1
Q
The two conflicting theories of the structure of the atom
A
- The Plum Pudding model: Thomson suggested that the atom was a positively charged sphere with electrons spread out evenly across the atom to account for its neutral charge, this suggest the atom has an low density.
- Rutherford: He disproved this by firing alpha particles (positively charged) passed a sheet of gold atoms, they expected the particles to pass straight through, however they bounced off from all different angles (but some passed straight through), suggesting there is a dense positive charge in the centre of the atom and electrons spread around the nucleus.
2
Q
What would’ve happened if they had’ve used aluminium instead of gold? (rutherford experiment)
A
gold atomic number (79) and aluminium (13), therefore aluminium has a nucleus almost six times smaller so the majority of alpha would’ve passed straight through as there is less chance of collision.
3
Q
Rutherford’s model of the atom (key points)
A
- Most of the fast charged particles went straight through, therefore the atom is mostly empty space.
- Some of the alpha particles are deflected back through large angles, so the nucleus must be smaller but high density.
- Alpha was repelled by nucleus so must have a positive charge.
- Atoms are neutral so electrons must be on the outside, separating one from the next.
4
Q
Nuclear model of the atom
A
-Nucleus containing protons and neutrons, and electrons orbit this core.
5
Q
Estimating the closest approach of a scattered particle
A
- Firing an alpha particle, you know its initial kinetic energy
- The particle momentarily is stopped and then turned back (deflected) at this point its electrical potential energy equals its initial kinetic energy.
- Ke = Eele = Q(gold) x q(alpha)/ k x r
- To find the charge of the nucleus you need to know the atoms proton number Z (how many protons in the nucleus) and the charge is Ze+ so the charge is the proton number x (1.6x10^-19)
6
Q
How PET scans works
A
- Oxygen-15 is an unstable isotope, so when it decays it emits a beta particle (electron) and a positron (electrons antiparticle) and a neutrino.
- The positron collides with an electron and annihilate creating a pair of gamma rays that travel in opposite directions and the PET scans then detect these rays.
7
Q
Particle annihilation
A
-When a particle and an antiparticle annihilate, the matter has been destroyed however energy is still there by the conservation of energy, so two gamma rays are produced.
8
Q
Antiparticles
A
-The exact same mass as the particle, but opposite charge and lepton or baryon numbers
9
Q
Electrons and positrons in uniform magnetic fields
A
- In a uniform magnetic field an electron and a positron will be deflected in opposite directions
- They will have paths of symmetrical curvature because they have the same magnitude of momentum.
- They move in a circular path but lose energy as they interact with atoms and slow down which results in the characteristic double spiral of pair production
10
Q
For each type of particle there is an…
A
Antiparticle of equal mass and opposite charge
Also of opposite baryon and lepton number
11
Q
After antiparticle annihilation..
A
Energy conservation results in two gamma rays (photon)
12
Q
In any particle annihilation
A
- Charge is conserved
- Momentum (linear and angular) in conserved
- Energy is conserved (including rest E =mc^2)
13
Q
Conserved quantities in electron-positron annihilation
A
- Energy is conserved: total energy before = total energy after
- Momentum is conserved: total linear momentum before = total linear moment after
- Charge is conserved: total charge before = total charge after
14
Q
Antiparticle pair annhilation
A
- Two gamma rays produced
- Gamma energy plus kinetic energy of electrons
15
Q
Antiparticle pair creation (two gamma rays)
A
-Very rare, cannot bring two identical photons together
16
Q
Antiparticle pair creation (of nature)
A
-Gamma energy close to nucleus, and the gamma energy is converted to mass to conserve energy and momentum
17
Q
Charged particles
A
-They are the source of the electrical and magnetic fields and these fields exert forces on other charged particles
18
Q
Charge is proportional to…
A
Charge is proportional to the quantum amplitude to create or destroy a photon.
-Charge is the strength of the interaction between an electron and a photon.
19
Q
When all the amplitudes are added up =>
A
Like charged repel and unlike attract
Adding up all the possible paths for a photon.
20
Q
Feynman diagrams
A
-They shows the possibilities of the paths of a photon to be combined
21
Q
Feynman diagrams: no photon exchange
A
The arrows pass straight from one electron to the positron
22
Q
Feynman diagrams: one photon exchange
A
-The arrows are joins by one gamma ray.
