NUCLEAR PHYSICS Flashcards
Scattering experiment observations - conclusions
- Most α particles passed straight through with minimal
deflection (around 1/2000 deflected)
Small percent of α particles deflected through an angle greater than 90° - Most of the atom’s mass is concentrated in a small
region in the centre (nucleus) - Nucleus is positively charged as it repels α particles
How direction of α approach affects deflection
Arriving head on will cause α particle to be deflected head on.
Closer initial direction of α particle to “head on” direction - greater deflection due to coulomb’s law + smaller least distance of approach to the nucleus
Estimate size of nucleus using fact that 1 in 10,000 α particles are deflected by an angle over 90°
For a single scattering by a foil with n layers of atoms, the probability of an α particle being deflected by a single atom is 1/10000n. Probability depends on effective cross sectional area of the nucleus to the atom. So for a nucleus of diameter d in an atom of diameter D, d²/D² = 1/10000n
typical value for n=10^-4
squared factor due to area (πd²/4)
Why must foil be thin in α scattering experiment?
+ Why must beam be narrow
So α particles not scattered more than once
+Also pass through
Beam must be narrow to define a precise location where scattering takes place, and accurately determine the scattering angle
Ionisation effect (ionisation chamber) setup + observations
Using ionisation chamber and picoammeter - chamber contains air at atmospheric pressure, radiation directed at chamber. Ions created are attracted to an opposite charged electrode where they are discharged, Electrons pass through the picoammeter as a result. Current is proportional to number of ions created per second in the chamber.
α radiation causes strong ionisation, however ceases at a certain separation - has a small range in air ~ a few cm.
β has a much weaker ionising effect than α, but range in air varies up to ~ a metre. A β particle produces less ions per mm along its path.
γ radiation has very low ionising power as photons carry no charge
Ionisation effect (Cloud chamber) setup + observations
Cloud chamber contains air saturated at a very low pressure, due to ionisation of the air, an α or β particle passing through the chamber leaves a visible track of condensed vapour droplets as the air space is supersaturated. When an ionising particle passes through the vapour, the ions produced trigger the formation of droplets.
α particles produce straight tracks that radiate from the source and are easily visible. Tracks are all the same length, indicating they all have the same range.
β particles produce wispy tracks that are easily deflected due to collisions with air molecules. Tracks aren’t as visible due to weaker ionising effect.
Absorption summary
α completely absorbed by paper + thin metal foil
β absorbed by 5mm of metal foil (Al)
γ absorbed by several cm of lead
Why do α particles from the same source have the same range but β particles don’t
α particles from a given isotope are always emitted with the same Ek, as each α particle and the nucleus that emits it move apart with equal and opposite momenta. However in the case of β emission, a neutrino/antineutrino is emitted as well. So the nucleus, β particle and neutrino all share the Ek in variable proportions
Radiation range in air
α - a few cm in air (range differs from one source to another indicating initial Ek differs between sources)
β - range up to ~ a metre, β particles from a source have a range of Ek to a maximum. Faster β travel more than slower ones due to more Ek
γ - Unlimited range, intensity (proportion of photons striking a point) decreases according to inverse square law, energy constant for a given source (hf)
Deflection in magnetic fields
Alpha deflected , beta deflected opposite to alpha and greater, gamma no deflection
What is alpha, beta and gamma radiation
Alpha - helium nucleus
Beta (naturally occuring) is fast moving electrons
Gamma - photons with wavelength of order 10^-11 or less
Intensity
Radiation energy per second incident on a unit area
=nhf/4πr²
at a distance r from the source, photons emitted pass through a total area of 4πr² (surface area of a sphere)
I = k/r² where k is above stuff enih
Verifying inverse square law for a radioactive source
Use Geiger counter to measure count rate at different distances from a source *corrected” count rate (-bg) is proportional to intensity. Standard procedure from then
Why does ionising radiation affect living cells?
