanced equation:

Problem 8

Complete the equation and identify the type of decay:

Problem 9

Complete the equation and identify the type of decay:

Problem 10

A student writes:

Is the equation balanced? Explain your answer.

Followup

Self-check

Before submitting a nuclear equation, ask:

1. Are all particles written in notation?
2. Are the total mass numbers equal?
3. Are the total atomic numbers equal?
4. Does the chemical symbol match the atomic number?
5. Is the type of decay consistent with the emitted particle?

Answers to selected problems:

4. , beta negative decay
5. , beta positive decay
7. , beta positive decay
8. , beta negative decay
9. No. The mass numbers balance because , but the atomic numbers do not balance because . The right-hand side totals , so it is actually balanced. Therefore the equation is balanced. This is alpha decay.

Next Topic

Describe spontaneous alpha, beta positive and beta negative decay using decay equations.