Radioactivity and Nuclear Equations
Nuclear chemistry is the study of changes in the nucleus of an atom, which is the dense central region
containing protons and neutrons (collectively called nucleons). These changes are different from
ordinary chemical reactions, which involve electrons.
Key Definitions and Concepts
Atomic Number (Z): Number of protons in the nucleus. It defines the identity of an element.
Mass Number (A): Sum of protons and neutrons in the nucleus.
Nuclide: A specific type of atom or nucleus characterized by its number of protons, neutrons, and energy
state. Denoted as:
𝐴
𝑋
𝑍
where X is the element symbol, A is the mass number, and Z is the atomic number.
Isotopes: Atoms of the same element (same Z) with different numbers of neutrons (different A). For
example, carbon-12, carbon-13, and carbon-14 are all isotopes of carbon.
Shorthand Notation: Nuclides can also be written as “Element-Mass Number” (e.g., carbon-14), C-14, or
¹⁴C.
Nuclear Energy States



Ground State: The lowest energy state of a nucleus.
Excited State: A temporary higher energy state.
Metastable State (m): A long-lived excited state. For example:
Technetium-99 (Tc-99) has a ground state and a metastable form: Tc-99m.
Tantalum-180 (Ta-180) has one ground state and several metastable forms, labeled by increasing energy.
Nuclear Reactions



Involve changes in the nucleus: the identity of an atom may change.
Conservation Laws: The sum of mass numbers and atomic numbers must be the same on both
sides of the nuclear equation.
Common particles in reactions include:
α (alpha particles): Helium nuclei (²⁴He)
β⁻ (beta-minus): Electrons (e⁻)
β⁺ (beta-plus): Positrons (e⁺)
γ (gamma rays): High-energy electromagnetic radiation
p⁺ (protons) and n⁰ (neutrons)
Radioactive Decay
Unstable nuclides undergo radioactive decay, transforming spontaneously into other nuclides:


The original is the parent nuclide
The resulting product is the daughter nuclide
Types of decay:

Alpha Decay (α):
Emits an alpha particle (⁴₂He)
Mass number decreases by 4, atomic number decreases by 2
Example: ²³⁸U → ²³⁴Th + α

Beta-minus Decay (β⁻):
A neutron turns into a proton; emits an electron
Atomic number increases by 1, mass number unchanged

Beta-plus Decay (β⁺):
A proton turns into a neutron; emits a positron
Atomic number decreases by 1, mass number unchanged

Gamma Decay (γ):
Emits high-energy photons
No change in atomic or mass numbers; often follows α or β decay

Proton Emission:
Loss of a proton
Atomic and mass numbers each decrease by 1

Neutron Emission:
Loss of a neutron
Mass number decreases by 1, atomic number unchanged
Types of Radioactivity
Radioactive decay is the spontaneous transformation of an unstable nucleus into a more stable one by
emitting particles or electromagnetic radiation. This results in the formation of a daughter nuclide and
often releases energy.
Types of Radioactive Decay
1. Alpha (α) Decay
What is emitted? An alpha particle (⁴₂He) – 2 protons + 2 neutrons.
Effect on nucleus:
Mass number decreases by 4
Atomic number decreases by 2
Occurs in: Heavy elements (A > 200, Z > 83)
Penetration: Very low – blocked by paper or skin
2. Beta-minus (β⁻) Decay
What is emitted? A high-energy electron and antineutrino
Effect on nucleus:
A neutron → proton
Atomic number increases by 1
Mass number remains unchanged
Occurs in: Neutron-rich nuclei
Penetration: Moderate – can be blocked by aluminum
3. Beta-plus (β⁺) Decay (Positron Emission)
What is emitted? A positron (β⁺) and a neutrino
Effect on nucleus:
A proton → neutron
Atomic number decreases by 1
Mass number remains unchanged
Special note: The emitted positron quickly annihilates with an electron, releasing two 511 keV gamma
rays
4. Gamma (γ) Decay
What is emitted? A gamma ray (high-energy photon)
Effect on nucleus:
No change in mass or atomic number
Only a drop from excited state to ground state
Often accompanies: α or β decay
Penetration: Very high – needs lead or thick concrete for shielding
5. Neutron Emission
What is emitted? A neutron
Effect on nucleus:
Mass number decreases by 1
Atomic number remains the same
Occurs in: Some unstable or bombarded nuclei
Penetration: High – can be slowed down by materials like water or plastic
6. Electron Capture
What is captured? An inner-shell electron
Effect on nucleus:
A proton → neutron
Atomic number decreases by 1
Mass number remains unchanged
Emits: X-rays when outer electrons drop to fill the inner vacancy
Nuclear Stability
Nuclear Structure and Forces