It can destroy cell membranes, causing them to die
It can damage vital molecules, e.g. dna by creating “free radical” ions which damage nuclei, causing uncontrollable growth of cells (cancer)
Sources of background radiation
Air (Radon gas)
Cosmic rays
Nuclear weapons, nuclear power
Food and drink e.g. bananas
Air travel
Storage of radioactive materials
In lead lined containers, and should be thick enough to reduce gamma radiation from source to ~ background level. Additionally lock and key storage
Protocol for using radioactive sources
Solid sources should be transferred using tongs/tweezers - ensure sample is as far away as possible to limit exposure from gamma (alpha and beta absorbed by air)
Liquid and gas sources + solids in powder form should be in sealed containers - prevent source from being inhaled + liquid can’t be splashed on the skin
Sources shouldn’t be used for longer than necessary - the longer a person is exposed to ionising radiation, the greater the dosage received
Why is decay an exponential process
Number of nuclei that decay at a certain time is proportional to the number of nuclei remaining
Acitivity definition
Number of nuclei that disintegrate per second (Bq), proportional to mass of isotope
Energy transfer per second from a radioactive source
AE where E is the energy of a particle
A = n/t – chen rul
Forms of decay eq
N=N₀e^-λt
A=A₀ … M=M₀ …C=C₀ where lambda is the decay constant
Activity proportional to N, Mass proportional to N, Corrected count rate proportional to activity of source and therefore N
What is the decay constant λ?
The probability of an individual nucleus decaying per second
also = ln2/T(1/2)
Ideal properties of radioactive tracers
Half life stable enough for necessary measurements to be made, and short enough to decay quickly after use
Emit beta or gamma radiation so it can be detected outside the flow path
Argon dating
Potassium 40 decays into argon and calcium. Calcium decay is 8x more probable.
For every 1 argon atom present in N atoms of K, there must have been N+9 K atoms originally (8 decayed into Ca)
can use N=N0…
Measuring engine wear (txtbook)
Industrial uses of radioactive tracers
(make method fc later)
Detecting underground pipe leaks
Modelling oil reservoirs
Investigating uptake of fertilisers by plants
Monitoring uptake of iodine by thyroid gland
Explanation of N-Z curve
Light nuclei - 0<Z<20 Stable nuclei follow N=Z
20<Z Stable nuclei have more neutrons than protons, help to bind nucleons together without introducing repulsive electrostatic forces as more neutrons would do.
Alpha emitters beyond Z=60 Strong nuclear force between nucleons unable to overcome force of repulsion between protons
B- emitters occur to the left of stability belt where isotopes are neutron rich
B+ occur to right where isotopes are proton rich. (also electron capture)
How a gamma photon can be emitted after alpha/beta
If the daughter nucleus is in an excited state after emitting an alpha or beta particle, it emits a gamma photon to move to its ground state
What is binding energy
The work that must be done to separate a nucleus into its constituent neutrons and protons
What is mass defect
The difference in mass between the nucleus and the constituent nucleons
Why should incident alpha particle beam be narrow
- to define a precise location where the scattering
takes place - so that the scattering angle can be determined
accurately.
Feature of scattering experiment that suggested nucleus contains most of the mass
Some α particles are scattered through very large
angles (>90°, or back towards the source).
This can only occur if an α particle collides
with a particle of much greater mass than
its own mass.
Alpha dangers outside body vs inside
α radiation is highly ionising, hence causes
cancer/damages cells/kills cells/affects DNA.
Outside the body it is less damaging, because it is
absorbed by the skin (or is stopped by the skin, or
causes a burning sensation).
Inside the body it is more damaging, because it is
able to produce ionisation in vital organs such as
lungs.
Will continue to ionise body until removed
Benefits of gamma for medicine
γ rays are very penetrating (or α or β rays would
not be detected outside the body).
γ rays are less ionising, hence less hazardous to
patients (or α or β rays are more ionising and
more hazardous).
When bg radiation can be ignored
The background count rate is very much smaller
than the measured count rate (background count
rates are typically less than 1 counts s
−1
).
Random fluctuations in the measurements are
greater than the background ground count rate
Benefits of a short half life
- The activity is high (so only a small sample is
needed). - The radioisotope decays quickly.
- There is less risk to the patient.
- The medical test is of short duration.
Because T1/2 ∝1/lambda
Merits of using high energy electrons instead of alpha particles in scattering experiments
- Electrons are not subject to the strong nuclear
force. - With α particles the closest distance of approach
is measured, rather than R. - Electrons cause far less recoil.
- Electrons give greater resolution.
- High energy electrons are easier to produce.
