Week 3 Flashcards
1
Q
What happens with radionuclides with binding energy higher than their neighbours?
A
Energetically favourable for nuclide with lower binding energy to decay into one with higher binding energy
2
Q
What is a parent nuclide?
A
Lower binding energy, decays
3
Q
What is a daughter nuclide?
A
Higher biding energy, decay product
4
Q
How does A and Z change for α decay?
A
A decrease by 4
Z decrease by 2
5
Q
How does A and Z change for β decay?
A
β-
A unchanged
Z decrease by 1
6
Q
How does A and Z change for γ decay?
A
γ - photon
A unchanged
Z unchanged
7
Q
How does A and Z change for positron decay?
A
β+
A unchanged
Z decreased by 1
8
Q
How does A and Z change for electron capture?
A
A unchanged
Z decrease by 1
9
Q
What is the numeric commonality in all decays?
A
A unchanged for all types
10
Q
How is energy from decay released?
A
Kinetic energy of the final state particles
11
Q
Formula for KE of final state particles
A
Difference between parent and daughter binding energies + a few MeV
12
Q
What is the hierarchy of ionisation?
A
Alpha most ionising, least penetrating (Thin sheet)
Beta - penetrate few mm
Gamma - several cm
13
Q
What is the relative speed of particles in decays?
A
Alpha - much lower than C
Beta - ultrarelativistically (just below C)
Gamma - C
14
Q
Define decay constant
A
Probability that atom will decay in unit time via particular decay mode
15
Q
What is a decay mode?
A
Probability that atom will decay in unit time via particular decay mode
16
Q
What is the formula fro number of atoms decaying in a time?
A
ΔN = - λ N Δt
17
Q
What is the result of integrating the first order linear ODE of number of decaying particles?
A
N (t) = No exp (-λ(t-to))
18
Q
A
Radioactive decay law
N (t) = No exp (-λ(t-to))
19
Q
What is the mean lifetime?
A
Average lifetime of a nucleus
T = 1/λ
20
Q
What is half-life?
A
Time for sample to reduce by half (factor of 2)
T1/2 = on 2/λ = T ln2
21
Q
What is the range of half lives?
A
> 10^10 years to 10^-24s
22
Q
What is activity of a sample?
A
The expected decays per unit of time
A = λN
23
Q
Units of activity
A
Becquerels or Curie
24
Q
Define Becquerels
A
- Activity of a quantity of radioactive material in which one nucleus decays per second
25
Define Curie
3.7x10^10Bq
- - Decays/sec oof 226/88 Ra per gram
- 1Bq/s
26
How to find half-life of 226/88 Ra?
- find the mass in kg of a sample from Mn and Mp (neglect binding)
- Find No ~number of nuclei in 1g/mass in kg (a)
- Find λ = Activity/No (b)
(Activity = 3.7x10^10Bq)
- Find t1/2 = Ln2 / λ
27
What is need to help find decay constant?
Knowledge of mode - different for each mode
28
What are branching fractions?
F, The fractions decaying each mode - higher values make mode more likely
Fi = λi/λ
29
What is the decay chain for 238/92 U?
- 14 stages
- 8 alpha
- 6 beta
- Ends up at stable Pb isotope
30
What are the lifetimes of individual stages of U -> PB?
10^-4 - 10^9 years
31
What’s formula for parent decay?
N1 = No exp (-λ1t)
32
How to find dN/dt for species later in decay chain?
DN2/dt = -λ2N2+ λ1N1
33
What happens if half-life of daughter is more than half the parents? (λ2<2 λ1)
At some point the concentration of the daughter exceeds the parents
34
How do parent and daughter populations evolve?
- As parent decays, daughter population grows faster than it decays
- After some time parents are depleted so daughter production rate falls -> daughter decay rate dominates
35
What happens if daughter half life i less than half the half life of the parent?
- Daughter nuclei decay too fast for their population to exceed parents
36
How does radioactive dating work?
Compares abundance of naturally occurring radioactive isotope to abundance of decay products
37
What method can be used to measure the age of the Earth?
Rubidium-strontium
38
What radiodating is used for organic material?
- Unstable 14/6C with life expectancy 8270years
- Stops being formed when something dies
14/6C -> 14/7N +e- +v
39
What is the formula to find the duration between the death of the organism and the present time?
