Fusion and fission

Theory of relativity

explain how space and time are linked for objects that are moving at a consistent speed in a straight line.

Einstein showed in his theory of relativity that matter can be considered a form of energy and hence, he proposed:

• Mass can be converted into energy

• Energy can be converted into mass

Some examples of mass-energy equivalence are:

• The fusion of hydrogen into helium in the centre of the sun

• The fission of uranium in nuclear power plants

• Nuclear weapons

• High-energy particle collisions in particle accelerators

The binding energy is equal to the amount of energy released in forming the nucleus, and can be calculated using:

E = (Δm)c²

• E = Binding energy released (J)

• Δm = mass defect (difference between the atoms mass and the sum of the masses of its protons and neutrons) (kg)

• c = speed of light (m s^-1)

The daughter nuclei produced as a result of both fission and fusion have a ____ binding energy per nucleon than the parent nuclei

higher

what does this therefore mean?

energy is released as a result of the mass difference between the parent nuclei and the daughter nuclei

Total binding energy of each nucleus = Binding energy per nucleon × Mass number

• Since reaction 1 releases more energy than reaction 2, its end products will have a higher binding energy per nucleon

  • Hence, they will be more stable

• This is because the more energy is released, the further it moves up the graph of binding energy per nucleon against nucleon number (A)

  • Since at high values of A, binding energy per nucleon gradually decreases with A

• Nuclear reactions will tend to favour the more stable route, therefore, reaction 1 is more likely to happen

Annihilation is:

When a particle meets its equivalent anti–particle they both are destroyed and their mass is converted into energy in the form of two gamma ray photons

Pair production is the _____ of annihilation

oppposite

Pair production is:

When a photon interacts with a nucleus or atom and the energy of the photon is used to create a particle–antiparticle pair

The presence of a nearby ____ is essential in pair production so that the process conserves both energy and momentum + why?

neutron

A single photon alone cannot produce a particle–anti-particle pair or the conservation laws would be broken

Pair creation is a case of what conversion?

energy —> matter

This means the energy of the photon must be above a certain value to provide the ______________ of the particle–antiparticle pair

total rest mass energy

what equation is used for pair production:

ΔE = c² Δm

• Δm = rest mass of the particle (kg)

• c = speed of light (m s^–1)

• ΔE = rest mass energy of the particle (J)

  Therefore, in order to create a particle & anti-particle pair, the energy carried by a single photon must be at least twice the rest-mass energy required, i.e.

2ΔE = 2(c² Δm)

This also means if a particle meets its anti-particle and annihilates, the energy carried away by each of the two photons E_photon is given by: 

E_photon = hf = hc/λ= c² Δm

Since the Planck constant is in Joules (J) remember to always convert the rest mass-energy from MeV to J.

Experiments into nuclear structure have found that the total mass of a nucleus is ___ than the sum of the masses of its constituent nucleons

less

What is this difference in mass is known as?

mass defect or mass deficit

Mass defect is defined as:

The difference between the measured mass of a nucleus and the sum total of the masses of its constituents

• Due to the equivalence of mass and energy, this decrease in mass implies that energy is released in the process

Since nuclei are made up of neutrons and protons, there are forces of repulsion between the positive protons

• Therefore, it takes energy, ie. the binding energy, to hold nucleons together as a nucleus

Binding energy is defined as:

The energy required to break a nucleus into its constituent protons and neutrons

(Avoid describing the binding energy as the energy stored in the nucleus – this is not correct – it is energy that must be put into the nucleus to pull it apart.)

• Energy and mass are proportional, so, the total energy of a nucleus is less than the sum of the energies of its constituent nucleons

• The formation of a nucleus from a system of isolated protons and neutrons is therefore an exothermic reaction - meaning that it releases energy

What is best for comparing nuclear stability?

binding energy per nucleon

The binding energy per nucleon is defined as:

The binding energy of a nucleus divided by the number of nucleons in the nucleus

A higher binding energy per nucleon indicates a ____ stability

higher

• In other words, it requires more energy to pull the nucleus apart

What has the highest binding energy per nucleon, which makes it the most stable of all the elements?

Iron (A = 56)

graph of binding energy per nucleon against nucleon number:

Key Features of the Graph:

• At low values of A:

  • Nuclei tend to have a lower binding energy per nucleon, hence, they are generally less stable

  • This means the lightest elements have weaker electrostatic forces and are the most likely to undergo fusion

• Helium (⁴He), carbon (¹²C) and oxygen (¹⁶O) do not fit the trend

  • Helium-4 is a particularly stable nucleus hence it has a high binding energy per nucleon

  • Carbon-12 and oxygen-16 can be considered to be three and four helium nuclei, respectively, bound together

• At high values of A:

  • The general binding energy per nucleon is high and gradually decreases with A

  • This means the heaviest elements are the most unstable and likely to undergo fission

Do not begin your curve at A = 0, this is not a nucleus!

Binding energy can be calculated using the equation:

ΔE = c²Δm

• Where Δm is the mass defect of a nucleus

Δm can be calculated using:

Δm = Zm_p + (A – Z)m_n – m_total

Where:

Z = proton number

A = nucleon number

m_p = mass of a proton (kg)

m_n = mass of a neutron (kg)

m_total = measured mass of the nucleus (kg)

Nuclear fission is defined as:

The splitting of a large, unstable nucleus into two smaller nuclei

What particularly undergoes fission?