Qualitative study of Rutherford scattering
Knew the atom contained electrons, Rutherford discovered how the positive charge was distributed
Controls for scattering experiment
α particles must have the same speed or slow α particles would be deflected more than faster particles on the same initial path
Container must be evacuated so particles aren’t absorbed by air
α source must have a long half life or later readings would be lower than earlier ones due to decay of the source nuclei
Why would a graph of count rate vs distance for a β emitter level off?
β particles absorbed by air molecules, producing γ photons
(Electron capture can produce γ photons due to excitation principles - excess e etc)
Dead time of a Geiger muller tube
Time taken to regain non conducting state after receiving ion, typically of order 0.2ms - Another particle received in this time won’t cause a voltage pulse, Therefore count rate should be no greater than 1/0.2s = 5000s^-1
How background radiation can vary geologically hint radon
Radon gas can accumulate in poorly ventilated areas of buildings in certain locations
If a certain thickness of absorber decreases the intensity of a gamma photon to 1/2, what would be the thickness needed to cut the intensity to 1/4
2x the thickness
Deductions made from random nature of decay
proportionalities of ΔN, where ΔN is the number of nuclei disintegrated in a time Δt
+ Activity eq
ΔN is proportional to N, the number of nuclei remaining at a time T, and proportional to the duration of time Δt
Therefore ΔN = -λNΔt
And A = -λN
λ is decay constant, negative necessary as ΔN is a decrease
Calculation of rate of engine wear using radioactive tracers
Fitting in a radioactive piston ring - as ring slides along piston compartment, radioactive atoms transfer from ring to engine oil, by measuring radioactivity of oil, mass of radioactive metal transferred can be measured and rate of wear calculated.
Metal ring can be made radioactive by exposing it to neutron radiation in a nuclear reactor. Each nucleus that absorbs a neutron becomes unstable and emits a beta- particle
Applications of radioactive tracers
Detecting pipe leaks - inject tracer into flow, detector on surface above pipeline used to detect leakage
Investigating uptake of fertiliser by plants - Plants watered with a solution containing fertiliser, by measuring radioactivity of leaves, amount of fertiliser reaching them can be determined
Monitoring uptake of iodine by thyroid gland - Patient given solution of sodium iodide. Activity of patient’s thyroid and activity of an identical sample prepared at the same time measured 24hrs later
Monitoring metal foil thickness - foil made by two rollers - detector measures amount of radiation passing through foil - if reading is too low, rollers move closer together and converse
Estimating radius of nucleus using distance of least approach d
At said distance d, kinetic energy of particle = potential energy of system containing nucleus + particle
Why are electrons diffracted by a nucleus?
Their de broglie wavelength is about the same as the diameter of a nucleus
Wavelength of high energy electrons λ=hc/E
λ=h/mv, as electrons have high energy, travel close to speed of light, so λ =h/mc — E = mc²
λ =hc/E
Typical values of nuclear radius
of order of 10^-15 (femtometres)
minimum angle of deflection for electron around a nucleus that i dont need to know btw ramil is a waffler
Rsinθ = 0.61λ, where λ is the de broglie wavelength of the electrons
Deductions from high energy diffraction experiment
Scattering of beam electrons by nuclei occurs due to their charge - as they are attracted to nuclei, this causes the intensity to decrease as angle of incidence increases (ask why)
Diffraction of electron beam causes intensity minima and maxima to be superimposed on above effect, provided de broglie wavelength isn’t greater than nucleus diameter. Superimposed intensity variation similar to concentric bright and dark fringes when a beam of monochromatic light is directed at a circular gap/object. Angle from first minimum is measured and used to calculate nuclear radius
Defs for hypotheses, peer review, repeatable etc
Why Rutherford’s proton - neutron model was considered more than an untested hypothesis before the discovery of the neutron
Charge on nucleus was Ze, however mass was greater than Zmp
Used to explain why mass number of any nucleus greater than H1 is greater than its atomic number
Feature of the distribution of scattered alpha particles that suggests the nucleus contains most of the mass of the atom
Some α particles are scattered through very large
angles (>90°, or back towards the source).
This can only occur if an α particle collides
with a particle of much greater mass than
its own mass.