The probability of an even creation is found by squaring the resultant amplitude
23
Q
Feynman diagrams: Simple interaction (electron and gamma photon interact)
A
-Photon is absorbed at by electron and emitted after
24
Q
Feynman diagrams: Simple interaction (electron emits gamma photon)
A
-Electron emits photon and absorbed photon later
25
Feynman diagrams: Simple interaction (electron and gamma photon creation)
-Photon creates electron and antiparticle (positron) pair,
| positron annihilates with another electron and emits a photon
26
Hadrons
- Particles that feel strong interaction
- This strong interaction is the force that holds neutrons and protons together
- Hadrons aren't fundamental particles, they're made up of smaller particles called quarks
- There are two types of hadrons (baryons and mesons)
27
Baryons
- Baryons are neutrons and protons
- Proton is the only stable baryon
- All baryons except protons decay to a proton
28
Baryon number
- The number of baryons in a reaction is called the baryon number.
- Its the number of baryons
- The proton and the neutron each have a baryon number B= +1
- The total baryon number in a any particle reaction never changes
29
Leptons
- Leptons are fundamental particles which don't feel the strong interaction force.
- The only way they can interact is via the weak interaction force and gravity
- Electrons are very stable and there are two more leptons called muons and tau which are heavier than electrons
- Muons and tau are unstable and decay eventually into normal electrons
- The electron, muon and tau all come with their own neutrino Ve, Vμ, Vt
- Neutrinos have zero or almost zero mass and zero electric charge, they are passing through us all the time.
30
Lepton numbers
-Each lepton is given a lepton number of +1 but the electron, muon and tau types of electrons have to be counted separately.
31
Electron (symbol, charge lepton number)
symbol: e^-
charge: -1
Le : +1
Lt +Lμ : 0
32
Electron neutrino (symbol, charge lepton number)
symbol: Ve
charge: 0
Le : +1
Lt +Lμ : 0
33
Muon (symbol, charge lepton number)
symbol: μ−
charge: -1
Lμ : +1
Lt +Le : 0
34
Muon neutrino (symbol, charge lepton number)
symbol: Vμ
charge: 0
Lμ : +1
Lt +Le : 0
35
Tau (symbol, charge lepton number)
symbol: T
charge: -1
Lt : +1
Le +Lμ : 0
36
Tau neutrino (symbol, charge lepton number)
symbol: Ve
charge: 0
Lt : +1
Le +Lμ : 0
37
Neutrons decay into protons
-The neutron is an unstable particle that decays into a proton.
n -> p + e- + Ve- (antineutrino has Le = -1, so the total lepton number is 0)
(Free neutrons not held in the nucleus have a half life of about 15 mins)
38
Antiparticle symbols
-Same symbol but with a line over the top to indicate the anti.
39
Matter and antimatter from energy
- Energy can turn into mass and mass can turn into energy from the conservation of energy. Also from Einsteins equation E =mc^2
- When energy is converted into mass you have to make equal amounts of matter and antimatter
40
Example: An electron and a positron are produced from a single photon. Find the minimum energy of the photon.
-Energy before = energy after
Energy > 2mc^2
= 2 x (9.11x10^-31) x (3x10^8)
41
Amplitudes for particles arriving at the same time (fermions)
- The amplitude for two identical particles arrive at exactly the same point in space-time, subtract: they add up with opposite phase.
- Result: the total amplitude is zero and such particles never come together in exactly the same state
42
Fermions
- Electrons and neutrons are fermions and obey Pauli exclusion principle
- They have a half integer spin (intrinsic angular momentum)
- No two fermions can exist in exactly identical energy quantum state
43
Bosons
- Photons are bosons and can join other photons in the same state
- Bosons have an integer spin
- Identical photons can be at the same point in space-time and add up with the same phase
- So bosons are inclusive and are able to be in the same state.
44
Intrinsic spin
Boson = an integer multiple h/2 π
Fermion = an integer spin of multiple 1/2(h/2 π)
(connected to the adding or subtracting of amplitudes)
45
Beta decay + conservation laws
- PET scans have beta decay where the unstable nucleus emits a positron
- If this happens a nucleus has too many protons for the number of neutrons
46
Baryons are made up of...