T = 1/λ ln (1+ NN/Nc)
NN = amount of 14/7 N
NC = amount of 14/6 C
40
What is the Q value?
The energy associated with the change in nuclear mass in decay
41
What Q is needed for decay?
>0
42
Q factor
Binding energy after decay - binding energy before decay
43
What does Q tell us about daughter nucleus?
If daughter very stable, binding energy is high and more energy will be released
44
What are Z to A relations depending on nuclei size?
Z~0.41A for heavy
Z~A/2 for lighter
45
How does the initial mass of the nucleus affect the alpha particle?
Heavier initial nucleus -> higher kinetic energy
46
Formula for T α?
Kinetic energy of α, Tα = (1 - 4/A)Q
47
What did Geiger Nutall notice?
α with larger Q had shorter half-lives
Log λ = a + b log R
R = range of α particles in the air
λ = decay constant
48
What did Swinne add to Geiger Nutall?
Suggested alpha particle velocity instead of log R
49
What did Gamow/Condon and Gurney add to Geiger Nutall?
Alpha decay is a quantum tunnelling process, which successfully explained law
50
What binds alpha particle to nucleus?
Strong force in ‘quasi-bound’ state
51
What do we approximate the nuclear potential well to?
A spherical well of radius R (R = nucleus radius)
52
Formula for fine structure constant
α = e/ (2Ehc)
53
Formula for Coulomb repulsion between alpha particle and daughter nucleus
Vc = (2 ZD α ℏ c) / r
Zd = (Z - 1) = atomic number of daughter
54
Where is the Q value on a potential barrier graph?
Below the top of the potential barrier
55
Under what conditions is the alpha particle unable to cross the potential barrier from inside the nucleus?
- When rb (radial distance at which kinetic energy of the alpha particle = Coulomb energy) > nuclear radius
- Kinetic energy insufficient
56
What’s the Gamow factor?
Describes the likelihood of an alpha particle (or other particles) overcoming the Coulomb barrier (the electrostatic force between the positively charged alpha particle and the positively charged nucleus).
57
How does increasing radius affect Gamow factor?
Increasing distance from the nucleus decreases the Coulomb barrier, increasing the likelihood of tunneling (higher Gamow factor).
Increasing nuclear charge (Z) makes tunneling harder, leading to a smaller Gamow factor (lower probability of tunneling).
58
Relationship between decay half-life and tunnelling probability
Inversely proportional
59
Which force is involved in beta decay?
Weak force
60
Which conservation law is important for alpha particles?
Energy and momentum (non-relativistic)
61
Which conservation law is important for beta decay?
Charge
62
What problems with beta decay led to new theories?
- electron/position measured with continuous not discrete energy spectrum as with alpha
- Spins go from 0 to 1 +/- 1/2 suggesting angular momentum not conserved
63
What solution to the beta decay problem did Pauli propose?
- new, very light spin 1/2 particle also emitted -> neutrino
- only works if spin 1/2, no charge and no nuclear force interaction
64
Beta - decay in words
Neutron converts into protein, electron and anti-neutrino
65
Positron decay in words
Proton converts to neutron, a positron and electron type neutrino
66
When does beta decay happen naturally?
Free neutrons with T 898s
67
When does positron decay happen naturally?
- Only for proton inside nucleus as decay has negative Q
68
Define electron capture in words
-Usually lowest shell in atom
- Electron and proton convert into neutron and neutrino
69
When does electron capturehappen naturally?
When proton inside nucleus (usually with some shells filled) joins with an electron to form a neutron
70
When are beta decays energetically possible?
When total initial mass >total final mass
71
What is ignored when calculating electron binding energies?
Electron binding energy term
72
Difference between atomic and nuclear masses
Atomic - converted from nuclear
Nuclear - based on periodic
73
Which particles are stable compared to neutrons?
Free protons
74
Typical scale/units of nuclear and electrons
Nuclear ~ GeV
Mc^2 ~ 0.511MeV
75
What is the valley of stability
Narrow band in table of nuclide with stable nuclide
76
What is the shape of SEMF curve?
Parabola with minimum at Zmin = β /2γ
77
For which nuclei is pairing term important?
