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1. Introduction

Nuclear chemistry is the branch of chemistry that deals with the composition, structure, properties and reactions of atomic nuclei.

Ordinary chemical reactions mainly involve the rearrangement of electrons surrounding the nucleus. Nuclear reactions involve changes in the nucleus itself.

Nuclear changes can release very large amounts of energy because nuclear binding energies are much greater than ordinary chemical bond energies.

Main topics in nuclear chemistry

• Radioactivity
• Nuclear decay
• Alpha, beta and gamma radiation
• Nuclear reactions
• Nuclear stability
• Mass defect
• Binding energy
• Nuclear fission
• Nuclear fusion
• Radioisotope applications

2. Atomic Nucleus

The nucleus is the small, dense central part of an atom. It contains protons and neutrons, collectively called nucleons.

Proton

A proton has a positive charge of +1 and approximately one atomic mass unit of mass.

Neutron

A neutron has no electrical charge and has a mass close to one atomic mass unit.

Atomic number

Atomic number identifies the element.

Mass number

Therefore:

Nuclear notation

Here A is the mass number, Z is the atomic number and X represents the element.

Example

Sodium-23 contains:

3. Isotopes, Isobars and Isotones

Isotopes

Isotopes are atoms of the same element having the same atomic number but different mass numbers.

Example:

All have six protons but different numbers of neutrons.

Isobars

Isobars have the same mass number but different atomic numbers.

Example:

Isotones

Isotones have the same number of neutrons but different atomic numbers.

4. Nuclear Reaction

A nuclear reaction is a process in which the nucleus of an atom changes and one or more new nuclei or particles are produced.

In a nuclear reaction, conservation laws must be obeyed.

Important quantities that are conserved include total charge and total nucleon number.

Example

This is alpha decay.

Check the mass numbers:

Check atomic numbers:

5. Radioactivity

Radioactivity is the spontaneous disintegration of an unstable atomic nucleus with the emission of radiation.

The process is spontaneous because it does not require a continuous external supply of energy to cause each individual decay.

Natural radioactivity

Radioactivity shown naturally by unstable nuclides is called natural radioactivity.

Examples include radioactive isotopes of uranium, thorium and radium.

Artificial radioactivity

Some radioactive nuclides are produced artificially by nuclear reactions.

Important characteristics

• Radioactive decay is spontaneous.
• It is a nuclear process.
• It is largely independent of ordinary chemical conditions.
• The decay follows a statistical law.
• Different radioactive nuclides have different half-lives.

6. Types of Radiation

The three commonly discussed radioactive emissions are:

1. Alpha (α)
2. Beta (β)
3. Gamma (γ)

They differ in mass, charge, penetrating power and ionizing power.

7. Alpha Radiation

An alpha particle consists of two protons and two neutrons.

Therefore, an alpha particle has:

• Mass number = 4
• Charge = +2
• Two protons
• Two neutrons

Alpha decay

In alpha decay:

Properties

• High ionizing power
• Low penetrating power compared with beta and gamma
• Deflected by electric and magnetic fields
• Positive charge

8. Beta Radiation

Beta radiation consists of high-speed particles produced during nuclear transformations.

Beta-minus decay

In beta-minus decay, a neutron changes into a proton, producing an electron and an antineutrino.

Therefore, at the nuclear level:

In beta-minus decay:

Beta-plus decay

In beta-plus decay, a proton changes into a neutron and a positron is emitted along with a neutrino.

Therefore, the atomic number decreases by one while the mass number remains unchanged.

9. Gamma Radiation

Gamma radiation consists of high-energy electromagnetic radiation emitted by an excited nucleus.

Gamma emission does not change the atomic number or mass number.

Properties

• No mass charge
• No electric charge
• Very high penetrating power
• Lower ionizing power than alpha particles
• Not deflected by electric or magnetic fields

10. Comparison of Alpha, Beta and Gamma Radiation

A common exam point is:

11. Nuclear Equations

A nuclear equation must be balanced with respect to nuclear charge and nucleon number.

Alpha decay

Beta-minus decay

Beta-plus decay

Gamma emission

Worked example

Complete the following alpha decay:

Alpha emission decreases mass number by 4:

Atomic number decreases by 2:

Element 86 is radon.

12. Radioactive Decay Law

Radioactive decay follows first-order kinetics.

If N is the number of radioactive nuclei remaining at time t, the rate of decay is proportional to N.

where λ is the decay constant.

On integration:

Therefore:

Common logarithm form

Therefore:

This equation is very important for numerical problems.

13. Decay Constant

Decay constant is the probability per unit time that a particular radioactive nucleus will decay.

It is represented by λ.

