Nuclear_Physics_All_Flashcards
(142 cards)
1
Q
What are isotopes, isotones and isobars?
A
Isotopes: same Z, different N; Isotones: same N, different Z; Isobars: same A, different Z.
2
Q
Why was mass spectrometry important to learn about the existence of isotopes?
A
It revealed atoms of the same element (same Z) with different masses, confirming isotopes.
3
Q
If a particle has orbital angular momentum l = 1 and spin s = 3/2, which values of total angular momentum j are possible?
A
j = |l - s| to |l + s| in steps of 1 → j = 1/2, 3/2, 5/2.
4
Q
How many different quantum states exist for each value of j?
A
Each j state has 2j + 1 states: j=1/2→2, j=3/2→4, j=5/2→6.
5
Q
Why does the fact that 14_7 N has integer spin show that neutrons cannot be composite object made from a proton and an electron?
A
A composite neutron (fermion) made from p + e⁻ would yield half-integer nuclear spin; 14N has integer spin, so this model is invalid.
6
Q
Which types of interaction are important for photons from nuclear processes or x-rays?
A
Photoelectric effect, Compton scattering, pair production.
7
Q
What is the difference between how photons interact with matter compared to charged particles?
A
Photons interact probabilistically via discrete events; charged particles lose energy continuously through ionization and excitation.
8
Q
How would you calculate the necessary thickness of shielding to decrease the amount of photons to a given fraction?
A
Use I = I₀e^(-μx); solve for x: x = -ln(I/I₀)/μ.
9
Q
What is a straggling function and where is it relevant?
A
It describes the statistical spread in energy loss of particles in matter; important in dosimetry and detector resolution.
10
Q
What does the Bethe-equation describe?
A
The mean energy loss per unit length (dE/dx) for charged particles traversing matter.
11
Q
Why is the Bethe equation often plotted as a function of βγ?
A
Because βγ = v/c * E/mc² is a convenient relativistic variable for comparing particles of different mass.
12
Q
What is qualitatively the shape of the Bethe equation curve?
A
It decreases at low βγ, reaches a minimum (MIP), then slowly increases (relativistic rise).
13
Q
What is a minimum ionising particle?
A
A particle for which dE/dx is at its minimum; typically near βγ ≈ 3–4.
14
Q
Show the mean energy loss per distance for a minimum ionising particle in iron is about 13 MeV/cm.
A
See notes.
15
Q
What kind of signals would α, β, and γ particles as well as high energy protons and muons produce in a cloud chamber?
A
α: thick short tracks; β: thin curved tracks; γ: usually no track; protons: thick straight tracks; muons: long straight tracks.
16
Q
How does the range of particles in a medium scale with mass and charge?
A
Range decreases with higher charge (Z² scaling in stopping power) and lower mass; also energy and velocity dependent.
17
Q
What is the Bragg peak?
A
The sharp increase in energy deposition near the end of a charged particle’s range.
18
Q
How does the Bragg peak occur?
A
It results from increasing dE/dx as the particle slows (from Bethe equation).
19
Q
How can the Bragg peak be used in tumour treatments?
A
To focus damage at tumor depth with minimal exit dose — advantage over photon irradiation.
20
Q
What are activity, dose, and equivalent dose?
A
Activity: decays/sec (Bq); Dose: energy/kg (Gy); Equivalent dose: dose × radiation weighting factor (Sv).
21
Q
Which types of radiation are particularly dangerous at a given dose?
A
High LET radiation like α and neutrons due to dense ionization.
22
Q
Why is it nevertheless often not dangerous to be near a source of α radiation (assuming no other radiation is present)?
A
α particles are easily stopped by skin or even paper.
23
Q
How does photon vs charged particle penetration through a thin wall compare as thickness increases?
A
Photon attenuation is exponential; charged particles stop more sharply due to range cutoff.
24
Q
What is a cross section? What dimension does it have?
A
Probability of interaction per target area; units: area (barns = 10⁻²⁸ m²).
25
What is a differential cross section?