Even-A nuclei
78
How do graphs of mass excess vs atomic number differ for even vs odd?
- Even: even-even parabola, wide triangles pointing inside curve for beta decays
- Odd: 2 smooth parabolas
79
Pattern of beta decay for A odd
- Nuclei to left of A value decay via β -with increasingly longer half-lives as move closer to valley of stability
- Nuclei to right of A value decay via β+ or electron capture with shorter half-lives moving away from valley
80
Pattern of beta decay for A even
- Zigzag from the pairing term, odd-odd lie higher than even-even
- Decays only happen towards lower masses i.e. from point of zig zag to parabola ( to right for β+, to left for β-)
- *Can be 2 stable nuclei in mass chain i.e. same A value, Z different
- * Can have double β or double (+/-), technicall EC too though never seen
* = not sending A-odd
81
Why are neutrinos hard to detect?
Tiny cross section
82
What is and isn’t conserved in β- decay?
Lepton number conserved
Parity not conserved
83
What is γ decay often seen in conjunction with?
Alpha or beta decay when daughter is in excited state and makes 1 or more further transitions
84
What does the energy of the emitted photon equal?
Energy difference between quantised initial and final states
85
Difference in energy of atomic excitation and nuclear excitation
Atomic few eV
Nuclear hundreds of ~100keV
86
Difference in wavelength of atomic excitation and nuclear excitation
Atomic hundreds of nm
Nuclear pm or 1000fm
87
How are gamma rays described in terms of energies?
E γ
88
γ ray lifetimes
10^-13 - 10^-10 secs
- but some excited states metastable with longer lifetime
89
Difference between nuclear and atomic excitation
Atomic excitation refers to the process in which an electron in an atom absorbs energy and moves to a higher energy level (a higher orbital). This happens when the atom is exposed to energy sources like light or heat.
Nuclear excitation occurs when the nucleus of an atom absorbs energy, causing the nucleus to enter a higher energy state.
90
Define nuclear isomers
Nuclear isomers are different forms of the same nucleus that have the same number of protons and neutrons but differ in energy due to the arrangement of the nucleus' internal particles. These isomers are in different excited states, meaning the nucleus has higher energy compared to the ground state.
91
92
Define isomer transitions
Isomer transitions refer to the process where a nuclear isomer moves from a higher energy state (excited state) to a lower energy state. This transition happens by the emission of gamma radiation, which releases the excess energy, allowing the nucleus to return to a more stable state.
93
Describe energy-momentum conservation for gamma decay
- Mass less but carry small amount of momentum
- If parent at rest, daughter recoils with non-relativistic momentum
94
Define radiation modes
Radiation modes refer to the different ways that energy can be released from a nucleus or atom.
- electric transition
- magnetic transition
95
Define selection rules
Selection rules are principles that determine which transitions between different energy levels are allowed or forbidden in atomic and nuclear systems.
96
Define selection rules for electron orbital angular momentum
- Δl = ±1: The orbital angular momentum quantum number (l) can change by 1 during an allowed transition.
97
Selection rule for electron spin quantum number
- ΔS = 0: The spin quantum number (S) must stay the same during a transition (this means spin can't change in electric dipole transitions).
98
Selection rule for electron magnetic quantum number
- Δm_l = 0, ±1: The magnetic quantum number (m_l), which determines the orientation of the orbital, can change by 0 or ±1.
99
Selection rule for electron principal quantum number
Δn: The principal quantum number (n) can change, but the change in n doesn't have a strict rule (except it must lead to a valid energy difference).
100
Selection rule for electron total angular momentum
- ΔJ = 0, ±1: The total angular momentum quantum number (J) can change by 0 or ±1, but J = 0 → J = 0 is forbidden (this means the total angular momentum cannot stay the same).
101
Selection rule for nuclear spin quantum number
ΔI = 0, ±1: The nuclear spin quantum number (I) can change by 0 or ±1, but the transition I = 0 → I = 0 is forbidden.
102
Selection rule for nuclear total angular momentum
ΔJ = 0, ±1: The total angular momentum quantum number (J) of the nucleus can change by 0 or ±1.
103
Selection rule for nuclear parity
Δπ = ±1: The parity (π), which indicates whether the nuclear wave function is symmetric or antisymmetric under inversion, changes by ±1 (parity must flip in certain transitions like M1 transitions).
