1
Q
What did the alpha-particle scattering experiment allow us to determine?
A
The structure of a nucleus.
2
Q
How did the alpha particle scattering experiment work?
A
- A narrow beam of alpha particles was produced by a Polonium-210 source
- This was fired at a thin sheet of gold foil
- They were detected by a microscope in front of a zinc sulphide screen which fluoresced when alpha particles made contact
- The microscope arrangement was moved about an angle theta
3
Q
What observations could be made from the alpha-particle scattering experiment?
A
- Most alpha particles passed straight through: an atom is mostly empty space
- 1/2000 were deflected, and 1/10000 were deflected through theta > 90: mass is concentrated in a small area, and the nucleus carries a strong +ve charge
4
Q
Why was gold foil used in the alpha-particle scattering experiment?
A
- Gold foil is highly malleable
- This meant that it could be rolled out to produce a single layer of just one atom in thickness
5
Q
What physical law helps us model the scattering of alpha particles?
A
Coulomb’s law: considering the forces between two like-charged particles.
6
Q
How can Coulomb’s law be used to estimate the radius of a nucleus?
A
- An alpha particles passed straight has like charge to a positive nucleus, so electric forces do work against the alpha particle
- This means kinetic energy is transferred to electric potential stores
- Until kinetic energy is zero; this is where EP is a maximum. Using the EP equation we can determine the radius of the nucleus
7
Q
Why is the Coulomb estimation for nuclear radius an inaccurate measurement?
A
- The point of closest approach is determined by the inbound alpha-particle’s initial kinetic energy
- This can vary depending on the pd/electric field the particle is accelerated through
8
Q
Define atomic mass unit.
A
1/12th the mass of a carbon-12 atom.
9
Q
What formula links atomic radius with nucleon number A?
A
R=R0A^1/3
10
Q
What is the value of R0?
A
1.2x10^-15 m, i.e. 1.2 fm.
11
Q
Why is the density of the nucleus always constant?
A
- We know that density is the mass:volume ratio
- Mass increases as A
- Radius increases with A^1/3 —> Volume = 4/3 * pi * r^3 i.e. volume increases with A
- SO mass increases by the same factor volume increases, and density is constant
12
Q
Why is the strong nuclear force required to hold a nucleus together?
A
At small separations, the repulsive electrostatic force between protons is strong; the nuclear force is attractive at these separations to oppose this.
13
Q
What types of particle does the strong nuclear force act between?
A
Nucleons (protons, neutrons)
14
Q
What is the range of the strong nuclear force?
A
Very short at roughly 3fm.
15
Q
Describe how the strong nuclear force varies with radius.
A
- Below 0.5 fm the force is repulsive
- Up to 3.0 fm the force is attractive instead
16
Q
How can we determine the equilibrium position for a proton?
A
This is the radius at which the strong nuclear force exactly opposes the weak nuclear force, to produce zero net resultant force.
17
Q
How can we determine the equilibrium position for a neutron?
A
Neutrons are not affected by Fe, so the equilibrium position will be the radius at which the strong nuclear force has zero magnitude.
18
Q
Why can it be said that neutrons are the ‘glue’ holding a nucleus together?
A
They increase the strong nuclear force without contributing towards the electrostatic force it acts against, because they are uncharged particles
19
Q
What is an antiparticle?
A
These have opposite charge to the standard particle, and an identical rest mass.
20
Q
What happens when particles and antiparticles meet?
A
- Annihilation occurs
- Their masses are converted to a high energy pair of electrons
21
Q
What is pair production?
A
A high energy photon spontaneously produces a particle-antiparticle pair. Note the photons carries more energy than the combined rest masses of the two particles would suggest; this is converted to KE.
22
Q
What is the force responsible for beta decay?
A
The weak nuclear force.
23
Q
What is a fundamental particle?
A
A particle that cannot be divided into any smaller units.
24
Q
What might be examples of fundamental particles?
A
Quarks, leptons, neutrinos
25
What is a hadron?
Particles comprised of 2 or more quarks. These are subdivided into baryons and mesons.
26
What is a baryon?
Made up of x3 quarks, affected by SNF. Examples include protons or neutrons.
27
What is a meson?