Nucleus Composition: Contains protons and neutrons (nucleons), and is extremely dense (~1.8 ×
10¹⁴ g/cm³).
Size Comparison: Nucleus (~10⁻¹⁵ m) is much smaller than the whole atom (~10⁻¹⁰ m).
Strong Nuclear Force: Overcomes electrostatic repulsion between protons, acting only over very
short distances (<10⁻¹⁵ m).
Band of Stability



Stable nuclei lie in a region called the band (or belt) of stability, where the neutron-to-proton
(n:p) ratio is optimal.
Light nuclides: Stable at n:p ≈ 1:1.
Heavier nuclides: Require more neutrons (n:p > 1) to counteract proton repulsion.
Nuclear Decay Modes
1. Alpha (α) Decay



Emission of 2 protons + 2 neutrons.
Decreases atomic number by 2 and mass number by 4.
Common in heavy nuclei (Z > 83).
2. Beta-minus (β⁻) Decay



Neutron → proton + electron + antineutrino.
Increases atomic number by 1; mass number unchanged.
Reduces high n:p ratio.
3. Beta-plus (β⁺) Decay (Positron Emission)



Proton → neutron + positron + neutrino.
Decreases atomic number by 1.
Fixes low n:p ratio.
4. Electron Capture



Inner electron + proton → neutron + neutrino.
Decreases atomic number by 1; no change in mass number.
Often accompanied by X-ray emission.
5. Gamma (γ) Emission



Emission of high-energy photons from excited nuclei.
No change in mass or atomic number.
Often follows α or β decay.
6. Neutron Emission



Loss of a neutron.
Mass number decreases by 1; atomic number unchanged.
Can be spontaneous or induced.
Stability Considerations
Even-even nuclei (even Z and N) are especially stable due to nucleon pairing.
Magic Numbers (2, 8, 20, 28, 50, 82, 126) correspond to full nucleon shells and enhanced stability.
Doubly Magic Nuclei: Have both proton and neutron magic numbers — very stable.
All nuclei with Z > 82 are radioactive, but some (e.g. Bi-209) decay extremely slowly.
Decay Chains
Radionuclides far from the band of stability undergo a series of decays (decay series) until reaching a
stable nucleus.
Three main natural decay series: Uranium, Thorium, and Actinium (Neptunium series is extinct on Earth
due to short half-lives).
Penetration and Shielding
Alpha particles: Least penetrating; stopped by paper/skin.
Beta particles: Medium; blocked by plastic or glass.
Gamma rays & neutrons: Highly penetrating; require dense shielding like lead (γ) or water/concrete
(neutrons).
Nuclear Binding Energy
What is Mass Defect?
The mass defect is the difference between:
The total mass of individual protons, neutrons, and electrons in an atom, and
The measured mass of the actual atom.
For helium-4, the calculated mass is 4.0331 amu, but the measured mass is 4.0026 amu, giving a mass
defect of 0.0305 amu.
This “missing” mass has been converted into energy released during nuclear formation.
Einstein’s Mass–Energy Equivalence
Given by:
E = mc^2
where:
E = energy
m = mass (in kg)
c = speed of light
Convert mass from amu to g/mol → then to kg/mol:
0.0305 g/mol=3.05×10−5 kg
Binding energy for helium-4:
E=(3.05×10−5 kg/mol)⋅(3.00×108 m/s)2=2.74×1012 J/mol=2.74 TJ
Binding Energy per Nucleus
Divide molar energy by Avogadro’s number:
2.74×10^12J/mol / 6.022×10^23 = 4.55×10^−12J/nucleus=4.55pJ

Convert to MeV using:
1eV=1.602×10^−19J  28.4MeV
Binding Energy per Nucleon

Helium-4 has 4 nucleons →
28.4MeV/4=7.1MeV/nucleon
Radioactive Decay and Radiometric Dating

Radioactivity is the spontaneous decay of an unstable nucleus, releasing radiation.