The cross section per unit solid angle or energy: dσ/dΩ or dσ/dE.
26
What is q² and how is it related to the scattering angle in elastic scattering?
q² = |p_i - p_f|²; it relates to the momentum transfer and θ, |q|=2|p||sin(θ/2)
27
What does the Rutherford scattering cross section describe?
Scattering of charged particles off nuclei via Coulomb interaction.
28
How does the Rutherford cross section scale with q², E_kin, |p|, and θ?
dσ/dΩ ∝ 1/sin⁴(θ/2); inversely with q⁴ and E_kin².
29
How is the scattering potential related to the differential cross section in elastic scattering?
Fourier transform of the potential gives the scattering amplitude, from which dσ/dΩ is calculated.
30
Why might we find deviations from the Rutherford cross section when scattering α particles off a nucleus at increasing energies?
Due to nuclear forces becoming significant at short range, and finite nuclear size.
31
What are the advantages of using electrons as a projectile instead?
Electrons interact via well-understood electromagnetic force and probe charge distribution without strong interaction complications.
32
What kind of processes does the Mott scattering cross section describe?
Elastic scattering of relativistic electrons off spin-½ point-like particles.
33
What is a form factor, and how does it relate to the scattering cross section?
A correction factor accounting for finite size and structure of target; modifies the cross section.
34
How does the form factor relate to the (charge) density distribution of a nucleus?
It is the Fourier transform of the charge density distribution.
35
How does the form factor change when the size of a nucleus is increased (similar shape)?
Oscillation period decreases — higher frequency oscillations for larger nuclei.
36
What is the form factor for a Gaussian density distribution?
F(q) = exp(-q²σ²/2), where σ characterizes the distribution width.
37
What is the form factor for a homogeneous sphere?
F(q) = 3[sin(qR) - qR cos(qR)] / (qR)³, where R is the radius.
38
How do the oscillations change for a more realistic density distribution?
They are damped compared to sharp-edged distributions due to diffuseness of nuclear surface.
39
What do measured density distributions look like for actual nuclei?
Roughly constant central density with a smooth drop-off at the surface.
40
How does the nuclear radius scale with the mass (A) of the nucleus?
R ≈ R₀A^(1/3), where R₀ ≈ 1.2–1.3 fm.
41
How does the nuclear skin thickness scale with the mass of the nucleus?
It remains nearly constant (~2.5 fm), independent of A.
42
How does the density in the nucleus scale with the mass of the nucleus?
It is approximately constant (~0.16 nucleons/fm³), independent of A.
43
How do we know that the N-N interaction has a short range?
Nucleons in nuclei are tightly packed, and scattering data show rapid drop-off in potential beyond ~2 fm.
44
How do we know that the N-N interaction is repulsive at short distances?
Scattering phase shifts and saturation of nuclear density imply strong short-range repulsion.
45
What is qualitatively the shape of the radial potential?
Repulsive core at short distances, attractive in medium range (~1–2 fm), zero beyond.
46
Which part of this is captured by the Yukawa potential?
The attractive medium-range part: V(r) ~ -(g²/r)exp(-μr).
47
How would the nuclear force change if pions were a bit lighter or heavier?
Lighter pions → longer-range force; heavier → shorter-range force.
48
How do we know that the nuclear force is spin-dependent?
Different binding energies for singlet and triplet states (e.g., deuteron bound, diproton unbound).
49
Which other properties does the nuclear force have?
It is charge-independent, non-central (tensor component), and short-ranged.
50
Why are there no diprotons or dineutrons?
Spin-singlet N-N interaction is not strong enough to bind them; Coulomb repulsion also breaks diproton.
51
What experimental observation shows an exchange force component in the N-N interaction?
Dependence of nuclear properties on spin and isospin suggests exchange of mesons (pions).
52
How does the weight of different isotopes relate to the average atomic weight of an element?
The average atomic weight is a weighted mean based on isotopic abundance.
53
What is the Segrè chart?
