Week 4 Flashcards
1
Q
What other elements are in vicinity of stability?
A
Cr, Mn, Co, Ni
2
Q
Which elements experience fusion?
A
Lighter than iron
3
Q
Which elements experience fission?
A
Heavier than iron
4
Q
What happens to energy in fission?
A
Energy released
5
Q
What happens to energy in fusion?
A
Energy extracted
6
Q
How are elements upto iron peak produced?
A
Stellar nucleosynthesis
7
Q
Which are the alpha elements?
A
Z</= 22
8
Q
Which elements below iron peak are abundant?
A
Alpha elements
9
Q
Why are alpha elements named so?
A
Created by alpha process
10
Q
How are heavier elements below iron peak produced?
A
Less efficient processes: s-process and r-process
11
Q
How are elements with Z ~iron produced?
A
In large quantities in supernova due to explosive oxygen and silicon fusion followed by radioactive decay
12
Q
What is s-process?
A
Slow neutron-capture process wiht beta decay over hundreds of years
13
Q
What is r-process?
A
Multiple neutron captures and beta decays in short time (100 captures/sec)
14
Q
What happens to energy released in fission?
A
Becomes kinetic energy or final state particles e.g. photons
15
Q
Relative masses of final state particles
A
1 heavier, 1 lighter
16
Q
Why are spontaneous fission decay modes improbable in fission?
A
Coulomb barrier
17
Q
What is spontaneous fission decay?
A
Certain unstable heavier nuclei split into two nearly equal lighter ones
18
Q
What is/can be emitted during fission?
A
Kinetic energy
Particles - neutrons etc
19
Q
What model is used to explain fission?
A
SEMF
20
Q
How does Coulomb prevent spontaneous fission
A
Creates a potential barrier that resists the deformation needed to split
21
Q
What is used to explain liquid drop returning t spherical state?
A
Surface tension making spherical more energetically favourable
22
Q
What particle property encourages splitting?
A
Increased charge
23
Q
What shapes does a nuclei go through to split?
A
- Sphere
- Ellipsoid
- Peanut shape
- Two drop shapes with points pointing at each other
24
Q
Energetically, when does fission occur?
A
When squashed shape is energetically favourable over sphere
25
Define perturbation theory
A method used to study how small changes in a system can affect the behavior of the nucleus, such as its response to external influences like neutron bombardment or changes in energy.
26
What method is used for perturbation theory?
Taylor expansion of a simple model and see what happens at lowest order in expansion
27
What is preserved while changing shapes in perturbation?
Volume
28
What is the perturbation factor?
ratio of the change in the system’s response (e.g., fission rate or fission cross-section) to the change in the parameter.
29
Explain deformation parameter
Explains how much deformation from original shape
- positive = stretched, negative = flattened
30
What happens to Coulomb energy with deformation?
- Decreases*** check
- Protons get closer increasing repulsion
31
How do changes in Coulomb energy affect the molecule?
- decreased energy -> less stable
32
Formula for change in energy from deformation
ΔE=Bellipse - B SEMF
33
When do you get spontaneous fission based on ΔE in binding energies/SEMF?
- When Coulomb term is > surface charge term as Δe>0 indicating unstable nuclei
34
How does surface term act in fission?
Pull shape back to sphere
35
How does coulomb term act in fission?
Break apart shape
36
When is surface term negative for fission and why?
- Nucleons on the surface of the nucleus are not as strongly bound as those inside.
- Since they experience less attractive force, they effectively "want to pull" the nucleus apart, contributing negatively to the overall binding energy
37
What is the maximum atomic mass number for fission-stable nuclei?
~300
38
Why are nuclides with atomic mass>300 not found naturally
Almost instantaneously fission into smaller nuclei
39
When is it energetically favourable for nucleus to deform and eventually split?
When Z^2/A >/~ (2as)/ac is approximately equal to 51
40
What happens to nuclear energy as the nucleus becomes less spherical?
- Initially increases for ellipsoid due to decreasing binding energy
- Maximum where neck is formed
- Decreases as 2 fission fragments separate
41
When is total energy a minimum during fission?
