Chapter 18 Flashcards
Radioactive decay is a…
Random process
Why are ionising radiations beneficial?
- Ionising radiations are easily detected
- When absorbed, the energy from the radiation warms things up
- Energy carried by radiations means they can damage living matter (put to good use when sterilising medical equipment)
Radiation can help kill cancerous cells, but…
It must not damage any surrounding healthy tissue
Ionising an atom =
To knock an electron out of the atom (requires energy)
Difference between x-rays and gamma rays
X-rays = photons produced by accelerated electrons Gamma-rays = photons emitted by nuclei
Ionising radiations loose energy when…
They pass through matter
The more readily the radiation ionises atoms =
The less thickness of shield is required (less penetrating the radiation is)
How are labs etc. designed to prevent radiation risks
- Lead-lined canisters are used
- Thick steel + concrete walls shield nuclear reactors
The thickness of the shield increase as…
The energy of the radiation increases
Intensity of radiation decreases…
Exponentially with thickness
Graph of intensity I, against thickness, x
Exponential relationship
y decreases as x increases
Equation for the intensity I
I = I0 x e ^(-μx)
where I0 is the initial intensity of the beam, μ is the absorption coefficient of the material and x is its thickness.
What is the unit of the absorption coefficient?
The unit of μ is m–1.
What is ‘half-thickness’
The thickness needed to half the number of photons getting through.
Equation for half-thickness
X1/2 = ln(2)/ μ
Ways that photons are absorbed?
- Ionise atom or put atom in higher energy level
- Scattering from electrons
- Electron-position pair production
What factors are taken into account when considering how harmful the radiation will be?
-Energy of radiation
-Ionisation damage to cells
Depends on type of radiation and type of tissue
Absorbed does =
Number of joules absorbed per kilogram of tissue measured in Grays (Gy)
Activity in Becquerel’s =
disintegrations per second
Absorbed dose in grays =
Energy per kg
Does equivalent in Sievert =
Does in gray x quality factor
Probability of developing cancer =
From radiation = 5% per Sievert
Equation for risk =
Probability of event x consequence
Methods of transfer (types of radiation):
- Alpha
- Beta
- Gamma
- X-rays
- Photons
- Neutrons
- Cosmic rays
Symbol, relative charge, mass: Alpha
Symbol: α
Constituent: A helium nucleus (2 protons + 2 neutrons)
Relative charge: +2
Mass: 4
Symbol, relative charge, mass: Beta, beta-plus
Symbol: β
Constituent: Electron
Relative charge: -1
Mass: (negligible)
Beta-plus: This is a positron with +1 charge and negligible mass.
Symbol, relative charge, mass: Gamma
Symbol: Ɣ
Constituent: Short-wave, high frequency electromag wave
Relative charge: 0
Mass: 0
How ionisation works
When a radioactive particle hits an atom it can knock off electrons, creating an ion
Penetrating and ionising properties of alpha
-Strongly ionising and weakly penetrating. Slow speed and can be stopped by paper or a few cm of air. Alpha is affected by magnetic field
Penetrating and ionising properties of Beta and beta-plus
Weakly ionising and highly penetrating. Fast speed and can be absorbed by 3mm of aluminium. Beta is effect by magnetic field.
Beta-plus; annihilation by electron so virtually zero range.
Penetrating and ionising properties of Gamma
-Very weakly ionising and the most penetrating. The speed of light, and can be absorbed by many cm of lead or several meters of concrete. Gamma is not affected by the magnetic field.
The intensity of gamma radiation decreases with distance
- A gamma source will emit gamma radiation in all directions
- This radiation spreads out as you get further away from the source
- However the amount of radiation per unit area (intensity) will decrease the further you get from the source.
- When gamma travels through an absorbing material its intensity decreases exponentially
Equation for absorbed does
Absorbed does = energy / mass
Units of effective does:
Sievert (Sv)
Alphas ionising properties
Alpha particles are strongly positive so they can pull electrons off atoms, ionising them. Ionising an atom transfer some of the energy from the alpha particle to the atom. The alpha particle ionises many atoms and loses all its energy that why is causes so much tissue damage.
Beta ionising properties
The beta-minus particle has lower mass and charge than the alpha particle, but a higher speed. This means it can still knock electrons off atoms but has a lower number of interactions than alpha. This lower number of interactions means that beta radiation causes much less damage to body tissue.
Risk = probability x consequences
For example; ionising radiation can cause cancer but it can also be used to treat cancer. So the risk of serious damage cause by the treatment is considered acceptable if the treatment can improve the patients condition.
