Radioactivity Flashcards
What was the Rutherford scattering?
Diagram included
The experimental setup consists of alpha particles fired at a thin gold foil and a dector on the other side to detect how many particles deflected at different angles.
Diagram shown in document
What were the results of the rutherford scattering and conlcusions?
From this experiment, Rutherford results were:
The majority of α-particles went straight through (A)
This suggested the atom is mainly empty space
Some α-particles deflected through small angles of < 10o
This suggested there is a positive nucleus at the centre (since two positive charges
would repel)
Only a small number of α-particles deflected straight back at angles of > 90o
(C)
This suggested the nucleus is extremely small and this is where the mass and charge
of the atom is concentrated
It was therefore concluded that atoms consist of small dense positively charged
nuclei.
What was JJ Thomson’s model (1897)
Diagram included
Thomson discovered the electron
He then went on to propose the ‘plum pudding’ model of the atom
In this model:
The atom consists of positive and negative charges in equal amounts so that it is
neutral overall
They were modelled as spheres of positive charge with uniformly distributed charge
and density. The negatively charged electrons were thought to be stuck to the sphere
like currants in a plum pudding.
Diagram found in document
What is an alpha particle, where does it come from and its characteristics?
Alpha (α) particles are high energy particles made up of 2 protons and 2 neutrons (the
same as a helium nucleus)
They are usually emitted from nuclei that are too large.
Alpha is the most ionising type of radiation
This is due to it having the highest charge of +2e
This means it produces the greatest number of ion pairs per mm in air
This also means it is able to do more damage to cells than the other types of radiation
Alpha is the least penetrating type of radiation
This means it travels the shortest distance in air before being absorbed
Alpha particles have a range of around 3-7 cm in air
Alpha can be stopped by a single piece of paper.
What is beta particles, where do they come from and what are its characteristics?
Beta (β−) particles are high energy electrons emitted from the nucleus
Beta (β+) particles are high energy positrons (antimatter of electrons) also emitted from
the nucleus
β−
particles are emitted by nuclei that have too many neutrons
β+
particles are emitted by nuclei that have too many protons
Beta is a moderately ionising type of radiation
This is due to it having a charge of +1e
This means it is able to do some slight damage to cells (less than alpha but more than
gamma)
Beta is a moderately penetrating type of radiation
Beta particles have a range of around 20 cm – 3 m in air, depending on their energy
Beta can be stopped by a few millimetres of aluminium foil.
What are gamma rays, where do they come from and their characteristics?
Gamma (γ) rays are high energy electromagnetic waves
They are emitted by nuclei that need to lose some energy.
If these particles hit other atoms, they can knock out electrons, ionising the atom
This can cause chemical changes in materials and can damage or kill living cells.
Gamma is the least ionising type of radiation
This is because it is an electromagnetic wave with no charge
This means it produces the least number of ion pairs per mm in air
It can still cause damage to cells, but not as much as alpha or beta radiation. This is
why it is used for cancer radiotherapy
Gamma is the most penetrating type of radiation
This means it travels the furthest distance in air before being absorbed
Gamma radiation has an infinite range and follows an inverse square law
Gamma can be stopped by several metres of concrete or several centimetres of lead.
How do smoke dectectors work?
Smoke detectors contain a small amount of Americium-241, which is a weak alpha source
Within the detector, alpha particles are emitted and cause the ionisation of nitrogen and
oxygen molecules in the air
These ionised molecules enable the air to conduct electricity and hence a small current can
flow
If smoke enters the alarm, it absorbs the alpha particles, hence reducing the current which
causes the alarm to sound
Am-241 has a half-life of 460 years, meaning over the course of a lifetime, the activity of the
source will not decrease significantly and it will not have to be replaced.
How does thickness controls work/
Beta radiation can be used to determine the thickness of aluminium foil, paper, plastic, and
steel
The thickness can be controlled by measuring how much beta radiation passes through the
material to a Geiger counter
Beta radiation must be used, because:
Alpha particles would be absorbed by all the materials
Gamma radiation would pass through undetected through the materials
The Geiger counter controls the pressure of the rollers to maintain the correct thickness
A source with a long half-life must be chosen so that it does not need to be replaced often.
What is the inverse square law and what type of radiation does it apply to?