It is a random process, so not all nuclei decay at the same time.

The activity (A) of a radioactive sample is the number of disintegrations per second and is
proportional to the number of undecayed nuclei (N).

The decay constant (λ) is the probability that a single nucleus will decay per unit time.
Units of Activity

SI unit: Becquerel (Bq) = 1 disintegration per second

Curie (Ci) = 3.7 × 10¹⁰ Bq (used for large-scale sources)
Decay and Half-Life

Activity decreases exponentially over time:
o

Half-life (t₁/₂): time required for half of the radioactive atoms to decay.
It’s related to the decay constant by:
o

A=A0e^−λt
t1/2=ln2/λ
The half-life is constant for a given nuclide and unaffected by external conditions.
Radiometric Dating

Carbon-14 dating is used for once-living materials up to 50,000 years old.

Living organisms maintain a steady C-14 to C-12 ratio with the atmosphere.

Upon death, the ratio decreases as C-14 decays, allowing us to estimate age:
o
One half-life (5730 years): 50% C-14 left
o
Two half-lives (11,460 years): 25% C-14 left
Dating with Other Nuclides

Uranium-238 to Lead-206: Used for dating rocks; half-life = 4.5 billion years.

Potassium-40 to Argon-40: Also used in geological dating; half-life = 1.25 billion years.

These methods assume all daughter isotopes formed from the decay of parent isotopes.
Nuclear Fission
Nuclear fission is a nuclear process in which a heavy atomic nucleus (typically with a mass number over
200, such as uranium-235) splits into two or more smaller nuclei—called fission fragments—along with
free neutrons and a tremendous amount of energy. This occurs because the binding energy per nucleon
increases for nuclei closer to mass number 56 (the peak of stability), making fission energetically
favorable for heavy nuclei.
Fission Characteristics

Fission is typically induced by the bombardment of a heavy nucleus with a neutron.

The products of fission vary from reaction to reaction, but the total mass number and atomic
number are conserved.

In addition to prompt neutrons (released immediately), delayed neutrons may be emitted after
beta decays of the fission fragments.

The mass defect (the “missing” mass in the products compared to the reactants) is converted
into a large amount of energy via Einstein’s equation E=mc2E = mc^2E=mc2.
o
For instance, 1 mole of U-235 releases = 1.8×10^10 kJ.
o
1 kg of U-235 yields 2.5 million times the energy of 1 kg of coal.
Chain Reactions

Each fission event can release 2–3 neutrons. If these neutrons trigger further fission reactions, a
nuclear chain reaction occurs.

Neutrons are classified as:

o
Fast neutrons: High kinetic energy; typically escape or pass through nuclei without
causing fission.
o
Thermal (slow) neutrons: Lower energy; more effective at causing fission in fissile
materials like U-235 or Pu-239.
Neutrons can create generations in a chain:
o
Generation 1: The original initiating neutron.
o
Generation 2: Neutrons from fissions caused by Gen 1.
o
And so on.
Controlling the Reaction
Whether a chain reaction sustains, dies out, or escalates depends on the number of neutrons available
for further fission:

Critical mass: Minimum amount of fissionable material needed to maintain a chain reaction.

Subcritical mass: Not enough material—neutrons escape too easily and the reaction stops.

Supercritical mass: Excess material—reaction accelerates and energy output increases
exponentially.
Factors Affecting Critical Mass:

Shape: A sphere retains neutrons better than a flat shape.

Temperature: Higher temperatures reduce density, increasing neutron escape.

Purity of material: Impurities absorb neutrons or inhibit fission.

