Physics - nuclear energy

Basis of Atomic Theory

All matter is made up of tiny particles called atoms, which are the fundamental building blocks of everything in the universe.

Atoms are electrically neutral, meaning they have no overall charge because the number of positively charged protons is equal to the number of negatively charged electrons.

Each atom is composed of smaller subatomic particles, including protons, neutrons, and electrons.

Protons are positively charged particles located in the nucleus at the center of the atom, while neutrons are neutral particles that are also found in the nucleus.

Electrons are negatively charged particles that move around the nucleus in regions called electron shells or energy levels.

Atoms are held together by electrostatic attraction, which is the force of attraction between the positively charged nucleus and the negatively charged electrons.

The proton

The proton is a positively charged subatomic particle, meaning it carries a +1 electrical charge.

Protons are located in the nucleus, which is the dense central core of the atom.

Each proton contributes to the overall mass of the atom, with a relative mass of approximately 1 atomic mass unit.

The number of protons in an atom determines the identity of the element and is equal to its atomic number, meaning every element has a unique number of protons.

The neutron

The neutron is a subatomic particle that has no electrical charge, meaning it is neutral.

Neutrons are found in the nucleus of the atom alongside protons.

They are similar in size and mass to protons, making them one of the main contributors to the atom’s overall mass.

Each neutron has a relative mass of approximately 1 atomic mass unit, so it contributes significantly to the total mass of the atom.

The number of neutrons in an atom can be determined by subtracting the atomic number from the atomic mass (mass number).

The electron

The electron is a negatively charged subatomic particle, meaning it carries a −1 electrical charge.

Electrons move around the nucleus in regions called electron shells or electron clouds, rather than fixed paths.

Electrons have a very small mass compared to protons and neutrons, with a relative mass of about 1/1800 of a proton, so their contribution to the atom’s overall mass is negligible.

In a neutral atom, the number of electrons is equal to the atomic number, which is the same as the number of protons, ensuring the atom has no overall charge.

Quarks

Quarks are fundamental particles, meaning they are some of the smallest known building blocks of matter and are not made up of anything simpler.

Quarks combine together to form larger subatomic particles, such as hadrons, including protons and neutrons.

Atomic number

The atomic number is the number of protons in the nucleus of an atom. It is one of the most important properties of an element because it determines what element the atom is.

Each element has a unique atomic number. For example, hydrogen has an atomic number of 1 (one proton), while carbon has an atomic number of 6 (six protons). This means no two different elements can have the same atomic number.

Atomic Mass

The atomic mass is the total mass of an atom’s nucleus, which is found by adding together the number of protons and neutrons.

Atomic mass is measured in units called atomic mass units (amu), which is the standard SI-related unit used for particles at the atomic scale.

Protons and neutrons each have a relative mass of approximately 1 amu, so they account for nearly all of the atom’s mass.

Electrons have a mass that is extremely small in comparison, so their contribution to the overall atomic mass is considered negligible.

Isotopes

An isotope occurs when different forms of the same element have the same number of protons but different numbers of neutrons in their nuclei.

Because the number of protons is the same, isotopes are the same element and have the same atomic number.

However, isotopes have different atomic masses due to the different numbers of neutrons.

Despite this difference in mass, isotopes have the same chemical properties because they have the same number and arrangement of electrons.

Radioisotopes

Radioisotopes are radioactive forms of an element’s isotopes, meaning they have unstable nuclei that can decay over time.

An element may have several different isotopes, but only some of these are radioisotopes, while others are stable.

Radioisotopes are defined as atoms that contain an unstable combination of protons and neutrons, or excess energy within their nucleus, which causes them to emit radiation in order to become more stable.

Radioactivity

Radioactivity is the emission of ionising radiation or particles that occurs when an unstable atomic nucleus spontaneously decays or breaks down.

This process happens because the nucleus contains an unstable combination of protons and neutrons, causing it to release energy or particles in order to become more stable.

Radioactive decay

Radioactive decay is the process by which an unstable atomic nucleus spontaneously releases energy and/or particles in order to become more stable.

This occurs because the nucleus has an imbalance of protons and neutrons or excess energy, making it unstable. To correct this, the nucleus emits ionising radiation in the form of particles (such as alpha or beta particles) or electromagnetic energy (such as gamma rays).

Radioactive decay is a random but predictable process, meaning it is impossible to know exactly when a single atom will decay, but the overall rate of decay for a large group of atoms can be measured using half-life.

As a result of radioactive decay, the original atom may change into a different element or a different isotope, depending on the type of radiation that is emitted.