A particle comprised of a quark-antiquark pair. These carry the SNF. They are heavy and unstable, explaining the weakness of the SNF.
28
What are leptons?
Fundamental particles with low mass. They do not feel the SNF, only the WNF.
29
What are the three flavours of quark we need to know about?
Up (+2/3e), Down (-1/3e), and Strange (-1/3e)
30
What is beta-minus decay?
A neutron is converted into a proton and an electron.
31
Why might a nucleus undergo beta-minus decay?
It contains too many neutrons.
32
Why might a nucleus undergo beta-plus decay?
It contains too many protons.
33
What is beta-plus decay?
A proton is converted to a neutron and a positron (anti-electron)
34
What is always released during beta decay as a side product?
A neutrino or antineutrino, depending on which is required to conserve lepton number.
35
What did Wolfgang Pauli predict the existence of in order to explain conservation principles in beta decay?
(Anti)electron neutrinos
36
Give some properties of neutrinos.
They carry zero charge, are produced during beta decay, feel the WNF and hardly interact with matter.
37
What is the lepton number of an electron neutrino?
1
38
How is one baryon converted to another during beta decay?
One of the up quarks is transformed to a down quark, and vice versa, as a result of the weak nuclear force.
39
What makes a nucleus unstable and thus radioactive?
Containing too many protons or neutrons.
40
What is alpha radiation?
The emission of a helium nucleus (alpha particle)
41
What is beta radiation?
Emission of a fast moving electron or positron.
42
What is gamma radiation?
Emission of high energy photons travelling at the speed of light (they are EM waves, after all!!)
43
How can electric fields be used to assess the nature of radiation occurring?
In an electric field, beta will be deflected the most, followed by alpha, whilst gamma is undeflected as it has no charge.
44
Why are alpha particles deflected less than beta particles in an electric field?
- They have greater mass
- Since Fe = mv^2/r, for a given velocity, the radius of the circular path they describe is larger
- So they are deflected less
- We could also consider this in terms of centripetal acceleration!!
45
Why are alpha and beta particles considered ionising? Why does this give them such a short range?
- They have high mass and charge
- They interact with surrounding particles to ionise them
- They lose energy quickly so are easily stopped; they have a short range
46
Why are gamma rays non-ionising?
They have no charge. However, this makes them highly penetrating; it requires centimetres of lead to stop them.
47
What are the nuclei before and after a decay process called?
Parent and daughter nuclei.
48
Why do radioactive sources undergo a decay chain rather than just a single decay?
The daughter nuclei produced during radioactive decay are often active themselves.
49
Where a nucleus contains less than 20 protons, how many neutrons must it have to remain stable?
The number of protons must be roughly equal to the number of neutrons.
50
What can a Segre plot tell us about the link between the nature of radioactive decay and the composition of the nucleus?
- Neutron number is the X axis, Proton number is the Y axis
- All stable nuclei occupy a narrow stability band
- Nuclei to the right undergo beta-plus decay, and nuclei to the left undergo beta-plus
- Nuclei with more than 82 protons undergo alpha decay
51
What does a Segre plot tell us about the composition of stable nuclei as mass increases?
- As a nucleus gains more protons, the electrostatic force increases
- A greater SNF is required to oppose this
- So more neutrons are needed than protons to achieve stability
52
Give the exponential equation that we used to model radioactive decay.
N = N0 * e^-(lambda)T
53
How are half-life and decay constant lambda linked?
T(1/2) = ln 2 / lambda
54
Why are subsequent half-lives constant in radioactive decay?
- Half life is described by an exponential function
- This means there is a constant-ratio relationship between values for undecayed nuclei
- So the same time is taken for the number of undecayed nuclei to halve each time
55
Give an interactive expression that can be used to approximate radioactive decay.
DN/dT = -(lambda)T
56
Why can an iterative function be used to approximate the nature of radioactive decay?
- We know that the rate of change of nuclei undecayed depends on number of nuclei and time
- So dN = NdT
- Thus dN/dT is proportional to N
- Linked by a rate constant lambda
57
Define half-life.
The average time taken for half of the radioactive nuclei in a sample to decay.
58
Define decay constant.