```
Three quarks (baryons include protons and neutrons)
-They have a baryon number of 1
```
47
Baryon number of antiprotons and antineutrons
-1
48
Properties of antineutrinos:
- Must be neutral (to conserve charge)
- Must be an antilepton with lepton number -1
- Must carry away energy
- Must carry away linear momentum
- Must interact extremely weakly with matter
49
Rest energy of antineutrino
Rest energy= 0
| Momentum p=E/c
50
Momentum
p =E/c
51
Weak interaction
-A neutron can change into a photon by emitting a W- boson; which then decays into an electron + antineutrino
-A proton can change into a neutron by emitting a W+ boson; which decays into a positron + neutrino
Rarely: a neutrino can interact with an electron by knocking it out of the atom by exchanging a neutral Z boson.
52
List of Leptons
- Electrons
- Positrons
- Neutrinos
- Antineutrinos
53
List of Baryons
- Proton
- Antiproton
- Neutrons
- Antineutrons
54
Slower alpha particles (reduce the energy with an absorber) =
Less energetic alpha particles turned around further from nucleus
55
Using a smaller charged nucleus than gold (replace foil by metal of smaller atomic number)
Particle (alpha) gets closer to nucleus of less charged and is deflected less
56
Quarks
- Quarks are fundamental particles
- To make protons and neutrons you need two types of quark (up and down quarks)
- 'strange' quarks let you make more particles with a property called strangeness
- Three other types of quark, top, bottom, charm
- The antiparticles of hadrons are made from antiquarks.
57
Up Quarks (symbol, charge, baryon number, strangeness)
```
Name: up
Symbol: u
Charge: +2/3
Baryon Number: +1/3
Strangeness: 0
```
58
Down Quarks (symbol, charge, baryon number, strangeness)
```
Name: down
Symbol: d
Charge: -1/3
Baryon Number: +1/3
Strangeness: 0
```
59
Strange Quarks (symbol, charge, baryon number, strangeness)
```
Name: strange
Symbol: s
Charge: -1/3
Baryon Number: +1/3
Strangeness: -1
```
60
Anti-Up Quarks (symbol, charge, baryon number, strangeness)
```
Name: anti-up
Symbol: u (with line on top)
Charge: -2/3
Baryon Number: -1/3
Strangeness: 0
```
61
Anti-Down (symbol, charge, baryon number, strangeness)
```
Name: anti-down
Symbol: d (with line on top)
Charge: +1/3
Baryon Number: -1/3
Strangeness: 0
```
62
Anti-Strange Quarks (symbol, charge, baryon number, strangeness)
```
Name: anti-strange
Symbol: s (with line on top)
Charge: +1/3
Baryon Number: -1/3
Strangeness: +1
```
63
Baryons are made from...
Three quarks
-Evidence for quarks came from hitting protons with high-energy electrons. The way the electrons scattered showed that there were three concentrations of charge (quarks) inside the proton
64
Proton quark make up
Total charge: uud = 2/3 + 2/3 - 1/3 = 1
| Baryon number: 1/3 + 1/3 + 1/3 = 1
65
Neutron quark make up
Total charge: udd = 2/3 - 1/3 - 1/3 = 0
| Baryon number = 1/3 + 1/3 + 1/3 = 0
66
Gluons
- Gluons provide the force between quarks; they attract one another by exchanging particles called 'gluons'
- The name for the forces that hold these things together are gauge bosons
e. g. gluons for quarks, photons for electromagnetic interactions...
67
Separating quarks
- If you try to separate quarks, the gluon field between them increases in energy, increasing the attraction between them.
- If you keep pulling eventually the energy in the gluon field will be enough that a quark-anti-quark pair is produced by the conservation energy.
68
Electrons in atoms exist in discrete energy levels
-Electrons in atoms can only exist in certain well-defined energy levels. Each level is given an number with n=1 representing the lowest possibly energy state.
-Electrons move up and down energy state by emitting a photon
The energy levels are so small that they use the eV (electron-volt) instead of a joule.
69
eV
Electron-volt is the kinetic energy carried by an electron after it has been accelerated through a p.d of 1 volt.
70
Energies
-All electron energies are negative because of the way the zero energy is defined
71
Free electron
-An electron is free and no longer bound to an atom when it has a potential energy of zero- the atom becomes ionised.
72
Energy carried by each photon ->
E = E2-E1 = hf =hc/λ
73
Electrons are ferminons so...
