Problems Flashcards
1
Q
Change in Z for beta - decay
A
Z+1
2
Q
Change in Z for beta + decay
A
Z-1
3
Q
Neutrino for B- decay
A
V bar (both have ‘-‘ signs)
4
Q
Neutrino for B+ decay
A
V ( no bar)
5
Q
Atomic mass
A
Mass of nucleons and electrons
6
Q
Nuclear mass
A
Mass of nucleons
7
Q
Exponential decay law
A
N = No e^-λt
8
Q
How to write Q formulae
A
M (nuclear) x c^2
9
Q
Activity of sample formula
A
A sample = A measured - A background
10
Q
Convert counts/hour to Bq
A
Divide by 3600
11
Q
How to obtain age of sample from carbon dating
A
- Find number of atoms in 12carbon = mass of sample *avogadros / 12(because atomic mass)
- Find No, number of atoms in 14Carbon = abundance of 14C * number of 12C
- Find λ -> λ = ln2/ (t1/2 in seconds)
- Ao = N14C x λ
- Solve activity formula for T (careful of ‘-‘ sign!!) A(t) i.e. measured = λNo = Aoe^-λt
12
Q
When to use non relativistic for particles?
A
When energy is low compared to mass
13
Q
How to determine kinetic energy of daughter particle in decay (non-relativistic)
A
E.g. finding for particle a
- Equate momentum of daughter particles (Pa = Pb = MaVb = MbVb)
- Solve for Vb
- Equate Q and non-relativistic KE (Q = Ka + KB = 1/2MaVa^2 + 1/2MbVb^2)
- Sub in 2.
- Factor out 1/2 MaVa^2 and equate to kinetic energy
6.Now have equation in terms of Q, Ka, Ma, Ma - solve for Ka
14
Q
Geiger Nuttall Law
A
Larger Q value = smaller half life
15
Q
Endothermic
A
Q<0
16
Q
Exothermic
A
Q>0
17
Q
How to calculate excitation energy for e.g. 235U?
A
E ex = 235U* - 235 = 235U + n = 236U
19
Q
Fast neutrons needed
A
Activation >excitation
20
Q
Slow neutrons needed
A
Activation <excitation
21
Q
Why is spontaneous fission unlikely above A90, Z40 ?
A
- Surface term too high for Coulomb repulsion to overcome
22
Q
Spontaneous fission ability criterion
A
- Critical value of Z^2/A
- Spontaneous fission only likely when >51 (i.e. coulomb repulsion overwhelms surface tension
23
Q
Why is neutron negligibly affected by Coulomb barrier
A
Neutral
24
Q
Fissile mass increase by 10%, what does shell model predict for fragments?
A
Lower mass fragment takes most of additional mass
25
Q
Energy profile for critical chain reaction
A
Rise from zero
Reaches constant value
26
Critical chain reaction
Steady reaction - exactly 1 new fission per fission
27
Supercritical chain reaction
- Grows rapidly
- >1 new fission per fission
28
Subcritical chain reaction
- Dies out
<1 new fission per fission
29
Timing of prompt vs timing of delayed neutrons
- Prompt -> fission process
- Delayed -> radioactive decay of fission products
30
Fission isomers
Quasi-stationary states in the second minimum of double humped potential
31
Relevance of double humped potential
- First hump = nuclear fission barrier - energy needed to deform nucleus
- Second hump = separation barrier - nucleus fully splits into 2
32
Fission barrier
Energy barrier nucleus must overcome for fission
33
PP chain (Peepee, don’t pee, hee-hee hurts to pee)
1. Peepee: Protons -> to form deuterium
P + p -> D + e+ + v
2. Don’t pee: Deuterium fuses with proton
D + p -> He-3 + γ
3. Hee-hee: Helium-3 nuclei
HE-3 + HE-3 -> He-4 ++2p
Product of He-4, γ, positron, neutrinos
34
CNO cycle ( Can’t No PC Police Own Prince Harry)
1. Can’t: 12C + p -> 13N + γ
2. No: 13N -> 13C + e+ + v
3. PC: Proton capture by 13C: 13C + P -> 14N + γ
4. PoliCe: Proton capture by 14N : 14N + p -> 15O + γ
5. Own: Oxygen-15 beta decay: 15O -> 15N + e+ + v
6. Prince Harry: Proton capture to 4He: 15N + p -> 12C + 4He
12C regenerated
35
Comparative Q values for CNO and PP
Roughly the same
36
When does pp chain dominate ?