A plot of proton number (Z) vs neutron number (N) for known isotopes.
54
What is the valley of stability?
A region on the Segrè chart where stable nuclei reside; balance of N and Z minimizes mass/energy.
55
How are the proton and neutron numbers related qualitatively for observed nuclei?
Stable nuclei have N ≈ Z for light elements; N > Z for heavier ones.
56
What is the binding energy of a nucleus?
The energy required to separate all nucleons in a nucleus.
57
What is the mass excess and how is it related to the binding energy?
Mass excess = actual mass - mass number; related via binding energy = Δmc².
58
What are approximately the masses/atomic numbers for the most bound nuclei?
Around iron (Fe), A ≈ 56, Z ≈ 26.
59
What is the Q value and how does it relate to spontaneous processes?
Q is the energy released; Q > 0 means spontaneous decay is energetically allowed.
60
How would you calculate the Q value for different decay processes?
Q = (mass_initial - mass_final) * c² or use mass excesses.
61
Does it make a difference if you use the mass excess or binding energy?
No; both relate to mass difference, just with different conventions.
62
Which types of nuclei typically undergo α, β+, or β− decays?
α: heavy nuclei; β+: proton-rich; β−: neutron-rich.
63
What is the parity of a particle?
It is the intrinsic symmetry under spatial inversion; can be +1 or −1.
64
What is the nuclear spin?
Total angular momentum of a nucleus, resulting from nucleon spins and orbits.
65
What are even-even, even-odd (odd-even), and odd-odd nuclei?
Even-even: even N, Z; even-odd: even N, odd Z; odd-odd: odd N and Z.
66
What are spin and parity of even-even nuclei?
Ground state usually 0⁺ due to pairing effects.
67
Can you think of an example where the nuclear spin would be relevant?
In MRI (magnetic resonance imaging), where nuclear spin aligns with magnetic fields.
68
What are the terms of the semi empirical mass formula (SEMF)?
Volume, surface, Coulomb, asymmetry, and pairing terms.
69
How are the first two terms related to the liquid drop model? Why do they scale with A as they do?
Volume term ~A (bulk binding); surface term ~A^(2/3) (fewer neighbours at surface).
70
What does the Coulomb term represent?
Electrostatic repulsion between protons; reduces binding energy.
71
What is the Fermi gas model?
A model where nucleons are treated as free particles in a potential well, obeying Pauli exclusion.
72
How does the Fermi gas model relate to the Pauli principle?
Each quantum state is singly occupied; explains need for neutrons to fill states beyond protons.
73
How does it explain why nuclei with a more equal number of neutrons and protons tend to be more strongly bound?
Balanced N ≈ Z minimizes kinetic energy and asymmetry term.
74
How does the SEMF explain the shape of the valley of stability (relating N and Z)?
Minimizing SEMF with respect to N shows stable N > Z for heavier nuclei.
75
How does the dependence of the binding energy on Z for fixed A change when A is even or odd?
Even A → pairing stabilizes nuclei; odd A → less binding, especially odd-odd.
76
Which properties of nuclei cannot be described by the SEMF?
Magic numbers, shell effects, spin/parity — these require quantum models.
77
Which magic numbers are known?
2, 8, 20, 28, 50, 82, 126.
78
What is the basic idea behind the shell model?
Nucleons move in quantized orbitals within a mean nuclear potential, similar to electrons in atoms.
79
What do the quantum numbers n_r, l, and m mean?
n_r: radial node count; l: orbital angular momentum; m: projection of l.
80
Why is there no principal quantum number for this problem (compared to the hydrogen atom)?
The nuclear potential is not Coulombic, so energy depends on l and spin-orbit interaction.
81
What is the Woods-Saxon potential? Why is it a reasonable choice?
A smooth, finite potential well modeling the nuclear force's finite range and saturation.
82
How does the W-S potential compare to a harmonic oscillator and to a spherical infinite potential well?
It is more realistic: finite depth and smoother walls than square or harmonic wells.
83
How does the spin-orbit interaction change the number of energy levels?