-They also obey the pauli exclusion principle; this states no two fermions can be in exactly the same quantum state at the same time. In the context of energy levels, that means no more than two electrons can be in the same energy level at the same time.
74
Evidence = Line Spectra
- The spectrum of white light is continuous
- You get line absorption when light with a continuous spectrum passes through a cool gas
- At low temps most electrons in the gas atoms will be at their ground states
- Photons of the correct wavelength are absorbed by the electrons that excite them to higher energy levels
- These wavelengths are then missing from the continuous spectrum when it comes out from the gas
- When an electron falls into lower energy levels, it emits a photon. Emission spectra show the wavelengths of photons emitted. Made up of a series bright lines corresponding to the wavelengths emitted
75
De Broglie
-Because light has both particle and wave like characteristics, De Broglie suggested that electrons should have a wave-like characteristic.
76
Standing waves in electrons
- When electrons are in orbit around a nucleus they should behave like standing waves
- Similar to a standing wave they only exist at certain well-defined frequencies
- The wavelength of the electron waves should fit the circumference of the orbit a whole number of times.
- The principle quantum number is equal to the number of complete waves that fit the circumference
- Electrons are trapped by a potential well made by the nucleus, like standing waves being fixed at the ends
77
Energy levels in a hydrogen atom are
E = 13.6eV / n^2
78
Relativistic factor
γ = Etotal / Erest
79
Alpha particles being close to the nucleus
-The large energy of the alpha particles means that they can get very close before being deflected
80
When is Potential energy highest when an alpha particle is fired at a gold nucleus
-It's PE is highest when closest to the nucleus
| Here its initial kinetic energy = electrical potential energy
81
MeV
Mega electron volts
82
Isotopes
-Nuclei with same charge, but different numbers of neutrons. Atoms of isotopes are identical in chemical properties, different is mass.
83
Isotope proton number
- Number of protons decides positive charge on the nucleus and so there must be an equal number of electrons to make it neutral
- But different numbers of neutrons can change mass and may make the isotope radioactive
84
How to work out the number of neutrons
```
Z= atomic number
A= mass number
N = A- Z = number of neutrons
```
85
Wavelength of electrons
λ = h/p
| where h= planks constant and p= momentum
86
Wavelength of an electron using its rest energy
λ = h/ p => hc/ E
Because p = E/c
87
Graph of nucleus scattering
Volume of nucleus against mass = straight line
88
Equation involving volume of nucleus and mass
4/3πr^3 proportional to A (mass)
SO r = r0 A^1/3
where r0 is the value of a single nucleon and r = radius
89
How to work out the density of nuclear matter
- Find the volume of the nucleus from graph (or given directly)
- Work out vol per nucleon
- You're given the mass of a nucleon
- Use density = mass/ volume
90
Strange quark
-Strange quark is unstable and decays into an up quark, an electron and an electron antineutrino
91
Baryons are heavier than...
The proton and the neutron
92
Mesons are lighter than...
The proton and heavier than the electron
93
Leptons are lighter than...
The electron
94
Baryons consist of...
Three quarks
95
Antibaryons consist of
Three antiquarks
96
Anti matter is seen today only in...
- Pair production
- Radioactive decay
- In high energy particle accelerators
97
Quarks were discovered by..
Deep inelastic scattering
98
High energy: deep inelastic scattering
-Electron can hit one quark, and be scattered. Exchange of high energy protons lead to the creation of a set of particles and antiparticles.
99
Kinetic energy required in scattering experiments
Ke = e^2 / 4π e0 r
=> e^2 k
100
Quarks attract one another by exchanging..
Particles called gluons
| -They are the 'glue' that keeps the protons, neutrons and other hadrons in one piece
101
When quarks exchange gluons it changed their...
'color'
- Color is the strong interaction analog to charge in the electromagnetic force.
- It comes in three forms like the primary colours of blue, green and red
- It has nothing whatever to do with real color, but provides three distinct quantum states.
102
Color force
The color force involves the exchange of gluons and is so strong that the quark-antiquark pair production energy is reached before quarks can be separated. Another property of the color force is that it appears to exert little force at short distances so that the quarks are like free particles within the confining boundary of the color force and only experience the strong confining force when they begin to get too far apart.
103
When you try to separate two quarks..