The intensity of a physical quantity, like light or radiation, is inversely proportional to the square of the distance from the source. This applies to gamma radiation as well.
What is the inverse square law for gamma radiation?
Equation
l=k/x^2
Where:
I = intensity of the gamma radiation (W m–2)
k = constant of proportionality
x = the distance from the source (m)
What is another way of writing the inverse square law for gamma radiation?
l1 and l2
l1/l2 = (x2/x1)^2
I1= intensity of the gamma radiation at x1
(W m–2)
I2= intensity of the gamma radiation at x2
(W m–2)
x1= the initial distance from the source (m)
x2= the subsequent distance from the source (m)
What are some natural sources for background radiation?
Radon gas from rocks and soil
Heavy radioactive elements, such as uranium and thorium, occur naturally in rocks in
the ground
Uranium decays into radon gas, which is an alpha emitter
This is particularly dangerous if inhaled into the lungs in large quantities
Cosmic rays from space
The sun emits an enormous number of protons every second
Some of these enter the Earth’s atmosphere at high speeds
When they collide with molecules in the air, this leads to the production of gamma
radiation
Other sources of cosmic rays are supernovae and other high energy cosmic events
Carbon-14 in biological material
All organic matter contains a tiny amount of carbon-14
Living plants and animals constantly replace the supply of carbon in their systems
hence the amount of carbon-14 in the system stays almost constant
Radioactive material in food and drink
Naturally occurring radioactive elements can get into food and water since they are in
contact with rocks and soil containing these elements
Some foods contain higher amounts such as potassium-40 in bananas
However, the amount of radioactive material is minuscule and is not a cause for
concern.
What are some man made sources of radiation?
Medical sources
In medicine, radiation is utilised all the time
Uses include X-rays, CT scans, radioactive tracers, and radiation therapy
Nuclear waste
While nuclear waste itself does not contribute much to background radiation, it can be
dangerous for the people handling it
Nuclear fallout from nuclear weapons
Fallout is the residue radioactive material that is thrown into the air after a nuclear
explosion, such as the bomb that exploded at Hiroshima
While the amount of fallout in the environment is presently very low, it would increase
significantly in areas where nuclear weapons are tested
Nuclear accidents
Accidents such as that in Chernobyl contributed a large dose of radiation into the
environment
While these accidents are now extremely rare, they can be catastrophic and render
areas devastated for centuries.
What is called when you account for background radiation?
Background radiation must be accounted for when taking readings in a laboratory
This can be done by taking readings with no radioactive source present and then subtracting
this from readings with the source present
This is known as the corrected count rate.
What to consider when handling radioactive sources?
When choosing a source to work with, the following characteristics are preferred:
Short-lived isotopes are preferred to long-lived ones
The smaller the amount of radioactive material, the better
The risk associated with radioactive materials depends on the amount and type of radiation
For example, alpha radiation is more ionising than gamma radiation but does not
penetrate as far
The biggest risks when working with radioactive sources are exposure and contamination
Contamination happens when a piece of radioactive material is transferred onto a
person, or a personal item, where it can then decay and cause damage
The radiation hazard warning safety symbol is used to warn about hazardous materials,
locations or objects.
What are some precautions when using radioactive sources?
Precautions must be taken to reduce the risk of harm when using radioactive sources. These
include:
Keeping radioactive sources shielded when not in use, for example in a lead-lined box
Wearing protective clothing to prevent the body from becoming contaminated
Keeping personal items outside of the room to prevent these from becoming
contaminated
Limiting exposure time so less time is spent with radioactive materials
Handling radioactive materials with long tongs to increase the distance from them
Monitoring the exposure of workers, such as radiographers, using detector badges
How can Gamma radiation be used to treat cancer?
Gamma radiation can be used to destroy cancerous tumours
The gamma rays are concentrated on the tumour to protect the surrounding tissue
Less penetrating beta radiation can be used to treat skin cancer by direct application to the
affected area.
What are some precautions for the patient?
Precautions for the patient:
The patient should be protected with lead to cover parts of the body not to be
exposed to radiation
The exact dose should be calculated carefully
The dose should be directed very accurately at the cancerous tissue to minimise
damage to healthy tissue.
What are some precautions for the radiographer?