At scission point: When neck is formed just prior to breaking apart
42
What mechanism leads to spontaneous decay fission?
Tunnelling
43
Compare spontaneous decay and α decay
- Spontaneous less likely
- α half lives much shorter
44
Formula for nuclear radii of fragments
-r(1) = r(o) A(1) ^ (1/3)
45
When is the maximal potential during fission?
Scission point: point of separation of 2 fragments
46
Magnitude of maximum potential during fission
Coulomb potential for 2 electrically charged spheres with charges Z1e and Z2e whose centres are separated by r1+r2 (IMAGE A)
47
Formula for fission energy released
Q = B(A1,Z1) + B(A2,z2) - b ( a, z1+z2)
48
Fission energy released in words
Difference between initial potential energy and final potential energy (when fission products are wifely separated)
- difference between sum of B of fragments and B of parent
49
Formula for potential of barrier height
V height = Vmax - Q
50
Potential barrier height formula in words
Difference between potential energy at point of scission and the release of the fission energy
51
Why is potential barrier height potential not very good?
Involves small difference between near equal quantities so fractional error amplified and Vmax overestimated
52
Order of Q
200MeV
53
Order of barrier height
10MeV
54
Why is Vma overestimated?
Assumes fragments can be considered as spherical, which they cannot
55
How do fission barrier heights from using Shell model differ from using equation?
- Higher
- Especially where magic N or magic Z
56
Why does spontaneous fission only occur if barrier height <10MeV?
- tunnelling probability decreased exponentially with increasing barrier height
57
When does spontaneous decay fission occur
Only for Z>220 as barier height sufficiently low
58
Describe 2 humps in double-bumper potential
- First, V(q) has ground state then a barrier
- Second minimum (II) then another barrier which leads to fission
59
What are fission isomers?
Quasistationary states in second minimum
60
What is shape of nuclide in first minimum
Prolate equilibrium (stretched)
61
What are type I excited states?
Found in first minimum in double humped
- have deformations similar to ground state
62
How do type I and type II states differ?
- I = deformations δ~ 0.35
- II = >2x I
63
How does fission from first minimum in double humped occur?
- When fission coordinate tunnels through first barrier into second minimum and finally through to outer barrier
64
Which nuclei require greatest amount of energy for disintegration?
N~ 50 ( A~90)
65
How do fission isomers compare to their nuclides
- Isomers have mush larger fission decay rate
- Isomers have lower and narrower potential barriers
66
What is excitation energy in double humped potential
- Excitation energy corresponds to metastable state between 2 maxima
67
Which terms are added by Shell-Model effects?
- Symmetry energy -> which prefers Z=N
- Pairing energy -> even-even, even-odd, odd-odd
68
Define asymmetric mass contribution
Spontaneous fission decay never leads to equal nuclides - heavier fragment closer to original, lighter is much smaller
69
How do mass distributions vary depending on mass
Heavier - overlap well
Lighter - huge variation as takes all the change in mass fraction
70
How are average masses different for heavy and light fragments in Shell-Model?
- Heavier -> mass constant ~140
- Lighter -> increases linearly as A increases as all added nucleons go to lighter fragment
- Liquid drop - would expect average masses to scale with mass of drop
71
Why does the variation happen in mass distributions between heavy and light mass fragments
Due to Shell-Model
- Heavy : A 125 to 132 = stable nuclei with Z/a ~0.39
- Doubly magic at A = 132
- Light: no overlap with even singly magic
72
What are prompt neutrons
Neutrons emitted simultaneously with fission process (t ~ 10^-16s)
73
Describe prompt release of energy in fission
Q is the difference between binding energy of parent nuclide and fission products
74
Where
75
What state are fragments often produced in?
Excited
76
Why are fission fragments not overly stable
Neutron- rich i.e. excessive for stability
77
What happens to neutron rich fission products
Beta decay in long decay chain until stability
78
What happens during long beta decay of neutron rich fragment
- Gamma ray emission as excited daughter nuclides
79
How may gamma rays emitted per fission event?
