1
Q
What was Rutherford’s Experiment and what was the result?
A
Firing alpha particle through a gold foil.
A few particles reflected though large angles as a result of colliding with the nucleus) meaning that atoms contained a small nucleus
2
Q
What is Z?
A
The atomic number (The number of protons)
3
Q
What is N?
A
The number of neutrons
4
Q
What is A?
A
Nucleon number/ Mass number (A=Z+N) (Nucleon number = total number of protons and neutrons) Approximately the mass of the nucleus measured in u (amu)
*we mean their rest masses
5
Q
What is 1u approximately equal to?
A
1.6605389211732 x 10^-27 kg = 931.494MeV/c^2
6
Q
What did Rutherford find?
A
That the nucleus is tens of thousands of times smaller in radius than the atom itself. Hence, we can model a nucleus as a sphere with a radius R that depends
on the total number of nucleons (neutrons and protons) in the nucleus.
7
Q
What is the equation for the radius of an atomic nucleus?
A
R = R0A^1/3 R0 = 1.2 x 10^-15 m = 1.2 fm
8
Q
What is the equation for the mass of a nucleus and volume of a nucleus?
A
M = A x 1.66 x 10^-27 kg
V = 4/3πR^3 = 4/3πR0^1/3A
volume V of the nucleus (which we treat as a sphere of radius R)
9
Q
What is the density of a nucleus?
A
ρ=A/V=constant
ALL NUCLEI HAVE APPROXIMATELY THE SAME DENSITY
10
Q
What are isotopes?
A
Nuclides with the same Z but different N
11
Q
What is binding energy?
A
The energy required to separate nucleons
(using masses of neutral atoms)
E_B= (ZM_H + Nm_n − A/ZM)c^2
where m_n is the mass of the neutron, M_H is the mass of the neutral hydrogen atom (to account for electrons) and A/ZM is the mass of the neutral atom with Z
protons and N neutrons, c^2 = 931.5 MeV/u.
12
Q
Why is the total rest energy greater (E_0) of the separated nucleons grater than the rest energy of the nucleus?
A
Because energy must be added to a nucleus to separate it into its individual protons
and neutrons
13
Q
What is the rest energy of a nucleus?
A
E0 - EB
14
Q
What is the binding energy
of a nucleus
with Z protons,
N neutrons
A
E_B= (ZM_H + Nm_n − A/ZM)c^2
where mn is the mass of the neutron, MH is the mass of the neutral hydrogen
atom (to account for electrons) and M is the mass of the neutral atom with Z
protons and N neutrons, c^2 = 931.5 MeV/u.
The masses of
other atoms are approximately equal to A atomic mass units.
15
Q
What is mass defect?
A
The difference between the mass of the nucleus and the
combined mass of the constituent nucleons.
16
Q
What is the equation for mass defect?
A
Mass of a nucleus is always less than the total mass of its nucleons by an the mass defect amount
ΔM = ZM_H + Nm_n − A/ZM = E_B/c^2
17
Q
What is the binding energy per nucleon?
A
E_B/A
measure of how tightly a nucleus is bound
18
Q
What are the steps to find nuclear properties?
A
- Identify the target variables,
assemble the equations needed to solve the problem. - Solve for the target variables. for binding energy
calculations ( get enough precision )
19
Q
What is the force that binds protons ad neutrons together in the nucleus?
A
Strong Interaction in nuclear context its nuclear Force
20
Q
What are the characteristics of nuclear force (from observation of nuclei)?
A
- Does not depend on charge; the binding is the same for protons and neutrons
- Short-ranged, of the order of 10^-15 m (nuclear size); otherwise nuclei may grow
to very large sizes by pulling in more protons and neutrons - On short distances the force is much stronger than any other force; otherwise the
nuclei would not be stable - Nucleons cannot interact with all other nucleons in a nucleus; otherwise the
nuclear matter density would not be constant and the binding energy per nucleon would not be almost the same for all large nuclei. Nucleons interact by nuclear
force only with a few other nucleons nearby. This is called saturation and is analogous to covalent bonding in molecules and solids. - Nuclear force favours binding of pairs of protons and neutrons with opposite spins; it is particularly favourable to have pairs of pairs: a pair of protons and a
pair of neutrons, each of them having opposite spins; an example is an a-particle
which is exceptionally stable
21
Q
How can we gain more insight into nuclear structure?
A
Using the liquid-drop model and shell model
22
Q
What is the liquid drop model?
A
Foundation: nuclei have approximately the same density.
The model (the basic principles) has been successfully used to explain binding energies of the nuclei.
Protons and neutrons are like molecules in liquid held together by strong-range interaction and surface-tension effects
23
Q
How do you derive the total binding energy of the nucleus using the liquid drop model?