Precautions for the radiographer:
The radiographer should handle the source remotely with tongs or a machine
The radiographer should be protected by a screen
The radiographer should be a long way from the source while the dose is given
The source should be immediately stored in its lead case once the dose is given.
What are radioactive tracers and why is it preferred for them to have a short half-life?
Radioisotopes can be used as ‘tracers’ to monitor the processes occurring in different parts of
the body
Radioactive tracers with a short half-life are preferred because:
Initially, the activity is very high, so only a small sample needed
The shorter the half-life, the faster the isotope decays
Isotopes with a shorter half-life pose a much lower risk to the patient
The medical test doesn‘t last long so a half-life of a few hours is enough.
What are two examples of radioactive tracers?
One example is Iodine-131
This isotope is known to be specifically taken up by the thyroid gland making it useful
for monitoring and treating thyroid conditions
It emits beta particles which means it will stay concentrated on the thyroid area and
nowhere else in the body
It has a short half-life of 8 days meaning it will not be around too long to cause
prolonged exposure
Another isotope commonly used as a tracer is Technetium-99m
It is a gamma emitter with an energy of about 140 keV which is ideal for detection
It has a half-life of 6 hours so it is ideal for use as a tracer, but will not remain active
for too long and can be tolerated by the body
Gamma radiation is ideal as it is the most penetrating so it can be detected outside
the body
Also, gamma is the weakest ioniser and causes minimal damage
As well as this, technetium-99m may be prepared easily at the hospital when required
making it a cost-effective treatment
What type of radiation is used to sterilise medical equipment and why?
Gamma radiation is widely used to sterilise medical equipment
Gamma is most suited to this because:
It is the most penetrating out of all the types of radiation
It is penetrating enough to irradiate all sides of the instruments
Instruments can be sterilised without removing the packaging
The general public might be worried that using gamma radiation in this way might cause the
equipment itself to become radioactive, however, this is not the case because:
In order for a substance to become radioactive, the nuclei have to be affected
Ionising radiation only affects the outer electrons and not the nucleus
The radioactive material is kept securely sealed away from the packaged equipment
so there is no chance of contamination.
The definition of radioactive decay
The spontaneous disintegration of a nucleus to form a more stable nucleus,
resulting in the emission of an alpha, beta or gamma particle.
What does it mean for radioactive decay to be random and spontaneous?
Radioactive decay is a random process, this means that:
There is an equal probability of any nucleus decaying
It cannot be known which particular nucleus will decay next
It cannot be known at what time a particular nucleus will decay
Radioactive decay is a spontaneous process, this means that:
The rate of decay is unaffected by the surrounding conditions.
The rate of decay is not affected by the presemce of other nuclei in the sample
How can the random nature of radioactive decay be proven?
The random nature of radioactive decay can be demonstrated by observing the count rate of
a Geiger-Muller (GM) tube
When a GM tube is placed near a radioactive source, the counts are found to be
irregular and cannot be predicted
Each count represents a decay of an unstable nucleus
These fluctuations in count rate on the GM tube provide evidence for the
randomness of radioactive decay.
What is the average decay rate?
Since radioactive decay is spontaneous and random, it is useful to consider the average
number of nuclei that are expected to decay per unit time
This is known as the average decay rate.
What is the defintion of the decay constant?
The decay constant λ is defined as:
The probability that an individual nucleus will decay per unit of time.
What is the defintion of activity?
Activity, or the number of decays per unit time
What is the equation for activity?
A=ΔN/Δt=-(Lambda)N
A = activity of the sample (Bq)
ΔN = number of decayed nuclei
Δt = time interval (s)
λ = decay constant (s-1)
N = number of nuclei remaining in a sample
What are the units for Activity?
The activity of a sample is measured in Becquerels (Bq)
An activity of 1 Bq is equal to one decay per second, or 1 s-1
What does the equation for Activity show?
The greater the decay constant, the greater the activity of the sample
The activity depends on the number of undecayed nuclei remaining in the sample
The minus sign indicates that the number of nuclei remaining decreases with time.
However, for calculations it can be omitted
What is the graph for radioactive decay, what is it called and features of the graph?
In radioactive decay, the number of undecayed nuclei falls very rapidly, without ever
reaching zero
Such a model is known as exponential decay.
The key features of this graph are:
The steeper the slope, the larger the decay constant λ (and vice versa)
The decay curves always start on the y-axis at the initial number of undecayed nuclei
(N0)
Graph is in the document
What is the general equation used for expotential decay?