~10
80
How does total energy produced in fission relate to prompt fission energy (from initial fission reaction)?
~10% higher
81
What happens when daughter nuclide is produced in sufficiently excited state?
Can decay be neutron emission, up to several minutes after beta decay
82
What are delayed neutrons?
Emitted by daughter nuclides which are sufficiently excited, minutes after initial fission decay
83
How often does delayed neutron emission occur?
- Rare ~1/1000 fission events
84
In what timescale are most neutrons emitted during fission?
~99% in 10^-16 secs
85
How soon are delayed neutrons released ?
~s
86
Approx intents it’s of delayed neutrons compared to whole number
~1%
87
What does average number of neutrons released depend on?
Energy of the incident neutron
88
How much energy in incident neutron is required to cause emission of additional neutron?
6-7 MeV for every additional neutron
89
Which type of fission is most likely?
Induced >spontaneous due to small tunnelling probability
90
How does induced fission occur?
- Parent nucleus bombarded with a neutron
- Neutrons do not see Coulomb barrier so penetrate nucleus and bump it up over activation energy for fission
91
Define activation energy for fission
Minimum amount of energy required to start the fission process in a nucleus. It is the energy needed to overcome the energy barrier preventing spontaneous fission
92
What happens to excess energy in induced fission?
Released as vibrational energy
93
Requirements for absorption of neutron in induced fission
- Neutron absorbed if binding energy of isotope with atomic number A+1 exceeds binding energy of isotope with atomic number A
- Ie. Energy of 2 joined > energy of initial nuclide
94
When is induced fission prompt?
- Neutron absorption energy (difference in binding energies) is treated than height of fission potential barrier (i.e. no tunnelling needed)
95
When do bombarding neutrons not need to be energetic?
- Binding energy of extra neutron > potential barrier
96
Name for nuclides that can fission with thermal neutrons?
Fissile
97
What are thermal neutrons
Low energy neutrons absorbed by fissile nuclides
98
Kinetic energy of thermal neutrons
~0.025eV
99
Describe resonance capture
- When neutron’s energy matches energy level of nucleus, it can be absorbed in to it
100
Name for nuclides requiring neutrons of sufficient kinetic energy for fission?
Fissionable
101
Which isotopes tend to be fissile and why?
- Odd number of neutrons
- Pairing term - significantly increases binding energy
102
How much kinetic energy needed in fissionable?
Difference between binding energy and barrier height
103
Which form of uranium is fissile?
235U
92
104
Which form of uranium is fissionable?
238U
92
105
What is notable about 238 U and 232 Th
92 90
- Fissionable, but can beta -decay in 2 stages into fissile nuclide
106
What concept is used in breeder reactors
- Fissionable decaying into fissile
- Stage 2 beta 4 days
107
Which types of nuclides require higher energy neutrons for fission?
Even as energetically stable
108
What is critical energy in fission
minimum energy needed to ensure that each fission event produces enough neutrons to trigger additional fission events, leading to a self-sustaining chain reaction.
109
What are probabilities of fissile and fissionable
Fissile high as low energy requirements
Fissionable low as high energy neutron required
110
Which property determines whether an isotope is fissile?
Fission cross section
111
Describe fissionable cross-sections
Neutron-fission cross-section: High
Absorption cross-section: Low
112
Define neutron absorption cross-section
Measure of probability that a neutron will be absorbed by a nucleus
113
Describe fission cross-section as function of kinetic energy curve for fissile U
- 1: Low energy cross-section ~ 1/v
- 2: Region of resonances
- 3: Smooth, rolling
114
Why thermal neutrons required for 235U?
Cross section Vs kinetic energy highest in low energies
115
Where are largest reaction cross-sections in resonance region?
- At distinctive neutron energies that result in states of compound nucleus with relatively long lifetimes
Compound nuclide = nuclear resonances
116
Describe fission cross-sections of fissionable (but nonfissile)
- Zero upto threshold energy
- Relatively smooth at all energies
- No fission at all in thermal region
117
What is the threshold energy?