Neutron reflectors: Materials like graphite or beryllium can surround fissionable material to
reflect escaping neutrons back into the core, lowering the required critical mass.
Nuclear Power

Nuclear fission is the process in which a heavy atomic nucleus splits into smaller, more stable
nucleus with intermediate mass numbers.

This process releases a tremendous amount of energy, largely because the total binding energy
per nucleon increases as nuclei approaches iron (Fe-56), which is at the peak of nuclear stability.

Fission often produces two smaller nuclei and two to three free neutrons.

Neutrons released can trigger further fissions, leading to a nuclear chain reaction.

Natural fission is rare; it typically requires induced neutron bombardment.
Energy Release

The energy release from fission is due to the conversion of a small amount of mass into energy,
as described by Einstein’s E=mc^2

1 mole of U-235 undergoing fission releases about 1.8 × 10¹⁰ kJ.

1 kg of uranium-235 produces roughly 2.5 million times more energy than 1 kg of coal.
Chain Reactions and Critical Mass

A chain reaction occurs when neutrons from one fission induce further fissions.

For the chain reaction to be self-sustaining, the number of neutrons produced must equal or
exceed the number lost.

The minimum amount of fissile material needed to sustain this is called the critical mass.
o
Subcritical mass: Not enough to sustain a chain reaction.
o
Supercritical mass: Leads to an increasing rate of fission.

Factors affecting critical mass include:
o
Shape: Spheres minimize neutron loss.
o
Purity: More pure material means better chances of fission.
o
Temperature: Hotter materials are less dense; neutrons escape more easily.
o
Neutron reflectors (like graphite) reduce neutron loss and reduce needed mass.
Neutrons and Fission Dynamics

Neutrons released are typically fast-moving.

These must be slowed down (moderated) to efficiently induce fission in fissile materials.

Some neutrons are prompt, while others are delayed, released after beta decay of fission
products.

Fission chains are described in generations: 1st-gen neutron starts with it, 2nd-gen neutrons
come from first fissions, etc.
Nuclear Power
General Setup
Modern nuclear power plants use controlled nuclear fission to produce electricity. A functioning nuclear
reactor includes:
1. Nuclear fuel
2. Nuclear moderator
3. Neutron source
4. Control rods
5. Reactor coolant
6. Shield and containment system
1. Nuclear Fuels

Primary fuel: Uranium-235, a fissile isotope.

Fuel is enriched to 3–5% U-235 (natural uranium is only 0.7% U-235).

Encased in ceramic fuel pellets inside fuel rods; reactors may contain millions of pellets.
2. Nuclear Moderators

Function: Slow down fast neutrons to thermal energies, where fission is more likely.

Common moderators:
o
Light water (contains hydrogen): slows neutrons via elastic collisions.

o
Heavy water (contains deuterium): even better; less neutron absorption.
o
Graphite: used in older reactors.
Moderators also act as neutron reflectors, helping maintain a uniform neutron distribution.
3. Neutron Source

Spontaneous fission in uranium is rare, so external neutron emitters are used to start the chain
reaction.

Example: Beryllium-9 with an alpha emitter (like plutonium-239 or americium-249).
4. Control Rods

Made of neutron-absorbing materials: boron, cadmium, hafnium.

Control the reaction by adjusting how many thermal neutrons remain available.

Neutron multiplication factor (k) describes the reaction status:

o
k < 1: Subcritical — reaction dies out.
o
k = 1: Critical — steady output.
o
k > 1: Supercritical — increasing reaction.
In emergencies, rods are fully inserted to halt the chain reaction.
5. Reactor Coolants

Transfers heat from the reactor core to a turbine, where electricity is generated.

Common coolants: Water, molten sodium, molten salts, or lead-based liquids.

Coolant systems often use two separate loops to avoid radioactive contamination reaching the
turbine.
6. Shield and Containment System

Multilayer protection to contain radiation:
1. Steel shell absorbs neutrons.
2. Thick concrete shield blocks gamma and X-rays.
3. External dome prevents release during accidents.