Ionising radiation examples
Ionising radiation is any form of radiation capable of ionising neutral atoms or molecules.
-Alpha particles which each consist of helium nuclei (two protons and two neutrons)
emitted from massive unstable nuclei.
-Beta particles which consist of electrons or positrons emitted by nuclei that have an
excess of neutrons or protons respectively.
-Gamma radiation which consists of high-energy photons emitted by nuclei in excited
states.
-X-radiation which consists of high-energy photons emitted when fast-moving
electrons are stopped in an x-ray tube.
-Mesons from cosmic rays striking the atmosphere.
Alpha radiation
The alpha particles from any one type of decay all have the same energy, typically a few MeV. Being fast moving massive charged particles, alpha particles ionise strongly. The range of alpha radiation in air is of the order a few centimetres. In solid materials, alpha particles are stopped very easily, even by a thin sheet of paper. Thus the main danger to health from alpha radiation comes from ingesting or breathing in the radioactive material, when the alpha particles are stopped in body tissues, causing damage.
Beta radiation
Both electrons and positrons are known as beta particles, written β– and β+ respectively. In beta decay, neutrinos (or antineutrinos) are also emitted, and carry away energy and momentum. The energies of beta particles therefore vary, up to the maximum available from the decay, typically a few MeV. Beta particles have a range of about a metre in air. They penetrate thin layers of solid material, for example aluminium foil, but are stopped by a few millimetres thickness of metal.
Gamma radiation
The gamma photon energies for a particular excited state form a line spectrum characteristic of that isotope. The photon energy is typically 100 keV to 1 MeV. X-rays have the same nature, and similar properties, though generally have smaller photon energies. Gamma radiation has less ionising effect than alpha or beta particles of the same energy. Thus it passes through air with little absorption. The intensity of gamma radiation from a point source varies approximately as the inverse square of the distance from the source. Gamma photons are largely absorbed by lead plates of thickness about 50 mm.
Biological effects of ionising radiation
Ionising radiation can be injurious to health, but is also used in many kinds of medical
treatment and investigation. Intense gamma radiation is used to sterilize medical supplies and to preserve some foods.
Ionising radiation kills living cells as a result of damaging cell membranes beyond repair and
destroying the mechanism of replication in cells as a result of damaging the DNA strands in
cell nuclei. Ionising radiation also creates free radicals which affect cell chemistry.
Absorbed dose units
The SI unit of absorbed dose is the gray (Gy), equal to 1 J kg–1. This is a very large unit, comparable to the lethal dose.
What’s the average dose a person is exposed to per year (in Europe)?
The average occupational dose is about 2 mSv per annum
Risk
The current average dose received by the general public, much of it from background radiation including cosmic rays, is around 1 millisievert per year. Radiation safety limits attempt to ensure that risks due to radiation are no more significant than risks due to everyday activities.
What makes a nucleus stable?
-The balance between protons + neutrons
Plot of number of protons against neutron number for stable isotopes
Starts to follow N=Z then the curve slopes upwards
-A strong nuclear attraction acts equally between neutrons + protons
Pauli exclusion principle in terms of protons and neutrons
-Protons and neutrons obey the Pauli exclusion principle so a proton-neutron pair can occupy the same quantum state, but two neutrons or two protons cannot.
Larger nuclei =
More protons + neutrons
Increase in protons =
Increase in potential energy of their mutual electrical repulsion.
Exchanging virtual photons + energy of bound atoms
-The exchange of virtual photons hold atoms together. The total energy of the bound system is less that the energy of all the pieces pulled apart.
What must the energy of the bound nucleus must be less than?
-The energy of a bound nucleus must be less than the energy of its protons and neutrons taken separately.
How to find the binding energy of a nucleus
-Find the mass of the atom and the mass of the individual parts. Then use Erest =mc^2 to find their energy. The difference in energy of total bound and individual parts is the binding energy per nucleon.
What is u?
u= 1 atomic mass unit u = 1.66056 x 10^-27
Unstable nuclei =
Less strongly bound
Spontaneous radioactive decay happens because…
Nucleons seek possible lower energy states.
What does the plot of how energy varies with proton + neutron number show?
- This is the Nuclear landscape: The nuclear valley of stability’
- The more neutrons + protons added = stronger nuclear force
‘Fusion hill’
-Nuclei go down hill by nuclear fusion
‘Iron lake’
-Near iron are the most strongly bound + lie at the bottom of the valley
Where do stable nuclei lie in the ‘valley’?
-Stable nuclei lie along a narrow band of values of numbers of protons and neutrons. The more negative the binding energy, the more stable the nucleus.