It splits levels with same l but different j = l ± 1/2, explaining magic numbers.
84
Why is it important to explain the magic numbers?
They correspond to especially stable nuclei; not predicted by liquid drop model.
85
How many nucleons fit into a state with total angular momentum j?
2j + 1 nucleons (due to magnetic quantum number degeneracy).
86
How do you specify a state in terms of (nlj)^x (spectroscopic notation)?
n = shell index, l = orbital (s, p, d...), j = total angular momentum, x = number of nucleons.
87
How can we use the single particle shell model to find the nuclear spin and parity?
Determine configuration of unpaired nucleons; spin = j, parity = (−1)^l of that nucleon.
88
What is a valence nucleon?
A nucleon outside a closed shell, mainly responsible for nuclear properties.
89
What happens if a shell is missing one nucleon to be completely filled?
That nucleon determines spin/parity; behaves like a particle in that orbital.
90
In which cases does the single particle shell model make particularly accurate predictions?
Near closed shells (magic numbers), where residual interactions are minimal.
91
What is a decay chain?
A sequence of radioactive decays from one unstable nucleus to another until a stable one is reached.
92
How do the numbers of nuclei change over time for simple decays?
N(t) = N₀e^(-λt), where λ is the decay constant.
93
How do the numbers of nuclei change over time for series decays?
Requires solving coupled differential equations for each nuclide in the chain.
94
What happens in a series decay if λ_A ≪ λ_B or vice versa?
λ_A ≪ λ_B: B accumulates; λ_A ≫ λ_B: B decays quickly and doesn’t build up.
95
How do the different decay processes change N, Z, and A?
α: A–4, Z–2; β⁻: N–1, Z+1; β⁺: N+1, Z–1; EC: same as β⁺; A unchanged.
96
What is the Geiger-Nutall law?
log₁₀(T₁/₂) ∝ Z / √Q_α; relates α decay half-life to decay energy.
97
How would you predict the lifetime of a third isotope with Qα,3?
Use Geiger-Nutall law and known values of two other isotopes.
98
What is the quantum mechanical model behind α decay?
Gamow’s model: α particle tunnels through Coulomb barrier.
99
What is the Coulomb barrier?
Electrostatic potential energy barrier due to repulsion between α and daughter nucleus.
100
How can we broadly estimate the size of the barrier?
Distance at which nuclear and Coulomb forces are equal; typically a few femtometers.
101
How can we estimate the barrier height?
V ≈ (1/(4πε₀)) * (Z₁Z₂e²)/r, where r is nuclear separation.
102
Which ingredients are needed to estimate the decay constant?
Barrier width, height, α energy, transmission coefficient.
103
What is a transmission coefficient?
Probability that a particle tunnels through a potential barrier.
104
How does the decay constant scale with Q and Z? What about the lifetime and half-life?
λ ∝ exp(-const * Z / √Q); higher Q or lower Z → faster decay → shorter lifetime.
105
What does the energy distribution of the α particles look like qualitatively?
Discrete energy peaks (since α decay is two-body).
106
What does the energy distribution of β particles look like qualitatively?
Continuous spectrum up to endpoint energy (due to neutrino emission).
107
What is the reason for this difference?
α decay is two-body; β decay involves three particles (e.g., β⁻ + ν̄).
108
What is electron capture and which types of nuclei exhibit it?
A proton absorbs an inner electron and becomes a neutron; occurs in proton-rich nuclei.
109
How does the condition for Q > 0 change from β⁺ decay to electron capture?
β⁺ decay requires Q > 2m_ec²; EC only needs Q > 0.
110
How can we know if electron capture has happened?
Detect X-rays or Auger electrons from atomic rearrangement after inner shell vacancy.
111
Photons always carry angular momentum. What does this imply about transition between angular momentum states?
Photon emission must obey angular momentum conservation: ΔJ ≥ 1 for γ decay.
112
What is inner conversion?
Excited nucleus transfers energy directly to an atomic electron, which is ejected.