The fraction of a whole radioactive sample that decays per unit time; i.e. the probability that a single radioactive nucleus will decay in a given time.
59
Why is radioactive decay described as random?
- We cannot predict *which* nucleus specifically will decay next
- Each nucleus has the same probability of decaying per unit time
60
Why is radioactive decay described as spontaneous?
Decay is not affected by the presence of other nuclei in the sample, or external factors like pressure
61
Define radioactive activity.
The number of decays per second of a radioactive sample.
62
Give the equation we use to calculate activity of a radioactive sample.
A = (lambda)N
63
What are the units of activity?
Bequerel, Bq
64
Why can we use carbon dating to estimate the age of a radioactive sample?
- The ratio of 12C:14C in a given sample of dead tissue will differ to that in the environment
- This is because 14C has decayed over time which changes the ratio
- However the ratio of 12C:14C has remained constant over history
- The tissue of a living organism adopts this ratio whilst alive but cannot maintain it when dead
- So we can compare amounts of 14C
65
What assumption does radioactive carbon dating require us to make?
That the ratio of 14C:12C has remained constant throughout history.
66
What are the main limitations of radioactive carbon dating?
- If the sample is too old or small…
- The 14C amount may be indistinguishable from the background radiation
- The amount of 14C may simply be immeasurably small
67
What equation did Einstein propose linking mass and energy changes?
e=mc^2
(delta prefixes may be applicable here!!)
68
What are the two interpretations of Einstein's mass-energy equation?
1. Mass is a form of energy
2. Energy has mass
69
How can it be said that mass is a form of energy?
Consider e=mc^2 and the process of annihilation. When two antiparticles meet, the sums of their masses are fully transformed to the energies of two identical gamma photons.
70
How can it be said that energy has mass?
By e=mc^2 - a moving object, for example, has increased kinetic energy over its' rest mass, and thus has mass greater than its' rest mass. This effect isn't easily observed practically due to the incredibly small scale of such a mass difference.
71
How can the principle of mass-energy conservation apply to nuclear decay?
An unstable nuclei decays by losing a particle or photon. Mass-energy conservation suggests that these two variables must remain constant. If energy is released, there is a simultaneous loss in mass, known as the mass defect.
72
What is pair production?
An individual photon disappears; its energy is converted to the masses of the particle and antiparticle that are produced. A single electron has rest energy given by its' rest mass, equal to 0.51eV - thus any single incident photon must have an energy of at least 1.02eV.
73
What is binding energy?
The minimum energy required to completely separate an atomic nucleus into its' constituent nucleons.
74
What two processes can binding energy refer to?
- Input energy when deconstructing a nucleus
- Energy released when constructing a nucleus
75
Why does a nucleus have less mass and energy than its' constituents?
Energy equal to the binding energy is released when a nucleus forms. This is equated to a loss in mass.
76
Why can binding energy be considered a form of potential energy?
Binding energy is representative of the negative gravitational potential energies of all the nucleons comprising a given nucleus; this is negative because work must be done against these attractive forces to increase the potential energy to zero and release these nucleons.
77
Why is the binding energy of the product of a nuclear reaction always less than the reactant?
A reactant is always unstable in some way, so little energy is required to deconstruct these nuclei. However, the products are always more stable (the system always tends toward stability!) and thus more energy is required to break up such a product nucleus.
78
How can differences in binding energies help us to explain why nuclear fission/fusion processes release energy and cause mass to decrease?
The binding energies of the products is greater than the reactants (fission - two smaller, stable nuclei from one heavy; fusion - one more stable nuclei from two v. small, unstable)
More energy is released when the products form than when the reactants break down
Thus there is a net energy release
This is equated to a loss in mass
79
What is a mass defect?
The difference in mass of the products compared to the reactants due to differences in their binding energies.
80
What quantity do we use to compare binding energies of different nuclei/elements?
Binding energy per nucleon.
81
Describe the trend in binding energy per nucleon as A increases.
Up to 56: sharp increase with spikes at C, N , O which explains their high abundance.
Peak at A=56 which matches iron - none else have higher binding energy so this does not undergo fission or fusion readily.
Decrease as A increases beyond 56.
82
Why is binding energy small for smaller nuclei?