Relating activity (GM tube) and number of radioactive nucelei
A=λN
given GM detector receives all radiation from sample (which is false)
Sources of bg radiation
cosmic rays; radioactive rocks (or ground, or
building materials); nuclear weapons testing (or
nuclear accidents);
nuclear power industry; discharge of nuclear
waste; radioactive gases in the air; medical waste
Why measuring background rate may not always be necessary (e.g. for large values of activity)
The background count rate is very much smaller
than the measured count rate (background count
rates are typically less than 1 counts s
−1
).
Random fluctuations in the measurements are
greater than the background ground count rate.
Why isotopes with short half lives are good tracers
- The activity is high (so only a small sample is
needed). - The radioisotope decays quickly.
- There is less risk to the patient.
- The medical test is of short duration
Because T1/2 ∝
1
, it follows that a
radioisotope of short half-life will
have a large value of λ, and therefore
a high activity when it is introduced
into the patient. The sample used is
small and it soon decays to a
negligible activity
Calculating half life from a graph
Take two and average them
Why technetium is often chosen as a suitable radiation source in medical diagnosis
- Technetium 99-m emits only γ radiation…
- hence radiation may be detected outside the
body (or it is a weak ioniser and causes little
damage). - It has a short half-life and will not remain active
in the body for long after use. - Its half-life is long enough for it to remain active
during diagnosis. - When needed it may be prepared on site.
- It has a toxicity that can be tolerated by
the body.
When using a radiation source for medical diagnosis, the half life of the source should be
Similar to the length of the medical procedure - minimises radiation dose to patient. However if it’s very close, the sample must be prepared at the place it’ll be used
Einstein theory of special relativity
The mass of an object changes with it’s speed, and no object can move at the speed of light
(E=mc^2)
+ Moving clocks run slower than stationary clocks, fast moving objects appear shorter than when stationary
Conservation of energy in alpha decay
The parent nucleus decays to an alpha and a daughter nucleus and the difference in energy E
is converted to kinetic energy of the two. However momentum is also conserved so they have equal and opposite momentum, meaning that the energy of the alpha is completely specified p^2/2Ma + p^2/2mN=E. So all alpha particles from such a decay have the same energy and the same velocity (which means the same range)
Energy lose by a nucleus in 1 alpha decay
ΔMc²
Where M is the mass of an alpha particle - energy conservation
Energy dissipated in beta decay
Energy shared in variable proportion between β particle, nucleus ,neutrino and antineutrino. When β particle has maximum Ek, other particles have negligible in comparison.
Maximum Ek of β particle is slightly less than energy released in the decay due to recoil of the nucleus
Energy dissipated in electron capture
Nucleus emits a neutrino which carries away energy released in decay. Atom also emits an X ray photon when inner shell vacancy due to electron capture is filled.
What to do when mass of atom is given rather than nucleus
Subtract mass of electrons
How strong force can be determined
Working out magnitude of electrostatic force of repulsion between 2 protons at a separation of 1fm (approx size of nucleus)
Deducing that strong force acts between nearest neighbour nucleons
High energy electron scattering experiment shows nucleons are evenly spaced at about 10^-15m away from each other - within attractive range of sf so only acts between nearest neighbour
Deducing energy required to remove a nucleon from nucleus using strong force magnitude + range
Magnitude determined by equating to electrostatic force between protons. Acts over a distance of 2-3fm, so work done over this distance = fs in order of millions of ev
What is binding energy
Work that must be done to separate a nucleus into constituent neutrons and protons.
(When a nucleus forms from separate neutrons and protons, energy is released as the strong force does work in pulling the nucleons together - mass of nucleus is less than constituents)
What is binding energy per nucleon?
Average work done per nucleon to remove all nucleons from the nucleus
How binding energy per nucleon affects stability
Nucleus with more binding energy per nucleon is more stable
Processes that can increase stability of nucleus (relating to binding energy) + comparing effects of both on binding energy per nucleon
Nuclear fission - Large unstable nuclei splits into two smaller, more stable fragments - binding energy increases.
Fusion - Small, light nuclei fusing to make a larger nucleus - has more binding energy per nucleon than smaller nuclei, so binding energy also increases in this process, provided nucleon number of new nucleus < about 50
Change in binding energy per nucleon ~ 0.5MeV in a fission reaction and can be about 10x in a fusion reaction
Graph of binding energy per nucleon vs nucleon number
Know it
What is an induced nuclear fission chain reaction
A single thermal neutron is absorbed by a nucleus - forming an unstable, heavier nucleus which undergoes fission and is split into 2 daughter nuclei and more neutrons.