113
Why can there be several photon energies created as a result of inner conversion?
Electrons can be ejected from different atomic shells, each with unique binding energies.
114
What are some sources of natural background radiation?
Radon gas, cosmic rays, terrestrial isotopes (K-40, U-238), and internal body isotopes (C-14).
115
What kind of tunnelling models spontaneous fission?
Quantum tunnelling through the nuclear potential barrier, similar to α decay.
116
What are fissile and fissionable materials?
Fissile: can undergo fission with thermal neutrons (e.g., U-235); fissionable: can fission but not necessarily with thermal neutrons.
117
What is the basic chain reaction in the fission of 235U?
U-235 + n → fission products + 2–3 neutrons + energy; neutrons sustain further fissions.
118
What is a moderator?
A material that slows down fast neutrons to thermal energies.
119
Why do we (often) need moderators?
Thermal neutrons are more likely to induce fission in U-235; increases reactor efficiency.
120
What kind of materials make good moderators?
Light elements with low absorption: water, heavy water, graphite.
121
What are prompt and delayed neutrons?
Prompt: emitted instantly during fission; delayed: emitted seconds later by decay of fission fragments.
122
Why are delayed neutrons important for controlling fission?
They allow time for feedback systems to regulate the chain reaction.
123
Why is nuclear waste so radioactive?
It contains short- and long-lived fission products and transuranic elements.
124
Why is nuclear waste left on site for years before being transported for long-term storage?
Initial radioactivity is high; decay reduces heat and hazard over time.
125
What is the neutron multiplication factor k and how is it related to criticality?
k = neutrons produced / neutrons lost; k = 1 is critical, <1 subcritical, >1 supercritical.
126
What k factor does a nuclear power plant operate on?
Slightly above 1 (k ≈ 1.0001–1.01) to maintain steady power output.
127
What are the main components of a nuclear reactor?
Fuel, moderator, control rods, coolant, pressure vessel, containment.
128
What are some considerations for choosing fuel enrichment and moderator?
Fuel must sustain k ≈ 1; moderator must slow neutrons without high absorption or degradation.
129
Why are heavy elements created in the laboratory often proton rich compared to the valley of stability?
Due to use of light-ion fusion which adds more protons than neutrons; neutron-deficient products result.
130
What is the island of stability?
A predicted region of superheavy nuclei with relatively longer half-lives due to shell effects.
131
Why can’t we produce Helium from protons in one step?
Coulomb repulsion and conservation laws prevent simultaneous four-proton fusion; multistep reactions are needed.
132
How does the temperature relate to the order of magnitude of typical energies?
kT ≈ 0.086 MeV for T ≈ 10⁹ K; fusion requires energies ~10–100 keV, corresponding to T ~10⁷–10⁸ K.
133
Why do we think that we understand the initial element abundances in the universe?
Big Bang nucleosynthesis predictions match observed abundances of H, He, and Li.
134
Where does the deuterium in the universe come from?
Primordial nucleosynthesis shortly after the Big Bang.
135
Where does the Helium in the universe come from?
Mostly from Big Bang nucleosynthesis and stellar fusion.
136
How does the sun produce power?
Via the proton-proton chain: 4p → He + 2e⁺ + 2ν + energy.
137
Why is the weak interaction important for allowing the sun to produce power?
It allows a proton to convert into a neutron during p-p fusion, enabling deuterium formation.
138
What is the CNO cycle and where is it relevant?
A fusion cycle using C, N, O as catalysts to fuse protons into helium; dominant in hotter stars.
139
How are the elements up to iron created?
By fusion in stellar cores during their life cycles.
140
Where do the heavier elements come from?
Neutron capture during supernovae (r-process) and stellar evolution (s-process).
141
Why do we not try to create proton fusion in fusion power plants?
Too slow due to weak interaction; impractical for power generation.
142
What do we do instead of trying to create proton fission in nuclear power plants ?
Use D-T fusion: D + T → He + n + 17.6 MeV; requires lower temperature and higher cross-section.