The attractive forces acting. between nucleons are comparatively small.
83
Why is binding energy small for large nuclei?
Increasing repulsive electrostatic forces between protons reduce the overall energy needed to deconstruct the nucleus - despite the increase in SNF
84
What is induced fission?
A fissile parent nucleus absorbs a thermal neutron to produce an unstable isotope which immediately divides to form two stable daughter nuclei, alongside multiple neutrons
85
What is the most common fuel in nuclear power stations?
Uranium-235
86
Why must uranium ore be refined for use in a nuclear power station?
Uranium ore contains 235 and 238 isotopes. While 235 is fissile, it is only found at a very small proportion of 0.7:99.3. 238 simply captures thermal neutrons and does not undergo fission. So this ratio must be changed to provide more of the 235-U isotope in a given sample to make a reactor practically feasible.
87
How does 235-U undergo fission when a thermal neutron is absorbed?
236-U is formed
This is a highly unstable isotope
This divides, typically into 141-Bc and 92-Kr
3x fast neutrons are produced
88
How can the mass defect arising during fission be used practically to generate energy for us to use?
The mass defect stems from an energy difference
This is partially transferred to the kinetic stores of the nuclei produced (as well as photons, neutrinos emitted)
This is expressed as thermal energy and thus temperature
We use this phenomenon to heat steam to turn a turbine and thus generate electricity
89
What type of neutrons are EMITTED during fission?
Fast-moving neutrons
90
How can the neutrons produced during fission produce a chain reaction?
If slowed down sufficiently they can become thermal neutrons
These can be absorbed by surrounding fissile nuclei
This instigates further reactions, and since >1 neutron is produced per reaction typically, the rate of fission increases exponentially
This means energy released increases exponentially if uncontrolled
91
What are the main components of a fission reactor?
1. Coolant
2. Fuel rods
3. Moderator
4. Control rods
92
Describe the function of a coolant.
Transfers thermal energy produced during fission processes to drive a turbine eventually.
93
Describe the function of a fuel rod.
Contains enriched uranium dioxide (UO2) pellets to provide 235-U nuclei for fission processes.
94
Describe the function of a moderator.
Slows down fast moving neutrons produced during fission, so that they can go on to be absorbed by fissile nuclei to cause further fission processes to occur in a chain reaction. Usually water or graphite, as these do not absorb neutrons but rather cause a drastic loss in KE.
95
Describe the function of a control rod.
Usually made of boron or cadmium. Absorbs neutrons released during fission to different extents based upon their controlled height, in order to control the rate of the chain reaction. They are fully lowered to absorb all neutrons and inhibit the chain reaction fully.
96
What is a chain reaction?
Neutrons produced during the nuclear fission go on to induce fission in further nuclei.
97
Describe the environmental impacts of fission reactors.
238-U absorbs neutrons of intermediate energy to produce 239-U which divides to form plutonium nuclei. These are highly radioactive and very toxic, with a long half-life.
This means spent fuel rods cannot be disposed of as normal waste; they are bricked in lead-lined container deep underground, far away from food+water supplies in geographically and politically safe regions.
98
How does the Sun generate its' energy?
Nuclear fusion.
99
Why does nuclear fission require very high temperatures?
Particles must be within femtometer separations in order to undergo fission
Electrostatic repulsions are extremely strong at such separations
Significant EK equated to 3/2kT is required to allow nuclei to approach at such separations (KE -> PE)
100
Describe the proton-proton fusion cycle.
1. 2x protons fuse to from deuterium
2. Deuterium and a proton fuse to form helium-3
3. 2x helium-3 nuclei fuse to form helium-4 and 2x protons
4. The cycle repeats
101
Why does the proton-proton cycle repeat continuously given sufficient temperatures?
Two protons used to initiate a fusion process are additionally released at the end too.
102
What is the binding energy of a proton?
Zero!!
103
Why is fusion currently an unfeasible method of power generation on Earth?
Maintaining a sufficiently high temperature for fusion to occur is very technically demanding (and also requires lots of energy!! This negates the purpose somewhat...)
Such high temperatures also introduce difficulties with successfully containing the fuel used to run fusion in the first place.