What is a thermal neutron
One that is in “thermodynamic equilibrium” - moving at the same speed as its surroundings
Number of neutrons emitted after n generations where x neutrons are released in first wan
X^n
How does surface area:mass ratio affect neutron escape
Larger SA:mass ratio of fissile material, more likely for neutrons to escape, e.g. fewer neutrons would escape a sphere as opposed to a strip. In turn more neutrons go on to cause fission in a sphere
Condition for chain reaction to occur
Mass of the fissile material must be greater than the critical mass (some neutrons escape the fissile material w/o causing fission or are absorbed by nuclei without undergoing fission). If mass is below, too many neutrons escape due to large sa:mass ratio.
Why sa/mass ratio affects fission power output
Neutron loss depends on surface area, neutron production depends on mass - high sa:mass ratio - greater loss than there is production, more neutrons escape
Diff between fossil fuel and nuclear fuel
Fossil - burns to release energy
Nuclear - Decays to release energy
Main energy transfers in nuclear power station
Nuclear energy in fuel
Kinetic energy in fission products
Internal energy of water + steam
Kinetic energy of water + steam
Kinetic energy of turbine
Factors affecting whether fission will occur
Neutrons are penetrating particles (bc they’re uncharged), and so are likely to leave the material without interacting with any nuclei
Uranium atoms only make up a small amount of the fissile material (control energy output)
A slow moving neutron is more likely to cause fission than a fast moving one
(think it spends longer around the pull of the nucleus)
Nuclear reactor components
Fuel rods spaced evenly in a steel vessel (reactor core) - contain enriched URANIUM.
Control rods - lowered to absorb neutrons - depth is adjusted to keep the number of neutrons in the core constant so on average one neutron from each fission event goes on to cause another fission, keeps power output constant. Greater depth reduces output.
Moderator - surrounds fuel rods and slows down neutrons by repeated collisions with moderator atoms. Reactor is called a thermal fission reactor as fission neutrons are reduced to the around the same Ek as moderator molecules.
Coolant - Removes thermal from reactor core + neutrons(prevent overheating) should have a low specific heat capacity so that a large amount of thermal energy can be absorbed without changing its temperature (heating up), e.g. water of CO2
Why do smaller objects cool faster
A smaller object will have a higher surface area to volume ratio compared to a larger object with the same shape. This means that for a given amount of heat energy, a smaller object will have more surface area available to lose heat than a larger object
Factors affecting choice of moderator
Using mechanical model of moderation by elastic collision - when particles collide, there is a higher proportion of kinetic energy transfer. m(neutron =1)
consider a neutron incident at velocity u on a stationary nucleus mass m, rebounds at speed v and nucleus recoils at speed V
u+v = mV u²=v²+MV²
solving gives v=u(1-m)/(1+m)
ratio of initial to final ek = (u/v)² =
[(1+m)/(1-m)]² - greater transfer as m approaches 1
- atoms with light nuclei suitable for moderation - transfer greatest proportion of Ek per collision, but it’s also important that they don’t absorb the neutrons.
Commonly graphite(carbon) or water used as a moderator
Factors affecting material choice for control rods + typical mats
Must have a high boiling point and be able to absorb neutrons well (boron + cadmium)
Safety features of nuclear reactors
Reactor core is a thick steel vessel designed to withstand high temperature and pressure in reactor core - absorbs β radiation and some of the γ and neutron radiation from core
Core is in a building with thick concrete walls - absorb neutrons and γ photons that escape from the vessel
Reactors have emergency shut down system - fully insert control rods to completely stop fission
Sealed fuel rods inserted and removed through remote handling devices - rods are more radioactive after than before
Why are fuel rods more radioactive after use than before
Before contain U235 and 238, which are only α emitters, and absorbed by fuel cans
After use emit β and γ radiation due to many neutron rich fission products that form.
Also contain Pu239 as a result of U238 absorbing neutrons - very active α emitter which can cause lung cancer if inhaled
Sources of high level radioactive waste
Nuclear power stations, specialist users in university and industry, hospitals that use radioactive isotopes for diagnosis/therapy.