The unit of λ is inverse time, such as s⁻¹ or yr⁻¹.

A larger λ means faster radioactive decay.

14. Half-Life

Half-life is the time required for half of the original radioactive nuclei to decay.

If the initial amount is N₀, after one half-life:

The relationship between half-life and decay constant is:

Therefore:

After multiple half-lives

After n half-lives:

For example, after three half-lives:

So 12.5% of the original radioactive nuclei remain.

15. Mean Life

Mean life is the average lifetime of radioactive nuclei.

It is represented by τ.

Since:

We get:

Or:

Therefore, mean life is longer than half-life.

16. Activity

Activity is the number of radioactive disintegrations occurring per unit time.

From the decay law:

At the beginning:

As the number of radioactive nuclei decreases, activity also decreases.

17. Units of Radioactivity

Becquerel

The SI unit of activity is the becquerel (Bq).

Curie

The curie (Ci) is an older unit of radioactivity.

Therefore:

18. Radioactive Dating

Radioactive isotopes can be used to estimate the age of certain materials because radioactive decay occurs at a predictable statistical rate.

Carbon-14 dating

Carbon-14 is used to estimate the age of once-living materials.

The basic principle is that after an organism dies, the amount of carbon-14 decreases by radioactive decay.

The same equation can be written using activity because activity is proportional to the number of radioactive nuclei.

Radioactive dating is based on measured decay and appropriate assumptions about the system being dated.

19. Nuclear Stability

Not all nuclei are stable. Nuclear stability depends on the balance between attractive nuclear forces and electrostatic repulsion between protons.

Neutron-proton ratio

For lighter stable nuclei, the number of neutrons and protons is often similar.

For heavier stable nuclei, more neutrons are needed to help offset the increasing proton-proton repulsion.

Magic numbers

Certain numbers of protons or neutrons are associated with unusually stable nuclear arrangements.

Common magic numbers include:

General idea

Nuclei far from the band of stability tend to undergo radioactive transformations that move them toward a more stable neutron-proton arrangement.

20. Mass Defect

The mass of a stable nucleus is slightly less than the sum of the masses of its individual free nucleons.

The difference is called mass defect.

The missing mass has been converted into energy during formation of the nucleus.

Einstein's mass-energy relationship is:

Therefore:

21. Binding Energy

Binding energy is the energy required to separate a nucleus completely into its individual protons and neutrons.

It is also equal to the energy released when the free nucleons combine to form the nucleus.

Using mass defect

When mass defect is in atomic mass units

A useful conversion is:

Therefore:

Binding energy per nucleon

A larger binding energy per nucleon generally indicates greater nuclear stability.

22. Packing Fraction

Packing fraction is a quantity used in nuclear chemistry to describe the difference between the isotopic mass and its mass number on an appropriate atomic mass scale.

It can be expressed as:

Depending on the convention used in a particular textbook, the exact presentation may differ. Therefore, the definition and formula given in the course text should be followed in numerical problems.

23. Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus into two or more smaller nuclei with the release of energy.

Example

A simplified representation is:

The exact fission products can vary.

Chain reaction

Neutrons released during one fission event can cause additional fission events.

This produces a chain reaction.

Controlled chain reaction

In a nuclear reactor, the chain reaction is controlled so that energy is released at a manageable rate.

Why energy is released

The fission products have, on average, greater binding energy per nucleon than the original heavy nucleus. The difference appears as released energy.

24. Nuclear Fusion

Nuclear fusion is the combination of light nuclei to form a heavier nucleus with the release of energy.

Example

Deuterium and tritium are hydrogen isotopes.

Why fusion requires high temperature

Positively charged nuclei repel each other. Therefore, very high temperature and suitable conditions are required to bring nuclei close enough for the strong nuclear force to act effectively.

Sun and stars

Nuclear fusion is the main source of energy in the Sun and other stars.

25. Nuclear Reactor

A nuclear reactor is a device in which a controlled nuclear chain reaction is maintained to produce useful energy.

Main parts

• Fuel: Contains fissionable material.
• Moderator: Slows down fast neutrons in reactor designs that use thermal neutrons.
• Control rods: Absorb neutrons and regulate the chain reaction.
• Coolant: Transfers heat away from the reactor core.
• Shielding: Reduces radiation exposure outside the reactor.

Basic energy sequence

26. Applications of Nuclear Chemistry

Medical applications

• Diagnosis using radioactive tracers
• Nuclear medicine imaging
• Treatment of certain cancers
• Sterilization of medical equipment

Industrial applications

• Thickness measurement
• Leak detection
• Tracer studies
• Examination of welds and materials

Agriculture

• Tracer studies of nutrient uptake
• Investigation of plant metabolism
• Mutation breeding under controlled conditions

Archaeology and geology

Radioactive dating methods can help estimate the age of suitable materials.