These layers prevent radiation leaks and protect both people and the environment.
Nuclear Fusion
Nuclear fusion is the process where light nuclei, such as hydrogen isotopes (deuterium and tritium),
combine to form heavier nuclei, like helium, releasing significant energy due to mass loss converted
into energy (e.g., 1.69 × 10⁹ kJ per mole of helium-4). This occurs because the binding energy per
nucleon of the product nucleus is higher than that of the reactants. For example, fusing four
hydrogen nuclei into helium-4 results in a 0.7% mass loss, producing 1.7 × 10⁹ to 2.6 × 10⁹ kJ per
mole, depending on the pathway. On a per-gram basis, fusion of helium-4 yields more energy (6.5 ×
10⁸ kJ/g) than fission of U-235 (8.5 × 10⁷ kJ/g), and fusion reactants are abundant and inexpensive.
Fusion requires extremely high temperatures (≥15,000,000 K) to overcome electrostatic repulsion
between positively charged nuclei, creating a plasma where atoms are ionized. These conditions are
common in stars, like the Sun, where hydrogen fusion powers energy production. In stars,
subsequent fusion reactions (e.g., helium to beryllium-8, then carbon-12) produce heavier elements
up to nickel-56, which has one of the highest binding energies per nucleon. Heavier elements form
via neutron/proton capture during supernovae.
Fusion reactions are thermonuclear, requiring temperatures of 40 million K or more. Lighter nuclei
(mass numbers <40) with lower binding energies fuse to form more stable nuclei (mass numbers 40–
100) with higher binding energies. However, as heavier nuclei form, the energy released decreases
due to smaller binding energy differences.
On Earth, creating self-sustaining fusion reactors is challenging due to the difficulty of containing
plasma at such high temperatures. Current research focuses on magnetic confinement (e.g.,
tokamak reactors) and laser-based inertial confinement, but no operational, self-sustaining fusion
reactors exist yet, though small-scale controlled reactions have been achieved briefly.
Comparison to Fission:

Energy Output: Fusion produces less energy per mole than U-235 fission (1.8 × 10¹⁰ kJ/mol) but
more per gram due to lighter reactants.

Reactants: Fusion uses abundant hydrogen isotopes; fission relies on rare U-235.

Applications: Fission is used in nuclear power plants; fusion is not yet practical for electricity
generation.

Conditions: Fission is induced by neutrons at normal temperatures; fusion requires extreme
temperatures and plasma containment.
Nuclear Transmutation
Nuclear transmutation is the process of converting one nuclide (or nucleus) into another. This can occur
in several ways:

Radioactive decay (natural or induced)

Nuclear fusion (combining nuclei)

Nuclear fission (splitting nuclei)
The most significant historical example of artificial transmutation occurred in 1919, when Ernest
Rutherford bombarded nitrogen-14 with alpha particles (α) and observed the ejection of protons,
producing oxygen-17. This marked the first manmade nucleus.
Procedure for Transmutation
To initiate nuclear transmutation, high-energy particles like neutrons or alpha particles are required. The
process is typically carried out using particle accelerators, which increase the speed of particles through
magnetic and electric fields. The high speeds allow particles to overcome electrostatic repulsion and
induce transmutation reactions.
1. Particle Accelerators: These devices are used to impart kinetic energy to charged nuclear
particles.
o
Linear accelerators (linacs) use increasing tube lengths with alternating polarity to
accelerate particles.
o
Cyclotrons accelerate particles in a spiral path.
2. Transmutation Reactions:
o
The reaction is written in a condensed notation, showing the target nucleus, bombarding
particle, ejected particle, and product nucleus.
o
For example, when uranium-238 is bombarded with neutrons, it transforms into
neptunium-239, which then decays into plutonium-239.
Examples of Nuclear Transmutation

Transuranium Elements: These are elements with atomic numbers greater than 92, such as
neptunium and plutonium, which are synthesized through transmutation reactions. Neptunium239 and plutonium-239 are notable examples created in reactors via the bombardment of
uranium-238 with neutrons.

Plutonium and Curium: When plutonium-239 is bombarded with high-speed alpha particles, it
produces curium-244 (atomic number 96).