Half life

Half-life is the amount of time it takes for half of the radioactive atoms in a sample to undergo radioactive decay.

It is used to measure the rate at which a radioisotope decays. During each half-life, half of the remaining unstable nuclei break down, meaning the quantity of the substance decreases by 50% each time.

Half-life is a constant value for each specific radioisotope, so it cannot be changed by external conditions such as temperature or pressure.

For example, if you start with 100 radioactive atoms, after one half-life there will be 50 left, after two half-lives there will be 25, and after three half-lives there will be 12.5 remaining.

Alpha decay (α-decay)

Alpha decay occurs when a nucleus becomes unstable, often because it is too large or has an imbalance between protons and neutrons. In some heavy elements, the strong repulsion between the many positively charged protons makes the nucleus unstable.

To regain stability, the nucleus emits radiation in the form of an alpha particle, which is a positively charged particle made up of two protons and two neutrons (the same as a helium nucleus).

When this alpha particle is released, the atom loses two protons and two neutrons from its nucleus. As a result, the atomic number decreases by 2 and the atomic mass decreases by 4.

Because the number of protons changes, the original atom is transformed into a completely different element. This process helps the nucleus move toward a more stable arrangement of particles.

What are the products formed of Alpha Decay

Alpha decay produces a helium nucleus (alpha particle) and a new, smaller, more stable atom.

in the example of Uranium 238:

  Given that alpha decay always emits a helium ion, you can predict the new element formed by deducting  4 from  the mass number in this case it reduced from 238 to 234) and reducing the atomic number  by 2 (in  this case element 92 changed into element 90). 

Beta Decay (β-decay) 

Beta Decay (β-decay) is nuclear decay where a neutron is converted into a proton and a new element is formed.

• The atomic number increases by one because there is a new proton present therefore a new element is created.

• The mass number is unchanged. 

Beta particles can travel about a metre through air. They can pass through a sheet of paper or a layer of cloth but not through a sheet of aluminium or a few centimetres of wood. They can also penetrate the skin and damage underlying tissues. They are even more harmful if they are ingested or inhaled.  

Gamma decay (γ decay)

In gamma decay, only energy, in the form of gamma rays, is emitted.

Gamma decay occurs when a nucleus is in an excited state and has too much energy to be stable. 

This often happens after alpha or beta decay has occurred. 

Because only energy is emitted during gamma decay, the number of protons and neutrons remains the same. 

Therefore, an atom does not become a different element during this type of decay.

How to stop Gamma rays

Gamma rays are the most dangerous type of radiation. They can travel farther and penetrate materials more deeply than can the charged particles emitted during alpha and beta decay. 

Gamma rays can be stopped only by several centimetres of lead or several meters of concrete. 

They can penetrate and damage cells deep inside the body and are more powerful than x-rays.

half life and relation to nuclear decay

Half-life is directly related to nuclear decay because it describes how quickly a radioactive substance breaks down over time.

In nuclear decay, unstable nuclei spontaneously emit radiation to become more stable. However, this does not happen all at once—atoms decay gradually. The half-life is the time it takes for half of the unstable nuclei in a sample to decay.

For example:

• Start with 100 atoms

• After 1 half-life → 50 remain

• After 2 half-lives → 25 remain

• After 3 half-lives → 12.5 remain

Half-life is important because it shows that nuclear decay follows a predictable pattern, even though the decay of individual atoms is random. Each radioisotope has its own unique half-life, which allows scientists to measure decay rates and predict how long a substance will remain radioactive.

Radioactive dating

Radioactive isotopes, or radioisotopes, can be used to estimate the ages of not only of rocks, but also of fossils and artifacts made long ago by human beings. 

The age of Earth has been estimated on the basis of radioisotopes. 

The general method is called radioactive dating. 

If you know how much of an element was initially present in a sample, then at a later time you can record how much of the element has decayed in the sample (the amount of the element present will have decreased). As long as you know the half life of the element then you can estimate how old the sample is. 

Carbon dating

A radioactive isotope of carbon, carbon-14 (¹⁴C), is constantly formed in the atmosphere and mixes with normal carbon (¹²C). Plants take in carbon dioxide during photosynthesis, and animals eat plants, so all living things contain a small amount of carbon-14.
As long as an organism is alive, the amount of carbon-14 in its body stays constant. When the organism dies, it stops taking in carbon.
The carbon-14 in its body begins to radioactively decay into nitrogen.Carbon-14 has a half-life of about 5730 years.
Scientists measure how much carbon-14 remains in a sample and compare it to how much would be expected in a living organism.

By calculating how many half-lives have passed, they can estimate how long ago the organism died.