Why do the sides of the ‘valley’ rise?
-The sides rise because the Pauli exclusion principle theory; the extra neutrons or protons have to go ins sates of higher energy because both are fermions.
Emitting a electron (β-) =
Neutron becomes a proton
Emitting a positron (β+) =
Proton becomes a neutron
Naturally occurring radioactive isotopes
-Naturally occurring radioactive isotopes are left-over fossils from the formation of the earth and solar system.
Why can naturally occurring radioactive isotopes be dangerous?
-Thorium exists in many building materials, so bricks + concrete can leak radon gas into rooms, poor ventilation = danger from emitting alpha particles.
What is the name of the substance use in smoke alarms and their half-life?
Americium is use din smoke detectors with a half-life of 432 years.
What is the binding energy like around the element iron in the nuclear ‘valley’?
-The lowest point and the strongest binding energy is around the element iron.
How does radioactive decay change the nucleus?
-Radioactive decay takes a nucleus to a state of lower energy. Gamma emission does so without a change in number of protons + neutrons.
Total mass of a nucleus vs. constituent parts:
-The total mass of a nucleus is always less than the total mass of its constituent parts
Total energy =
rest energy + kinetic energy
What happens when you get rid of extra mass?
Getting rid of extra mass results in a decrease in energy state of the parent nucleus.
Rest energy equation
Erest = mc^2
Nucleons in a potential well
Nucleons are contained within a potential well created by the strong nuclear force (attractive - compared to grav well). Define the zero energy out of the well - free nucleon state (out of the ranger of the strong forces), so in the bottom of the well the nucleons have not lost potential energy.
Units of binding energy
MeV
How can you break the bound atom of iron?
-For iron you need to supply the largest amount of energy per nucleon to break it from a bound state.
Fission
-Fission is when a large nucleus breaks into two lower energy pieces.
Nuclear fission releases energy of the order…
1MeV per particle using e =kT
-Fission catches extremely hot sparks from inside supernovae where heavy elements were made.
How does fission work? (Example with U-235)
- A neutron comes towards U-235
- This then becomes U-236 and oscillates like a liquid drop
- U-236 breaks into two pieces
- Energy comes from electrical potential energy of two nuclei created close together
- It breaks into two daughter nuclei and two protons.
How does fission work - chain reaction?
- When the U-236 splits into two daughter nuclei and two protons, the protons then meet another U-235 and the process continues
- The chain reaction is self-sustaining at a steady rate if on average one neutron from a fission produces a further fission.
Chain reaction: sub-critical mass
-All the chains die out
Chain reaction: Critical mass
-Reaction continues at a steady rate
Chain reaction: super-critical mass
-Several new fissions follow each fission.
Rate of escape of neutrons relationship with surface area
Rate of escape of neutrons ∝surface area
Rate of production of neutrons relationship with volume
Rate of production of neutrons ∝ volume
Which ratio increases with size?
The ratio volume/ surface area increases with size.
Critical mass =
The minimum amount of mass for fission to be maintained.
How is fission used to produce energy?
Nuclear power stations;
- Use the energy from the reactions to heat water which sends steam to the turbo alternator.
- Water is used to slow down the reactions, because the slower they are the more likely they are to collide so creates a more sustainable reaction.
- As they are stopped, this energy is spread out as random thermal motion and the core heats the water pumped through it.
What is a major problem with the power stations?
-A major problem is disposing of the radioactive waste safely.
Fusion
- Fusion is the reaction of the stars. At very high temperatures small nuclei collide and fuse. As they do so energy is released.
- Very high energies are needed to get them close enough against the electrical potential barrier.
- Nuclear fusion in the sun is a slow process as one proton must decay to a neutron to form deuterium.
How does fusion work on the Sun?
-Two protons fuse, converting one to a neutron to form deuterium H-2
-The deuterium H-2 captures another proton to form He-3
-Two He-3 nuclei fue, giving He-4 and two free protons.
(Then the process repeats)
How does fusion work on Earth?
-Deuterium and tritium are heated to very high temperatures, producing He-4 and a neutron.
-Neutrons from their fusion then fuse with lithium in a ‘blanket’ around the hot gases.
-Which then creates helium and tritium.
Tritium is released and the process continues.
Why are fusion machines also harmful?
-Fusion generators also produce radioactive waste.
What is the standard notation of an element?
- The nucleon number or mass number (A) is at the top
- The proton number of atomic number (Z) is at the bottom
What makes an atom an isotope?
-Atoms with the same number of protons but different numbers of neutrons are called isotopes.