Copernicium: Lead-208 bombarded with zinc-70 results in the creation of copernicium-277, a
transuranium element. This element decays through a chain of reactions eventually leading to
bismuth-209.
Nuclear Medicine and Practical Applications

Medical Uses: Radioactive isotopes produced through transmutation are used in nuclear
medicine for imaging and treatment. They allow for tracking specific organs or areas of the body
using radiation produced by their decay.
Biological Effects of Radiation
Radiation, whether particle-based or electromagnetic, can cause biological damage when it interacts
with living cells. This damage occurs due to the high-energy emissions, which can ionize molecules or
break chemical bonds. Here’s a breakdown of how radiation affects biological systems:
Types of Radiation and Their Effects
1. Ionizing Radiation:
o
Alpha (α) and Beta (β) Particles: These have high energy compared to typical chemical
bonds. When they interact with living matter, they produce ions and molecular
fragments that are highly reactive, leading to cellular damage.
o
Gamma Rays (γ) and X-rays: These types of radiation also have significant ionizing power,
capable of penetrating deep into tissues and causing indirect molecular damage by
ionizing water molecules in cells. This produces hydroxyl radicals (OH), which can further
damage DNA and other biomolecules.
2. Non-Ionizing Radiation:
o
Examples include microwaves and light. These do not have enough energy to ionize
molecules but can cause heating by accelerating atomic motion. While they can harm
biological systems due to the heat produced, their effects are much less severe
compared to ionizing radiation.
Mechanism of Damage

Ionization and Fragmentation: High-energy radiation can break molecular bonds, directly
damaging important biomolecules like DNA, proteins, and enzymes. This can disrupt normal
cellular processes, leading to dysfunction.

Radicals and Indirect Damage: Ionizing radiation can also damage cells indirectly. For example,
the ionization of water molecules (H2O) creates hydroxyl radicals (OH•), which are highly
reactive and can cause further molecular damage, leading to cellular injury or death.
Measuring Radiation

Absorbed Dose: The energy deposited by radiation per unit mass, measured in grays (Gy). One
gray corresponds to one joule of energy deposited per kilogram of material.

Radiation Weighting Factor: The biological impact of different radiation types varies. For
example, alpha particles are much more damaging than gamma rays for the same absorbed
dose. This is taken into account using a radiation weighting factor, which adjusts the absorbed
dose to calculate the equivalent dose in sieverts (Sv).
o
Radiation Weighting Factors:

Gamma, X-rays: 1

Beta particles: 1

Alpha particles: 20

Neutrons: 10 (depending on energy type)
Tissue Sensitivity

Different tissues in the body have varying sensitivities to radiation. For example, reproductive
tissues are more sensitive to radiation than muscle tissues. To account for this, the equivalent
dose is multiplied by tissue weighting factors, and the effective dose is calculated to estimate the
overall damage to the body.
Radiation Exposure and Health Effects

Short-Term Exposure: High doses of radiation (e.g., 500 rems or 5 Sv) can lead to immediate
health effects, ranging from blood chemistry changes to death, depending on the severity of
exposure. A dose of around 500 rems has a 50% chance of causing death within 30 days.

Long-Term Exposure: Cumulative exposure to radiation throughout a lifetime increases the risk
of cancer and other health problems. Chronic exposure to low levels of radiation can lead to
long-term biological effects.
Radiation Detection
Different devices are used to detect and measure radiation, with each having specific strengths and
applications:

Geiger-Müller (GM) Counter: Detects ionizing radiation like alpha, beta, X-rays, and gamma rays.
It can be adapted to measure the energy of radiation and, in certain cases, serve as a personal
dosimeter.

Scintillation Counter: Uses a scintillator material that emits light when ionized. This light is
converted into an electrical signal to measure radiation.

Radiation Dosimeters: These devices measure personal exposure to radiation. Common types
include electronic dosimeters, film badges, thermoluminescent dosimeters (TLDs), and quartz
fiber dosimeters.
Background Radiation


People are constantly exposed to low levels of natural radiation from sources like cosmic rays,
radon, and naturally occurring radionuclides (e.g., carbon-14 and potassium-40).
Medical radiation, such as from X-rays or CAT scans, also contributes to an individual’s total radiation
exposure.