104
Which interactions are responsible for gamma decay?
EM interactions
105
Describe electric transitions
- One of EM transitions causing gamma decay
- denoted b y E1, E2 etc
- Have angular momentum l = 1,2…
- electric 2 pole transitions - dipole, quadruple etc
106
Describe magnetic transitions
- One of EM interactions leading to gamma decay
- Denotesd by M1, M2..
- Have angular momentum l = 1,2…
Magnetic 2l pole transitions - magnetic dipole, magnetic quadrupole
107
What is the difference in parity for beta decay and gamma?
Gamma is parity conserving, beta is not
108
When are electric dipole transitions permitted and why?
- Only permitted between initial and final states of opposite parity due to odd under parity transformation
- An electron moves between energy levels with a change in its orbital angular momentum (l) by 1 e.g. An electron in an atom absorbs a photon and jumps from one energy level to a higher one.
109
When are magnetic dipole transitions permitted and why?
- Parity does not change -> odd-odd or even-even
- Dipole is proportional to spin of nucleon making transition
- Transitions only permitted between initial and final states of same parity
110
What are parity transformations?
Transformation in spatial coordinates
- if keeps sign -> even
- if flips sign -> odd
111
Formula relating initial and final parities of electric transitions Ef
π sub i = (-1)^l π sub f
112
Formula relating initial and final parities of magnetic transitions Mf
π sub i = (-1) ^(l+1) πf
113
What is the third selection rule for photons?
- Photon has spin one, so transitions
between an initial state with Ii = 0 and a final state with If = 0 are strictly forbidden.
- If the ground state has spin zero and the lowest excited state also has spin zero, the excited state cannot decay via photon
- Conservation of momentum: the final state should have some orbital angular momentum to balance the photon’s spin angular momentum (1).
- Can decay with electron-positron pair as excitation energy >2x rest energy of elctron
114
Formula for average number of decays in time Δt
- n = λ N Δt
115
What is emitted in beta +?
Position and neutrino
116
What is emitted in beta -?
Electron and anti neutrino
117
What determines the size of fluctuations in decay around the average number of decays?
SQRT (n)
118
What distribution gives the probability of observing n counts in Δ t
Poisson
119
What gives the ratios of concentration of different radioactive daughters?
Ratios of different decay constants
120
What is a radioactive chain?
When parents decay into daughters which themselves are radioactive
121
When can a decay equilibrium be reached?
When parent has long half life
122
How does a photon decay correspond to a change in a nucleus’s charge and matter distribution?
- Shiuft in charge distribution -> change in E field (electric)
- Shift in current distribution e.g. orbitals o protons -> change in B field (magnetic)
123
Where does the energy released in alpha decay come from?
Mass of parent - (mass of daughter + mass of alpha particle)
124
By what factor is the kinetic energy of the alpha particle different to the Q value?
- Smaller
- By factor equal to ratio ofreduced mass of alpha:actual mass
125
What is the quantum mechanism of alpha decay?
- Quantum tunnelling
- Through potential barrier of strong force and Coulomb repulsion between alpha and daughter
126
What does the estimated half-life depend on and what does it agree with?
- Q-value
- Geiger-Nuttall observations
127
When do alpha particles have zero orbital angular momentum?
Even-even decaying to ground state of daughter nuclide
128
Which nuclides have considerably longer half lives?
Odd protons and/or neutrons
129
Why do nuclides with odd protons/neutrons have longer half-lives?
Probability of formation of alpha particle inside decaying nucleus is so small
130
What is the value of kinetic energy of emitted particle in beta decay (electron or positron)
- Any value upto Q-value
131
What happens to “leftover” energy in beta decay not turned into kinetic
- taken up by almost massless (anti)neutrino with spin 1/2 to conserve angular momentum
132
What is the value of l electromagnetic transitions?
Any value which preserves conservation of angular momentum
133
What is the difference in parity for Ef transitions?
(-1)^l
134
What is the difference in parity for Mf transitions?
(-1)^(l+1)
135
When is gamma emission strictly forbidden?
When initial and final states have spin 0 (as photons have spin 1 and need to conserve momentum)