What quatinties can be used?
X=X0e^-λt
X can be A,N or C
C = count rate at a certain time t (counts per minute or cpm)
A = activity at a certain time t (Bq)
N = number of undecayed nuclei at a certain time t
What is the defintion for Avogadro’s constant/
Avogadro’s constant (NA) is defined as:
The number of atoms in one mole of a substance; equal to 6.02 × 1023 mol-1
What is the equation with molar mass, number of moles and number of nuclei?
n=N/NA=M/Mr
M = Mass (g)
Mr= Molar mass (g mol^-1)
N= Number of Nuclei
NA=Avogradro’s constant (mol^-1)
What is the definition of a half life?
The time taken for the initial number of nuclei to halve for a particular isotope.
What is the half life time equal to and derive it
t(1/2) = ln2/λ
How would you achieve a straight line graph with exponential decay?
Straight-line graphs tend to be more useful than curves for interpreting data
Nuclei decay exponentially, therefore, to achieve a straight line plot, logarithms can
be used.
How does carbon dating work?
The isotope carbon-14 is commonly used in radioactive dating
It forms as a result of cosmic rays knocking out neutrons from nuclei, which then collide with
nitrogen nuclei in the air:
1
n + 14N → 14C + 1
p
Plants take in carbon dioxide from the atmosphere for photosynthesis, including the
radioactive isotope carbon-14
Animals and humans take in carbon-14 by eating the plants
Therefore, all living organisms absorb carbon-14, but after they die they do not
absorb any more
The proportion of carbon-14 is constant in living organisms as carbon is constantly being
replaced during the period they are alive
When they die, the activity of carbon-14 in the organic matter starts to fall, with a half-life of
around 5730 years
Samples of living material can be tested by comparing the current amount of carbon-14 in
them and compared to the initial amount (which is based on the current ratio of carbon-14 to
carbon-12), and hence they can be dated.
What is the reliability of carbon dating and why?
Carbon dating is a highly reliable ageing method for samples ranging from around 1000
years old up to a limit of around 40 000 years old
Therefore, for very young, or very old samples, carbon dating is not the most reliable
method to use
This can be explained by looking at the decay curve of carbon-14:
If the sample is less than 1000 years old:
The activity of the sample will be too high
So, it is difficult to accurately measure the small change in activity
Therefore, the ratio of carbon-14 to carbon-12 will be too high to determine an
accurate age
If the sample is more than 40 000 years old:
The activity will be too small and have a count rate similar to that of background
radiation
So, there will be very few carbon-14 atoms remaining, hence very few decays will
occur
Therefore, the ratio of carbon-14 to carbon-12 will be too small to determine an
accurate age
Carbon dating uses the currently known ratio of carbon-14 to carbon-12, however, scientists
cannot know the level of carbon-14 in the biosphere thousands of years ago
Therefore, this makes it difficult to age samples which are very old.
What is potassium-argon dating/
Ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope of
potassium-40
This happens when a potassium nucleus captures an inner shell electron, also known as
electron capture
40K + e– → 40Ar + ve
The potassium isotope can also decay by β–
emission to form calcium-40
40K → 40Ca + β– + vₑ
The half-life of the potassium-40 is 1.25 billion years
The age of the rock (when it solidified) can be calculated by measuring the proportion of
argon-40 to potassium-40
This method is accurate for dating rocks up to 100 million years old.
What is uranium lead dating?
While the potassium-argon method is best for ageing younger rocks, the uranium-lead
method has been critical in dating geologic events more than 100 million years old
Initially, there is only uranium in the rock, but over time, the uranium decays via a decay
chain which ends with lead-206, which is a stable isotope
Uranium has a half-life of 4.5 billion years and over time, the ratio of lead-206 atoms to
uranium-238 atoms increases
This ratio may be used to determine the age of a sample of rock
Uranium is so well studied that its decay constant is much better known than other isotopes,
such as potassium, making the uranium-lead dating technique the most accurate available
Why do we storage radioactive waste and how?