- Low mass stars (<1.3 M*)
- Lower temp ~ 10million K
37
When does CNO cycle dominate ?
- Higher mass (>1.3 M*)
- Higher temperature (~15-20 million K)
38
When does triple alpha process dominate ?
- Higher temperatures (~100 million K)
- Older stars who have exhausted hydrogen and using helium
39
Triple alpha process ( 2 men be bad he-men, see?)
1. 2 men (he) be:
4He + 4He -> 8BE
2. Bad he-men, see?
8BE + 4HE -> 12C + γ+ γ
40
Source of γ in triple process?
Mass defect
41
Big bang nucleosynthesis
Formation of first atomic nuclei, first 3 minutes after big bang
42
Quark era
First microseconds of Big bang nucleosynthesis
- Too hot for nuclear fusion
43
When were protons and neutrons formed in Big bang nucleosynthesis
1 second - minutes
44
protons and neutrons in Big bang nucleosynthesis
- Equal amounts, created once temperature cooled
45
Deuterium formation
- Around 3minutes into Big bang nucleosynthesis
- p + n -> d
46
Helium formation
- 3-20minutes into Big bang nucleosynthesis
- D + D -> 3He and photon
47
Results of Big bang nucleosynthesis
- 75% H
- 25% He
- Small amounts Li Be
48
Why no nuclei in Big bang nucleosynthesis with a>5?
- If 3p + 2n -> columb repulsion> nuclear force and unstable
- If 3n + 2P -> unstable, prone to beta decay of unpaired
49
S process
- Slow neutron capture process
- Nuclei capture neutrons -> become unstable -> beta decay -> p + new element
50
R process
- Rapid Neutron capture process
- Nuclei capture neutrons -> rapid beta decay -> p + heavier element
51
Conditions for r-process
- neutron rich
- Very high temperature (10^9 K)
- High neutron flux
52
Conditions for s-process
- Moderate temperature (2x10^8 K)
- Low neutron flux
- High density
53
Nuclei starting r-process vs s-process
R:
- Neutron rich isotopes
S:
- Stable, seed nuclei Fe-56, Ni -58
54
Form geometric series from decay chain
1. Formula for n
2. Formula for n+1
3. 2. - 1.
55
Fundamental particles (FUNDAMENTAL)
F - Fermions
U - up quark
N - Neutrino
D - Down quark
A - antiparticle
M - Muon
E - Elctron
N -Neutral boson - Z boson, photon
T - Top quark
A - Attractive boson (gluon, W/Z boson - force carriers)
L - Lepton
56
Composite particles (COMPOST)
C - Compositie
O - Omega baryon
M - Meson
P - Proton
O - Ona
S -Sigma baryon
T - Tetraquark
57
Strong force carriers
Gluons
58
Feel strong force
Gluons and quarks.