Isotopes of uranium and plutonium both undergo fission and are used as fuels in nuclear power stations

What happens during fission?

a neutron collides with an unstable nucleus, the nucleus splits into two smaller nuclei (called daughter nuclei) as well as two or three neutrons

• Gamma rays are also emitted

Why do the products of fission move away very quickly?

Energy transferred is from nuclear potential energy to KE

what is spontaneous fission?

nuclei to undergo fission without additional energy being put into the nucleus (rare)

Usually, for fission to occur the unstable nucleus must first absorb a ____

neutron

fission of uranium-235:

• Take, for example, uranium-235, which is commonly used as a fuel in nuclear reactors

• It has a very long half-life of 700 million years

• This means that it would have low activity and energy would be released very slowly

  • This is unsuitable for producing energy in a nuclear power station

• During induced fission, a neutron is absorbed by the uranium-235 nucleus to make uranium-236

• This is very unstable and splits by nuclear fission almost immediately

What is the significance of in fission, producing two or three neutrons which move away at high speed?

Each of these new neutrons can start another fission reaction, which again creates further excess neutrons

what is this process called?

chain reaction

What is the purpose of the moderator?

To slow down neutrons

What is the moderator?

a material that surrounds the fuel rods and control rods inside the reactor core

How does a moderator slow down reactions?

• fast-moving neutrons produced by the fission reactions slow down by colliding with the molecules of the moderator, causing them to lose some momentum

• The neutrons are slowed down so that they are in thermal equilibrium with the moderator, hence the term ‘thermal neutron’

  • This ensures neutrons can react efficiently with the uranium fuel

Purpose of a control rod

To absorb neutrons

How do control rods work?

number of neutrons absorbed is controlled by varying the depth of the control rods in the fuel rods

• Lowering the rods further ________ the rate of fission, as more neutrons are absorbed

• Raising the rods _____ the rate of fission, as fewer neutrons are absorbed

• decreases

• increases

what does it do?

• This is adjusted automatically so that exactly one fission neutron produced by each fission event goes on to cause another fission

• In the event the nuclear reactor needs to shut down, the control rods can be lowered all the way so no reaction can take place

What is the purpose of the coolant?

To remove the heat released by the fission reactions

How does the coolant work?

• The coolant carries the heat to an external boiler to produce steam

• This steam then goes on to power electricity-generating turbines

structure of nuclear reactor

Within the fuel rods, nuclei of uranium-238 quickly decay into nuclei of _______

• These nuclei are ______

• They have a long half-life of ____ years

plutonium-239

• extremely radioactive

• 24,000

What is the use of plutonium-239 decaying slowly?

• It will remain radioactive for a very long time

• So, it presents a risk of contamination for a long time

• It is classified as high-level radioactive waste

What are the three main types of nuclear waste?

• Low level

• Intermediate level

• High level

What is low-level waste?

• This is waste such as clothing, gloves and tools which may be lightly contaminated

• This type of waste will be radioactive for a few years, so must be encased in concrete and stored a few metres underground until it can be disposed of with regular waste

What is intermediate-level waste?

• This is everything between daily used items and the fuel rods themselves

• Usually, this is the waste produced when a nuclear power station is decommissioned and taken apart

• This waste will have a longer half-life than the low-level waste, so must be encased in cement in steel drums and stored securely underground

What is High-level waste?

• This waste comprises of the unusable fission products from the fission of uranium-235 or from spent fuel rods

• This is by far the most dangerous type of waste as it will remain radioactive for thousands of years

• As well as being highly radioactive, the spent fuel roads are extremely hot and must be handled and stored much more carefully than the other types of waste

How is high-level waste is treated?

• The waste is initially placed in cooling ponds of water close to the reactor for a number of years

• Isotopes of plutonium and uranium are harvested to be used again

• Waste is mixed with molten glass and made solid (this is known as vitrification)

• Then it is encased in containers made from steel, lead, or concrete

• This type of waste must be stored very deep underground

Where can Isotopes with long half-lives not enter?

water and food supplies

Where must these locations be?

geologically stable, secure from attack, and designed for safety

Fusion is defined as:

Small nuclides combine together to make larger nuclei, releasing energy

Low mass nuclei (such as _________) can undergo fusion and release energy

hydrogen and helium

What do the nuclei need to have to fuse?

both nuclei must have high kinetic energy

Why do they need high KE?

protons inside the nuclei are positively charged, which means that they repel one another

It takes a great deal of energy to overcome the electrostatic force

When two protons fuse, the element _____ is produced

deuterium

In the centre of stars, the deuterium combines with a tritium  nucleus to form a helium nucleus, plus the release of energy, which provides fuel for the star to continue burning

In the fusion process, the mass of the new heavier nucleus is ___ than the mass of the constituent parts of the nuclei fused together, as some mass is converted into energy. 

LESS

What happens with this energy?

Not all of this energy is used as binding energy for the new larger nucleus, so energy will be released from this reaction. The binding energy per nucleon afterwards is higher than at the start. 

fission e.g