Radioactive substances can be dangerous and some substances have very long half-lives
(even billions of years)
This means that they will be emitting harmful radiation well above background
radiation for a very long time
Waste products from nuclear power stations need to be appropriately stored for the
remaining time that they are radioactive
Common methods are water tanks or sealed underground
This is to prevent damage to people and the environment now and for many years
into the future
Sealing them underground means they are less likely to be dislodged or released due
to natural disasters.
What is the equation for power and activity?
P =ΔE/Δt = AE
This is the energy transfer per second from a radioactive source
What are the most common elements in the univese and why?
The most common elements in the universe all tend to have values of N and Z less than 20
(plus iron which has Z = 26, N = 30)
Where:
N = number of neutrons
Z = number of protons / atomic number
This is because lighter elements (with fewer protons) tend to be much more stable than
heavier ones (with many protons)
When will a nucleus be too unstable and what happens/
A nucleus will be unstable if it has:
Too many neutrons
Too many protons
Too many nucleons ie. too heavy
Too much energy
An unstable atom wants to become neutral to become stable
What happens to the neutron to proton ratio for light and heavy isotopes?
For light isotopes, Z < 20:
All these nuclei tend to be very stable
They follow the straight-line N = Z
For heavy isotopes, Z > 20:
The neutron-proton ratio increases
Stable nuclei must have more neutrons than protons
How does the imbalance between neutrons and protons effect stability and why?
This imbalance in the neutron-proton ratio is very significant to the stability of nuclei
At a short-range (around 1–4 fm), nucleons are bound by the strong nuclear force
Below 1 fm, the strong nuclear force is repulsive in order to prevent the nucleus
from collapsing
At longer ranges, the electromagnetic force acts between protons, so more protons
cause more instability
Therefore, as more protons are added to the nucleus, more neutrons are needed to
add distance between protons to reduce the electrostatic repulsion
Also, the extra neutrons increase the amount of binding force which helps to bind
the nucleons together.
Where are alpha emitters on N against Z graph?
Alpha-emitters:
Occur beneath the line of stability when Z > 60 where there are too many
nucleons in the nucleus
These nuclei have more neutrons than protons, but they are too large to be stable
This is because the strong nuclear force between the nucleons is unable to overcome
the electrostatic force of repulsion between the protons.
Where are Beta minus emitters on N against Z graph?
Beta-minus (β–
) emitters:
Occur to the left of the stability line where the isotopes are neutron-rich compared
to stable isotopes
A neutron is converted to a proton and emits a β–
particle (and an anti-electron
neutrino)
Where are alpha emitters on N against Z graph?
Beta-plus (β+
) emitters:
Occur to the right of the stability line where the isotopes are proton-rich compared
to stable isotopes
A proton is converted to a neutron and emits a β+
particle (and an electron neutrino)
Where are electron capture on N against Z graph?
When a nucleus captures one of its own orbiting electrons
As with β+
decay, a proton in the nucleus is converted into a neutron, releasing a
gamma-ray (and an electron neutrino)
Hence, this also occurs to the right of the stability line where the isotopes are proton-rich compared to stable isotope.
How and why does gamma emission happen?
Decays through gamma (γ) emission
A gamma particle is a high-energy electromagnetic radiation
This usually occurs after a different type of decay, such as alpha or beta decay
This is because the nucleus becomes excited and has excess energy.
How do nuclei exist in excited states and what happens afterwards/
In the same way that electrons can exist in excited states, nuclei can also exist in excited
states
After an unstable nucleus emits an alpha particle, beta particle or undergoes electron
capture, it may emit any remaining energy in the form of a gamma photon (γ)
Emission of a γ photon does not change the number of protons or neutrons in the
nucleus, it only allows the nucleus to lose energy
This happens when a daughter nucleus is in an excited state after a decay
This excited state is usually very short-lived, and the nucleus quickly moves to its ground
state, either directly or via one or more lower-energy excited states
One common application of this is the use of technetium-99m as a γ source in medical
diagnosis
The ‘m’ stands for metastable which means the nucleus exists in a particularly
stable excited state
Technetium-99m is the decay product of molybdenum-99, which can be found as a product in
nuclear reactors.
What is the closest approach method for estimating the nuclear radius?