Scientific research

Radioisotopes can be used as tracers to follow chemical and biological processes.

27. Radiation Hazards

Ionizing radiation can damage biological molecules and living tissues.

Possible biological effects

• Damage to DNA
• Cell injury
• Tissue damage
• Increased risk of cancer
• Acute radiation injury at sufficiently high exposure

Basic radiation protection principles

Radiation exposure is commonly reduced by considering:

• Time
• Distance
• Shielding

Exposure should be minimized by using appropriate procedures, monitoring and shielding.

28. Solved Numericals

Numerical 1: Number of neutrons

Calculate the number of neutrons in ²³₁₁Na.

Numerical 2: Half-life from decay constant

A radioactive substance has a decay constant of 0.231 min⁻¹. Calculate its half-life.

Numerical 3: Decay constant from half-life

The half-life of a radioactive isotope is 10 hours. Calculate its decay constant.

Numerical 4: Amount remaining after three half-lives

A radioactive sample initially contains 80 g of material. How much remains after three half-lives?

Numerical 5: Fraction remaining after four half-lives

What fraction of a radioactive sample remains after four half-lives?

Numerical 6: Time required for decay

A radioactive sample decreases from 1000 nuclei to 250 nuclei. If its half-life is 5 hours, calculate the time required.

Numerical 7: Mean life

Calculate the mean life of a radioactive substance whose half-life is 20 years.

Numerical 8: Activity

A sample contains 2.0 × 10¹⁰ radioactive nuclei and has a decay constant of 0.002 s⁻¹. Calculate its activity.

Numerical 9: Binding energy from mass defect

Calculate the binding energy of a nucleus if its mass defect is 0.010 u.

Numerical 10: Binding energy per nucleon

A nucleus has total binding energy of 56 MeV and mass number 7. Calculate its binding energy per nucleon.

Numerical 11: Decay constant using the decay equation

A radioactive sample decreases from 800 mg to 200 mg in 12 hours. Calculate its decay constant.

Numerical 12: Half-life from the previous result

Using λ = 0.1156 h⁻¹, calculate the half-life.

29. Practice Questions

30. Common Mistakes

• Do not confuse mass number with atomic number.
• In alpha decay, both A and Z decrease.
• In beta-minus decay, A remains the same and Z increases by one.
• In beta-plus decay, A remains the same and Z decreases by one.
• Gamma emission changes neither A nor Z.
• Half-life is not the time required for all nuclei to decay.
• After each half-life, half of the nuclei present at the beginning of that interval remain.
• The decay constant is not the same thing as half-life.
• Activity depends on both decay constant and the number of radioactive nuclei.
• Binding energy is not the same as mass defect. Mass defect is converted into binding energy.
• Fission involves splitting heavy nuclei, whereas fusion involves combining light nuclei.
• Do not write a nuclear equation without checking both mass number and atomic number.

31. TU Examination Preparation

Important 2-mark questions

1. Define radioactivity.
2. What are isotopes?
3. Define half-life.
4. Define decay constant.
5. What is mean life?
6. What is activity?
7. Define mass defect.
8. Define binding energy.
9. What is nuclear fission?
10. What is nuclear fusion?
11. What is a nuclear reactor?
12. What is a radioisotope?

Important 5-mark questions

1. Explain the properties of alpha, beta and gamma radiations.
2. Derive the radioactive decay equation.
3. Explain half-life and mean life and derive their relationship.
4. Explain mass defect and binding energy.
5. Explain nuclear fission.
6. Explain nuclear fusion.
7. Explain the applications of radioisotopes.

Important 10-mark questions

1. Explain radioactivity in detail. Discuss alpha, beta and gamma radiations with their properties and differences.
2. Derive the radioactive decay law and obtain the expressions for decay constant, half-life and mean life.
3. Explain mass defect, binding energy and nuclear stability.
4. Discuss nuclear fission, chain reaction and the working principle of a nuclear reactor.
5. Explain nuclear fusion and compare it with nuclear fission.

Numericals to prepare

• Number of protons and neutrons
• Half-life
• Decay constant
• Mean life
• Amount remaining after several half-lives
• Activity
• Radioactive dating
• Mass defect
• Binding energy
• Binding energy per nucleon

32. Quick Revision

Nuclear notation

Alpha decay

Beta-minus decay

Beta-plus decay

Gamma emission

Decay law

Half-life

Mean life

Activity

Mass-energy relation

Binding energy

Binding energy per nucleon

Radiation comparison

Nuclear processes

33. Quick Check