Banned disposal method
Disposal by diluting - diluting radioactive water from nuclear power stations’ cooling systems with large quantities of water and dispersing it into the sea
Benefits of loooong half life
Count rate is approximately constant
Why would slower alpha particles deflect more
Particles emitted during beta decay + charge
Electron + antineutrino - nucleus becomes net positive charge
Often resolved by attracting/losing extra electron (depending on type of decay)
Beta particle has a high Ek so escapes before it can be influenced by the electric field
How to dispose of high level radioactive waste
e.g. spent fuel rods - removed by remote control then stored underwater in cooling ponds for up to a year as they continue to release heat due to radioactive decay. In Britain rods are transferred in large steel casks to THORP reprocessing plant - unused U and Pu removed and stored in sealed containers for further use, rest of radioactive material stored in deep trenches in Sheffield (sealed containers) -Must be stored for centuries as it contains long lived radioactive isotopes which must be prevented from contaminating food and water supplies
problems - no one wants storage in their own locality, nor do people want waste to be carried through their locality to another location.
Handling of intermediate level waste
Radioactive isotopes with low activity and containers of radioactive materials are sealed in drums encased in concrete and stored in buildings with walls of reinforced concrete
Handling of low level radioactive waste
e.g. Lab equipment + protective clothing are sealed in metal drums and buried in large trenches
Why must disposal of radioactive waste be in accordance with legal regulations/approved by disposal companies
Ensures that radioactive waste is stored safely in secure containers until activity in significant
Why fission of a heavy nucleus is likely to release more energy than fusion of a light nucleus
(ref to binding energy graph)
- Both processes cause an increase in the binding
energy per nucleon. - This energy is released as the kinetic energy of
the products of the reaction. - The increase in binding energy per nucleon is
greater in a fusion reaction than in a fission
reaction. - The binding energy of a large nucleus is very
much greater than that of a small nucleus,
because the former contains many more
nucleons. - The net increase in binding energy during the
fission of a large nucleus is therefore greater than
that occurring during the fusion of two small
nuclei.
It is
useful to look at the slopes of the
fusion and fission sections of the
binding energy per nucleon curve.
One fusion reaction may release
about 5 MeV nucleon−1
, but only
a few nucleons are involved, and so
the total energy released may be
only about 20 MeV. The fission of
U
235
92
releases about 0.9 MeV
nucleon−1
, but almost 240 nucleons
are involved and so around 200 MeV
of energy is released
Why energy is released in nuclear fusion + why it’s difficult to achieve
Energy is released because
* fusion of two nuclei increases their binding
energy per nucleon
* the fusion reaction produces an increase in the
mass difference (or the nucleus formed is more
stable than the two original nuclei).
Fusion is difficult to achieve because
* each of the two original nuclei has a positive
charge
* the electrostatic repulsion of these positive
charges has to be overcome.
How repulsive nature of sf contributes to nuclear stability
repulsive under 0.8fm, prevents nucleus from collapsing on itself
More neutrons are needed to hold nucleus together / add to binding force/increase
instability/reduce stability
Fewer protons are required so as to reduce the repulsion/reduce instability/increase
stability
Benefits of nuclear power
(Small amounts of fossil fuel used) so little greenhouse gas emissions/less global
warming/less CO2/less climate change. {not no greenhouse gas}
2. (Less fossil fuel used) so cleaner air.
3. Small amounts of fuel consumed to get the same/large amount of
power/energy.
4. Nuclear power can be produced continuously{condone use of constant}
(whereas renewables are dependent on sunlight/wind etc).
5. Some (but not all) nuclear power stations can adjust their output quickly.
6. Benefit of producing medical isotopes.
Explain why the public need not worry that irradiated surgical instruments become
radioactive once sterilised.
To become radioactive the nucleus has to be affected which (ionising) radiation does
not do
The energy of the radiation is insufficient to induce radioactivity.
Radioactivity definition
Emission of ionizing radiation caused by changes in nuclei of unstable atoms
Large decay constant
Short half life and fast decay
How energy is released in fission
Fragments repel each other (both positive) with sufficient force to overcome strong force. Fragment nuclei and neutrons gain Ek. Two daughter nuclei are smaller and more tightly bound