Uses of Uranium 238

Uranium-238 is primarily used for the following purposes:

1. Nuclear Weapons (Plutonium Production) – Many nuclear weapons use plutonium-239, which is produced by bombarding uranium-238 with neutrons in a reactor.

2. Radiation Shielding – Due to its high density, depleted uranium (which is mostly (²³⁸U) is used in shielding for radiation protection in medical and industrial settings.

3. Armour-Piercing Ammunition – Depleted uranium is used in military applications for armour-piercing projectiles and tank armour because of its high density and ability to penetrate targets.

4. Geological Dating – The radioactive decay of uranium-238 to lead-206 is used in uranium-lead dating to determine the age of rocks and minerals.

5. Spacecraft Power Generation – In some cases, uranium-238 is used to produce plutonium-238, which is used in radioisotope thermoelectric generators (RTGs) to power deep-space probes like Voyager and Curiosity

Radioisotopes in medicine

Nuclear Scans: liquid radioactive tracers (radionuclides) are injected into patients: certain diseases, such as cancer, may absorb more/less of the tracer than normal tissues; special radiation-sensitive cameras create images that show where the tracer accumulates; cancer tumour may show up on the picture as a “hotspot”. E.g. Radium-226 & Caesium-137.

Radiation therapy (radiotherapy): cancer treatment that uses high doses of radiation to kill cancer cells and shrink tumours (by destroying their DNA).

How are emissions detected

A Geiger counter detects radiation when particles enter a gas-filled tube and ionise the gas.
This creates an electrical pulse, which is recorded as a “click.”

• Used to detect alpha, beta, and gamma radiation

• Measures the count rate (how many particles are detected per second)

Counts per minute

• CPM (counts per minute) is a measure of radioactivity, a unit of measurement for a Geiger counter. Technically, “It is the number of atoms in a given quantity of radioactive material that are detected to have decayed in one minute.

• Be careful – the counts per minute of 

the daughter product may contribute to 

The counts per minute (if unstable as well)

Absorbed dose

• Absorbed dose is the amount of radiation being absorbed by tissue in the body. 

• Absorbed dose = energy absorbed/mass of tissue    (in joules/kg)

Dose equivalent

• Dose equivalent is measured in Sieverts

• Dose equivalent (Sv) = Absorbed dose (Gy) x quality factor

Fission

Fission refers to the process in which a large, unstable atomic nucleus splits into two smaller nuclei, releasing energy, radiation, and often additional neutrons.

For example, when uranium-235 undergoes fission, it splits into two lighter elements and releases a large amount of energy.

Fusion is what powers the sun. Isotopes of hydrogen unite under extreme pressure and temperature to produce a neutron and a helium isotope. Along with this, an enormous amount of energy is released, which is several times the amount produced from fission.

Fusion

Nuclear fission takes place when a large, somewhat unstable isotope (atoms with the same number of protons but different number of neutrons) is bombarded by high-speed particles, usually neutrons. These neutrons are accelerated and then slammed into the unstable isotope, causing it to fission, or break into smaller particles.

 During the process, a neutron is accelerated and strikes the target nucleus, which in the majority of nuclear power reactors today is Uranium-235. This splits the target nucleus and breaks it down into two smaller isotopes (the fission products), three high-speed neutrons, and a large amount of energy.

E=mc2

• E = Energy (measured in joules, J)

• m = Mass (measured in kilograms, kg)

• c = Speed of light (≈ 3 × 10⁸ m/s)
  
  This equation shows that mass can be converted into energy.

Even a very small amount of mass can produce a huge amount of energy because the speed of light (c) is a very large number, and it is squared.

Electron Volts

• eV (electron volts) is the measure of the work done on an electron in accelerating it through a potential difference of one volt.

• Can be used to describe binding energy – e.g. binding energy of hydrogen is 13.6 eV

• Equal to approximately 1.6×10⁻¹⁹ J

critical mass

is the smallest amount of fissile material for a sustained nuclear chain reaction

When uranium 235 or plutonium 239 under goes nuclear fission it releases 2-3 neutrons. When one of these neutrons hits another uranium atom it causes another fission. If there are enough uranium atoms around, this reaction can go faster and faster, this is called a critical mass. If this reaction becomes uncontrolled there is a bomb, but when controlled, it may be used in a reactor to help produce electricity.

fissile

a material that is able to undergo fission and sustain a chain reaction. eg. Uranium 235,  Plutonium 239

SA: Volume

 this is the ratio that controls the speed of the reaction, The higher the SA the more area there is to react with. If the surface are is to large the reactions will become uncontrolled