59
Fundamental quarks
**U Don’t Stop Cooking Big Tacos**
- Up: +2/3
Up, charm, Top
- Down: -1/3
Down, strange, bottom
60
Fundamental leptons
***Electrons Make Tiny Neutrinos***
- Charged: (-1)
Electron, muon, tau
- Neutral, nearly massless
Electron neutrino, mon neutrino, tau neutrino
61
Fermions
Q - Quark
L - Lepton
62
Range of strong force
10^-15m
63
Mediates EM force
Photon
64
Mediates weak force
W+/- and Z0
65
Mediates gravity
Graviton
66
Intermediate vector boson
Force-carrying particle
67
Find boson range from energy
1. ΔE Δt > h/2 —->. ΔE Δt ~ h
2. Sub in v = Δ x/Δ t = c
3. Δx ~ hc/ΔE
4. Sub in ΔE = mc^2
5. Δx ~ hc/Mc^2
( Can use given energy for mc^2)
68
Relationship between mass and range of intermediate vector boson
Lower mass —-> Longer range
69
Convert GeV^-2 to meters
- x (hc)^2
70
Convert meters to picobarns
- 1 pb = 10^-12 b
- 1 barn = 10^-28m
71
Compton wavelength
- λc = h/mec
- λc = 2 π ℏ / mc
72
Determine relativistic from kinetic energy and mass
β = p/E
(P^2 = E^2 - m^2 = (K + m)^2 - m^2 = k^2 + 2Km)
( p = sqrt (K^2 + 2Km) )
73
Electron mass MeV
0.511
74
Proton mass MeV
938
75
3 formulas for Δx lab for a particle
1. Velocity,v * Δt lab
2. Velocity,v * γ * Δt particle
3. Δx particle / γ
76
Formula for particle (proper) time?
- Δt lab / γ
77
Relativistic Beta
BPE chemicals
- Beta = P/E = v/c
78
Inertial frame for mean lifetime
Particle’s i.e. proper time
79
what is the invariant quantity?
P μP μ (1 subscript, 1 superscript) = m^2c^c
- same in all inertial reference frames
80
Mn value
1.008665
81
Mh value
1.007825
82
How to calculate binding energy
Difference between measured mass and calculated mass
- Calculated mass = Z*Mh + (A-Z)Mp
83
What are Q values written in terms of?
Mass and c^2
E.g. Q = M neutron + M Carbon - M nitrogen)/c^2
84
Features of fundamental particles?
Quick Little Bastards Ferry Nonces Cars Whole
- Quarks - feel force
- Leptons - Nothing
- Bosons - carry force, Whole number spin (unlike others)
85
Types of quarks (6)
- Up, down, top, bottom, strange, charm
86
Types of Leptons (6)
Lepers Never Miss Their Ears
Leptons: Neutrino versions too of: muon, tau, electron
87
Types of bosons (3)
Higgs bosons were playing games (in) zoos
H - Higgs
W - W
P - Photons
G - Gluons
Z - Z
88
Forces by photons
PhotoMAGNETIC stars get Hella FAT Without Zippy Water
Photon - magnetic (EM)
Gluon - Strong force
Higgs - gives MASS to other particles
W,Z - Weak force
89
Types of hadron (2)
Baryons
Mesons
90
Baryons vs Mesons
Baryon - 3 quarks
Mesons - 1 quark and 1 antiquark
91
Name a meson
Pion
92
Name a baryon
Proton, neutron
93
Quarks in proton
UUD
94
Quarks in neutron
UDD
95
Steps to find spin parity value
1. S: Shell - check shell model to determine last unpaired electron
2. P: Precession (angular momentum) - use L (angular momentum) to find P: P = (-1) ^L
3. V: Value/total - Total angular momentum (j = L ± 1/2)
96
Angular momentum (L) based on shell
- S, P, D, F, G, H …
- 0, 1, 2, 3, 4, 5….
97
Parity based on odd/even
- Even - even = +
- Odd-A = (-1) ^L
98
Spin of zero
- Doubly magic
- Even-even
99
Data needed to find invariant mass
Energy and momentum
100
Features of fermions
- Half integer spin
- Anitparticels
- Pauli Exclusion
- Non-zero mass
101
Particles which don’t feel weak force
4 -
Gluons
Photon
Graviton
Higgs Boson
102
Relativistic momentum formula
P = γ mV = γ m β c
103
Relativistic energy equation
E = γ mc ^2
104
Relativistic energy-momentum formula
( mc)^2 = (E/c)^2 - p^2
105
Total energy in relativistic
Total energy = total kinetic energy +total rest mass
106
How to solve problems without β or γ
- As don’t know boost (i.e. relative velocity between references frames described by above) use invariant mass
107
Energy momentum formula for photon
E = pc
(Massless)
108
Fundamental massless particles
PGG
Photon
Gluon
Graviton
109
Relativistic gamma
GEM
Gamma = E/m