In the Rutherford scattering experiment, alpha particles are fired at a thin gold foil
Some of the alpha particles are found to come straight back from the gold foil
This indicates that there is electrostatic repulsion between the alpha particles and the
gold nucleus
At the point of closest approach, r, the repulsive force reduces the speed of the alpha
particles to zero momentarily
At this point, the initial kinetic energy of an alpha particle, Ek
, is equal to electric potential
energy, Ep
The radius of the closest approach can be found be equating the initial kinetic energy to the
electric potential energy.
What are the advantages of the closest approach method?
Alpha scattering gives a good estimate of the upper limit for a nuclear radius
The mathematics behind this approach are very simple
The alpha particles are scattered only by the protons and not all the nucleons that make up
the nucleus.
What are disadvantages of the closest approach method/
This method does not give an accurate value for nuclear radius as it will always be an
overestimate
This is because it measures the nearest distance the alpha particle can get to the gold
nucleus, not the radius of it
Alpha particles are hadrons, therefore, when they get close to the nucleus they are affected
by the strong nuclear force and the mathematics do not account for this
The gold nucleus will recoil as the alpha particle approaches
Alpha particles have a finite size whereas electrons can be treated as a point mass
It is difficult to obtain alpha particles which rebound at exactly 180°
In order to do this, a small collision region is required
The alpha particles in the beam must all have the exact same initial kinetic energy
The sample must be extremely thin to prevent multiple scattering.
What is the electron diffraction method?
Electrons accelerated to close to the speed of light have wave-like properties such as the
ability to diffract and have a de Broglie wavelength. The diffraction pattern forms a central bright spot with dimmer concentric circles around it
From this pattern, a graph of intensity against diffraction angle can be used to find the
diffraction angle of the first minimum.
What are the advantages to using the electron diffraction method?
Electron diffraction is much more accurate than the closest approach method
This method gives a direct measurement of the radius of a nucleus
Electrons are leptons; therefore, they will not interact with nucleons in the nucleus through
the strong nuclear force as an alpha particle would.
What are the disadvantages of the electron diffraction method?
Electrons must be accelerated to very high speeds to minimise the de Broglie wavelength
and increase resolution
This is because significant diffraction takes place when the electron wavelength is
similar in size to the nuclear diameter
Electrons can be scattered by both protons and neutrons
If there is an excessive amount of scattering, then the first minimum of the electron
diffraction can be difficult to determine.
What is the graph you get from the electron diffraction method?
What is the equation for de Broglie wavelength?
λ=h/mv
h = Planck’s constant
m = mass of an electron (kg)
v = speed of the electrons (m s−1)
What is the equation used to find the size of the atomic nucleus R?
sinθ=1.22λ/2R
θ = angle of the first minimum (degrees)
λ = de Broglie wavelength (m)
R = radius of the nucleus (m)
What is an estimate for the nuclear radii?
10^-15 or 1fm
What is the graph for Nuclear radius against Nucleon number and key features?
The key features of this graph are:
The graph starts with a steep gradient at the origin
Then the gradient gradually decreases to almost horizontal
This means that
As more nucleons are added to a nucleus, the nucleus gets bigger
However, the number of nucleons A is not proportional to its size r
Graph found in document
What is the equation for nuclear radius and nucleon/mass number?
R=R0A^(1/3)
R = nuclear radius (m)
A = nucleon / mass number
R0 = constant of proportionality = 1.05 fm
What is the graph that you get when you plot R against A^(1/3)?
The graph is provided in the document
What graph do you get for the logarithmic graph?
Therefore, a graph of ln R against ln A yields a straight line
Comparing this to the straight-line equation: y = mx + c
y = lnR
x = lnA
m (the gradient) = 1/3
c (y-intercept) = ln R0
Graph provided in the document
How to derive Nuclear density?
Get the equation
What is the equation for nuclear density?
ρ=3u/4π(R0)^3
Atomic mass unit, u = 1.661 × 10–27 kg
Constant of proportionality, R0 = 1.05 × 10–15 m
What does th nuclear density mean?
Since the mass number A cancels out, the remaining quantities in the equation are all constant
Therefore, this shows the density of the nucleus is:
Constant
Independent of the radius
The fact that nuclear density is constant shows that nucleons are evenly separated throughout the nucleus regardless of their size
What does the nuclear density being larger than the atomic density mean?
Nuclear density is significantly larger than atomic density, this suggests:
The majority of the atom’s mass is contained in the nucleus
The nucleus is very small compared to the atom
Atoms must be predominantly empty space