Energy below which fission cross-section is zero and always lies above resonance region
118
Energetically, when will fast neutrons be required?
When excitation energy is less than activation energy
119
Formula for excitation energy?
- E ex = [M* - M]c^2
= [(M + Mn) - M]c^2
120
How is nuclear energy realeased
Through fission chain reaction
121
How do fission chain reactions occur?
Neutrons emitted by fissioning nuclei induce fissions in other fissile or fissionable nuclei
122
What is k?
Multiplication factor which qualitatively describes the chain reaction
123
How to derive equation for number of fissions overtime?
1. No fissions
2. KNo = 1st, kkNo = 2nd etc
3. Rate of change of neutrons = dN/dt = (kN - N) /τ
4. Integrate via separation of variables
124
Formula for k
(Number of fissions in one generation) /(Number of fissions in preceding relation)
125
What is k’s maximum and why?
- 2
- Prompt neutrons produced in each fission reaction unlikely to exceed 2-3 (can only ever trigger this number of chain reactions)
126
When is chain not self-sustaining?
- K<1
- e.g. natural uranium ore where concentration of U so small, fission cross section low
127
When is decay chain self-sustained?
- K = 1
- Constant number of neutrons produced each chain
128
When is decay chain supercritical?
- K>1
- Accelerating chain reaction until all mass used up
129
Graph of possibilities for k values
IMAGE B - K vs time
- <1 subcritical
- 1 = critical
- >1 = supercritical
130
What is the critical mass?
Total mass the fissile material must exceed to ensure more than one neutron from fission event if absorbed and does not just pass through
- for all mass to be used up in supercritical decay chains
131
What is the critical mass?
Minimum amount of fissile material (like Uranium-235 or Plutonium-239) needed to sustain a self-perpetuating nuclear chain reaction.
- ensure neutrons absorbed, not just pass through
- for all mass to be used up in supercritical decay chains
132
What is the critical radius?
- minimum size of the material that allows for the chain reaction to occur without losing too many neutrons
- ensures that the material is large enough for neutrons to interact with the fissile material but not so large that neutrons escape before triggering more reactions
133
Absorption mean free path formula for decay chains formula
λa= (A x proton mass) / ( material density x absorption cross-section)
134
Why does formula for mean free path overestimate?
- Random walk of length L
- Average distance from starting point = L/SQRT (3n)
( n = number of scatterings neutron has before absorption)
135
Formula for critical radius of spherical sample
Rc = (1/ Sqrt(3n) ) x (A proton mass) / (density x absorption cross-section)
136
What does the correction for the critical radius formula depend on?
Average number of prompt neutrons emitted per fission event
137
What happens if mass>critical mas
- Will not have uncontrolled chain reaction
- Energy released causes spike into smaller masses
138
Which type of decay chain is needed for nuclear reactors?
Critical
139
How is decay controlled in nuclear reactors?
- Absorption controlled by interspersing fissionable fuel with cadmium or boron rods to absorb due to their high cross-sections
- Rods moved in and out to maintain k=1
140
How does boiling water nuclear reactor work?
- Absorbers set so K just below 1
- Delayed neutrons revitalise supply
- Long delay between prompt and delayed increase safety
(Fission energy used to boil water-> steam turbine)
141
Benefits of reactors with thorium?
- Reactor can be run in subcritical mode using fast nreutrons
- Radioactive waste more short lived
142
Describe fission in terms of binding energies
Combined binding energies of lighter fragments exceeds parent binding energy
143
What information does liquid drop model provide?
Describes nuclear splitting
144
What information does Shell Model provide?
Energy, stability, nucleon arrangements etc
145
What are the relative masses of fragments?
One bigger by 1.3-1.5 times the other
146
What are the relative atomic masses of fragments?
One bigger by 1.3-1.5 times the other
147
Which nuclides in a fission have more neutrons?
- Parent, as releases 2-3 prompt neutrons per fission event
148
Which is the important characteristic of induced fission?
Neutron multiplication factor,k
149
What value is K for chain reactions?
= or > 1
150