- The interaction between the gluons and the quarks gets stronger
- the gluon energy field increases
- By pulling them apart this increases the potential energy then you can give it enough energy to produce an quark and an antiquark
104
Fermions
Matter like
- Electrons
- Quarks
105
Bosons
Force like
- Photons
- Gluons
106
The standing waves in electrons can be seen by...
Using a scanning tunnelling microscope and are detected where the electron density is high and places where it is low.
-Where the electron density is high, the tunnelling current is large, as thought the surface has risen to meet the scanning needle.
107
Potential energy well
-The atom can be thought of as a box which traps electrons and the nucleus provides a potential energy well in which negative electrons can be bound and unable to escape
108
Energy levels in potential energy wells
En = n^2 E1
E1 because no energy level exceeds below n = 1
109
Kinetic energy in potential energy wells
- Ek = h^2/ 2mλ^2
and because En = n^2 E1
En = n2 (h2/ 2mλ2)
110
Small λ...
Higher energy
111
Large λ...
Low energy
112
Broglie relationship
p = h/ λ
```
p= momentum
h= planks constant
```
113
The smaller the 'box'
The narrower the wavelength and so the larger the momentum and kinetic energy
114
As a electron falls from one level to a lower energy level...
A photon is emitted
115
Discrete energy...
E= hf
116
Energy of a photon
-The energy of a photon is just the difference in energy between two of the possible energy levels of electrons in the atom.
117
Small radius of atom
KE + PE > 0
| -If the size is too small the kinetic energy is too large for electrical potential energy to bind the electron
118
Medium radius of atom
KE + PE = 0
119
Large radius of atom
KE + PE
120
Decreasing the size of the atom
- Electrostatic potential energy would get more negative (proportional to 1/r)
- Wavelength of the standing wave would get shorter, making the electron kinetic energy increase (proportional to 1/r^2)
121
Electron freeing itself from an atom...
- Shrinking an atom make the magnitude of the kinetic energy increase more rapidly than the magnitude of the potential energy
- There comes a point that shrinking making the Ke outweigh the negative PE and so the total energy becomes positive and the electron is free
122
Energy levels of hydrogen
En = -13.6eV/ n^2
123
Energy levels
- As n increases the energies get closer together
- If E > 0 the electron has positive total energy and breaks free from the atom
- Ionisation energy= energy needed to get an atom from the lowest energy (-13.6eV) up to zero energy
124
Electrons can make jumps between energy levels, emitting a photon...
E=hf = Einitial - Efinal.
125
Subatomic interaction =
=between gluons and quarks
126
Particles that feel the strong color force
Hadrons
127
Pair creation equation
hf = 2mc^2
128
Pair annihilation equation
2mc^2 = 2hf
129
Pair creation
Two identical gamma rays would come together to create an electron-positron pair. This should happen because energy, momentum and charge are all conserved.
130
Fermions
If two particles such as electrons or protons arrive at the same point in space-time, their quantum amplitudes subtract – that means they add up with opposite phase. The phasor arrows point in opposite directions leading to a total amplitude of zero leading to a situation where the two particles can never be at the same place at the same time. Particles like these are called fermions. Two electrons can occupy the same space if they have different ‘spin’ because they are said to have different quantum states as a result
131
Pauli exclusion principle
No two particles, electrons in atoms or protons and neutrons in nuclei, ever share the same quantum state.
132
Bosons
The amplitudes of two identical photons at the same point in space-time add up with the same phase. The total amplitude doubles if they have identical amplitudes to start with. This principle is used to good effect in a laser where many photons in the same state join together. Particle that behave this way are known as bosons. All particles whose exchange gives rise to forces, such as photons and gluons, are bosons.
133
Density of nuclear matter
r = r0 A^1/3
Where r0 is the radius of the Hydrogen-1 nucleus
Where A is the number of nucleons
-Can use this to work out the radius, to work out the volume to work out the density = m/v
134
Bohr's model of the atom
-Bohr reasoned that electrons occupy “stationary” states (of fixed energy, not fixed position) at different distances from the nucleus.
-Electrons can make “quantum jumps” from one energy state to another.
-Light is emitted when such a quantum jump occurs (from a higher to a lower energy state).
-Frequency of emitted radiation is determined by
E = hf
where E is the difference in the atom’s energy when the electron is in the different orbits.
A2 Level physics
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