Nuclear reactions

IB Physics SL· 5.3 Nuclear reactions· 25 min read

1. Balancing Nuclear Reaction Equations★★☆☆☆⏱ 15 min

All nuclear reactions conserve two core quantities across reactants and products: total atomic number (proton number) and total mass number (nucleon number). Conservation of electric charge is automatically satisfied if atomic number is conserved, so you only need to check these two values to balance any reaction.

📘 Definition

Nuclide Notation

$_{Z}^{A} X$

$Z$ = atomic number (number of protons), $A$ = mass number (total number of protons + neutrons), $X$ = chemical symbol of the nuclide.

📐 Worked Example

Complete the alpha decay reaction of uranium-238: $_{92}^{238} U \to_{?}^{?} Th +_{2}^{4} α$

1
Conserve total atomic number across both sides of the reaction
$92 = Z + 2 \implies Z = 92 - 2 = 90$
2
Conserve total mass number across both sides of the reaction
$238 = A + 4 \implies A = 238 - 4 = 234$
3
The resulting thorium nuclide is therefore
$_{90}^{234}\text{Th}$

Exam tip:

Always balance both atomic and mass number even if only one is requested — this catches simple arithmetic mistakes.

2. Mass Defect and Energy Release (Q-value)★★★☆☆⏱ 20 min

Per Einstein's mass-energy equivalence $E = m c^{2}$ , mass difference between reactants and products in a nuclear reaction is converted to energy. This energy change is called the Q-value of the reaction. A positive Q-value means energy is released (exothermic), while a negative Q-value means energy must be added (endothermic).

📘 Definition

Q-value

The net energy released or absorbed in a nuclear reaction, calculated from the mass difference between reactants and products.

📐 Worked Example

Calculate the Q-value for the alpha decay of U-238, given $m_{reactants} = 238.050788$ u, $m_{products} = 238.044616$ u. Use 1 u = 931.5 MeV/ $c^{2}$ .

1
Calculate the mass difference between reactants and products
$\Delta m = m_{\text{reactants}} - m_{\text{products}} = 0.006172 \text{ u}$
2
Substitute into mass-energy equivalence to find Q
$Q = \Delta m c^2 = 0.006172 \text{ u} \times 931.5 \frac{\text{MeV}}{c^2 \cdot \text{u}} \times c^2 \approx 4.2 \text{ MeV}$
3
The positive Q confirms 4.2 MeV of energy is released in this spontaneous decay.

3. Nuclear Fission★★★☆☆⏱ 15 min

Nuclear fission occurs when a heavy, unstable nucleus absorbs a slow neutron and splits into two smaller lighter nuclei (fission fragments), releasing energy and multiple free neutrons. These extra neutrons can trigger further fission events, creating a self-sustaining chain reaction used in nuclear power reactors.

📘 Definition

Nuclear fission

A nuclear reaction where a heavy nucleus splits into two lighter nuclei of comparable mass, releasing energy and free neutrons.

Example:

Fission of uranium-235 in commercial nuclear power plants

📐 Worked Example

Find the number of neutrons produced in this fission reaction: $_{0}^{1} n +_{92}^{235} U \to_{56}^{141} Ba +_{36}^{92} Kr + x_{0}^{1} n$

1
Check atomic number balance first
$\text{Total Z left} = 0 + 92 = 92; \text{Total Z right} = 56 + 36 + 0 = 92$
2
Balance mass number to solve for x
$1 + 235 = 141 + 92 + x(1) \implies 236 = 233 + x \implies x = 3$
3
This reaction produces 3 free neutrons, which can sustain a chain reaction.

4. Nuclear Fusion★★★☆☆⏱ 15 min

Nuclear fusion is the opposite of fission: two light nuclei combine to form a single heavier nucleus. Energy is released because the product nucleus has a higher binding energy per nucleon than the reactant light nuclei. Fusion is the energy source that powers stars like our Sun.

📘 Definition

Nuclear fusion

A nuclear reaction where two light nuclei fuse to form a single heavier nucleus, releasing large amounts of energy.

Example:

Proton-proton fusion in the core of the Sun

📐 Worked Example

Calculate the energy released in deuterium-tritium fusion: $_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n$ . Given masses: $m_{2} H = 2.014102$ u, $m_{3} H = 3.016049$ u, $m_{4} H e = 4.002603$ u, $m_{n} = 1.008665$ u.

1
Calculate total mass of reactants
$m_{\text{reactants}} = 2.014102 + 3.016049 = 5.030151 \text{ u}$
2
Calculate total mass of products
$m_{\text{products}} = 4.002603 + 1.008665 = 5.011268 \text{ u}$
3
Calculate energy released Q
$Q = (5.030151 - 5.011268) \times 931.5 \approx 17.6 \text{ MeV}$
4
This fusion reaction releases ~4x more energy per kilogram of fuel than fission.

5. Common Pitfalls

Wrong move:

Only balance mass number and ignore atomic number

Why:

Many questions only ask for the mass number of an unknown product, but mistakes in atomic number often lead to wrong mass values anyway

Correct move:

Always balance both atomic number and mass number for every nuclear reaction, even if only one is requested

Wrong move:

Reverse the mass difference when calculating Q-value

Why:

Subtracting reactant mass from product mass gives a negative Q for exothermic reactions that release energy

Correct move:

Always use $Q = (m_{reactants} - m_{products}) c^{2}$ , so positive Q means energy is released

Wrong move:

Confuse fission and fusion in exam questions

Why:

Both release energy, but for different mass ranges, so it is easy to mix up the definitions

Correct move:

Remember: Fission = Fissioning (splitting) a heavy nucleus, Fusion = Fusing (joining) light nuclei

Wrong move:

Leave energy in MeV when the question asks for joules

Why:

MeV is convenient for nuclear problems, but exam questions often require SI units for full marks

Correct move:

Convert MeV to joules by multiplying by $1.6 \times 1 0^{- 13}$ J/MeV when requested

6. Quick Reference Cheatsheet

Concept	Key Rule/Value
Balancing reactions	Conserve atomic number (Z) and mass number (A)
Q-value calculation	$Q = (m_{r e a c t an t s} - m_{p r o d u c t s}) c^{2}$ , +Q = energy released
Unit conversion	1 u = 931.5 MeV/ $c^{2}$
Nuclear fission	Heavy nucleus splits into two lighter nuclei
Nuclear fusion	Two light nuclei join to form one heavier nucleus

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · Paper 1
Balance nuclear reaction equation
2021 · Paper 2
Calculate energy from fission
2023 · Paper 1
Energy released in fusion reaction

Going deeper

syllabusIB Physics SL Official SyllabusFull unit 5 content outline

What's Next

Nuclear reactions are the foundation of all applied nuclear physics, from medical imaging to commercial power generation. The balancing and calculation skills you mastered here are required for all subsequent nuclear physics topics, and are regularly tested in both Paper 1 and Paper 2 IB exams. Next, you will explore radioactive decay kinetics and half-life calculations, which rely on your ability to balance decay reactions. This topic also connects to binding energy per nucleon trends, which explain why both fission and fusion release energy, and to energy production topics that cover the environmental impact of nuclear power.

→Nuclear fission and fusion