A nucleus will be unstable if it has…
- Too many neutrons
- Too few neutrons
- Too many nucleons altogether (too heavy)
- Too much energy
Some nuclei are more stable than others…
-The nucleus is under the influence of the strong nuclear force holding it together and the electromagnetic force pushing the protons apart.
Alpha emission happens in heavy nuclei
- When an alpha particle is emitted. the proton number decreases by two, and the nucleon number decreases by four
- Alpha emission only happens with very heavy atoms like uranium and radium
- The nuclei of these atoms are too massive to be stable.
Beta emission happens in neutron rich nuclei
- Beta-minus decay is the emission of an electron from the nucleus along with an antineutrino
- Beta decay happens in isotopes that have many more neutrons than protons
- When a nucleus ejects a beta particle, one of the neutrons in the nucleus is changed into a proton.
When a beta particle is emitted…
The proton number increases by one and the nucleon number stays the same.
-In beta-plus emission, a proton gets changed into a neutron. The proton number decreases by one, and the nucleon number stays the same.
Gamma radiation is emitted from nuclei with too much energy
- A nucleus with excess energy is said to be excited
- This energy can be lost by emitting a gamma ray
- During gamma emission, there is no change to the nuclear constituents- the nucleus just loses excess energy.
Conservation rules in nuclear reactions
-In every nuclear reaction energy, momentum, proton number/ charge and nucleon number must be conserved.
Equation for binding energy per nucleon (MeV)
Binding energy per nucleon = Binding energy (B) / Nucleon number (A)
What does it mean the more negative the binding energy is?
-The more negative the binding energy, th more energy is needed to remove nucleons from the nucleus
How do nuclear reactors work?
- They use uranium rod rich in U-235 for fuel.
- A chain reaction happens and is enhanced as they are slowed down by water a moderator.
- Nuclear reactors use supercritical mass and control the rate of fission using control rods.
- Control rods absorb neutrons to rate fo reaction is controlled.
What must be true for nuclear fusion?
-Nuclei can only fuse if they have enough energy to overcome the electrostatic repulsive force between them and get close enough for the strong interaction to bind them.
Nucleus
Every atom contains a nucleus which is composed of protons and neutrons. Because
neutrons and protons are similar in many respects they are collectively termed nucleons. The nucleon number (also called the mass number) A of an isotope is the number of protons and neutrons in each nucleus of the isotope.
How are particles held together in the nucleus?
The particles in the nucleus are held together by the strong nuclear force. The nucleus of an
isotope which has a proton number Z and a nucleon (mass) number A consists of Z protons
and N = A – Z neutrons. The symbol for an isotope is XA Z , where X is the chemical symbol of the element.
What is the proton number also equal to?
The proton number Z is also equal to the number of electrons in the atom, because a neutral atom must have the same number of negative electrons as positive protons.
Graph of binding energy against mass number (A)
Decreases as A increases, but then towards the end curves up slightly.
Alpha emission:
Alpha emission, in which the unstable nucleus emits two protons and two neutrons as a single particle
Electron emission (beta-minus):
Electron emission, together with an antineutrino, in which a neutron in the nucleus changes into a proton
Positron emission (beta-plus):
Positron emission, together with a neutrino, in which a proton in the nucleus changes into a
neutron
Gamma emission:
Gamma emission, in which a gamma-ray photon is emitted from a nucleus in an excited
state, which changes to a state of lower energy, without change of proton or neutron number.
Fission explained
A large nucleus may be considered like an oscillating liquid drop. If the nucleus oscillates too much, it can divide into two parts which repel each other electrostatically. The two fragments gain kinetic energy and also release two or three high-energy neutrons.
Exponential decay process
Radioactive decay is a random process. All nuclei of a radioactive isotope are equally likely to decay, thus the number of nuclei ΔN that decay in a given time Δt is proportional to the number N of nuclei of the isotope present at that time. Hence ΔN = – λ N Δt, where λ is the decay constant. Note that the minus sign indicates a decrease of N with time.
Radioactive decay
-Radioactive decay is the process in which unstable nuclei are transformed by emitting
particles.
-A radioactive isotope emits ionising radiation, in the form of alpha particles, beta particles or
gamma-ray photons. In doing so the nucleus decays to a state of lower energy.
-The activity (measured in Becquerels, Bq) of a radioactive isotope is the number of nuclei of
the isotope that disintegrate per second.
Units for activity of radioactive source
Bq (becquerels)
Equation for activity of radioactive isotope (exponentially decreasing with time)
A= A0 x e^-λt
Equation the number N of atoms of an isotope decreasing with time
N= N0 x e^-λt