A
- Binding energy per nucleon is roughly constant for large nuclei, hence the total binding energy is rising proportionally to A
- Nucleons on the surface are less tightly bound. This gives a negative term proportional to the surface area 4πR^2. R is proportional to A^1/3
- Electrostatic repulsion: every proton repulses other (Z - 1) protons. The repulsive potential (energy) is proportional to 1/R and hence, to 1/A^1/3. The energy is also proportional to Z(Z - 1) and is negative (opposite sign to the
attractive nuclear force) - Experimental results for binding energies show that the best description of binding energies is achieved with (N - Z)^ 2/A
- the nuclear force favours ‘pairing’ of neutrons and protons. This last term is positive (larger binding) when both
Z and N are even, negative if both Z and N are odd and zero otherwise. I
24
Q
What is the equation for the total estimate binding energy?
A
EB=C1A−C2A^2/3 −C3
Z(Z −1)/ A^1/3 −C4(A− 2Z)^2/ A ±C5A^−1/2
C1 = 15.75 MeV, C2 = 17.80 MeV, C3 = 0.7100 MeV, C4 = 23.69 MeV, C5 = 12 MeV (or 0 if Z and N are not both even or odd)
25
What is the semi empirical formula?
Used to calculate the masses of neutral atoms if the binding energy is determined from the liquid-drop model
semi-empirical - because the coefficients for the binding energy have been found using experimental data
but the formula for binding energy has theoretical grounds.
26
What is the formula for the mass of any neutral atom?
M = ZMH + Nmn −EB/c^2
| if EB is found from LDM
27
What is the shell model?
Predicts the existence of unusually stable nuclei (high binding
energy) containing magic numbers of protons or neutrons
It is analogous to the central-field approximation of a potential in
atoms.
28
Derive the shell model?
- Each nucleon moves in an averaged field (potential) created by other nucleons
-Potential energy due to the nuclear force is the same
for neutrons and protons and is similar to the spherical version of the square
well potential as in atoms.( protons are also affected by electric repulsion potential.)
29
What the graph for the shell model and what does it mean ?
- The shape of this
function: a spherical version of the square-well potential. The corners are somewhat rounded because the nucleus doesn’t have a
sharply defined surface.
- Electric potential: each proton interacts with a sphere with a charge (Z - 1)e
30
What does the shell model predict?
- Full solution of the Schrödinger equation for protons and neutrons in spherically
symmetric potentia
- A concept of filled shells and sub-shells
- Atoms with noble gas structure
- Unusually stable nuclear structure (magic numbers)
- In nuclei stable configurations are different due to different potential and strong
spin-orbit interactions
- Double magic numbers
-Filled shell or sub-shell configurations of nucleon energy levels in a nucleus:
big jump in energy is required to transfer to a higher energy level.
- Substantially higher binding energy compared to neighbouring nuclei (clearly
seen for light nuclei).
- Zero nuclear spin
31
What are the consequences of the shell model?
- Higher binding energy compared to neighbouring atoms.
| - For magic Z there is a higher number of stable isotopes.
32
What is radioactivity?
The process where unstable structures that decay to form other nuclides by emitting particles and electromagnetic radiation
33
What are odd-odd nuclides?
Nuclides have both odd Z and odd N.
For stable odd-odd:
2 1H, 6 3Li, 10 5B, 14 7N
No stable with A=5 or 8
34
What is the stability range of the Segrè chart?
```
Narrow Region
Low A: N =~ Z.
High A: N / Z is increasing up to 1.6
due to increasing influence of electric
repulsion
```
35
When does alpha decay occurs/is possible?
When the mass of the original neutral atom is bigger than the sum of the masses of final neutral atom and He-4.
36
What is alpha decay?
A nucleus is too big to be stable, emission of an a-particle, a
nucleus of He-4. Values of N and Z decrease by 2 each, A - by 4.
37
Why can alpha particles have two possible energies?
They have definite KE determined by conservation of momentum and energy, it depends on the energy level .
Alpha-particle travels through a potential energy barrier. Can go into excited state of the nucleus causing an emission of a
gamma-ray – g-decay (about 6% probability)or decay to ground state
38
What are the steps for showing alpha decay is energetically possible and calculating the kinetic energy?
LINE THEY REALSE 2 PARTICLES
- Check that the charge and the nucleon number are conserved.
- Calculate the mass difference
- Calculate the energy released
- Momentum conservation (negating relativistic corrections)
- Calculate the kinetic energies and velocities of the decay products
39
What is beta decay?
The decay which proceeds with the emission of an
| electron (β-decay) or a positron (β+ decay).
40
When does β- decay occur/when is it possible ?
N / Z ratio is too high for stability
Occurs when the mass of the original neutral atom is bigger than that
of the final atom (neglecting the mass of the neutrino)
*also neglect the binding energy of electron mass is not considered*
41
What happens in β- decay ?
The e charge of the nucleus Z increases by 1, the number of neutrons N decreases by 1, while the nucleon number A does not change.
(conservation law: lepton number should be conserved)
42
What are the steps for showing β- or β+decay is energetically possible and calculating the kinetic energy of emitted particle ?
CONTINUOUS THE RELEASE 2 PARTICLES
- Check that the charge and the nucleon number are conserved and lepton number conservation
- Calculate the mass difference (shows decay is energetically possible)
- Calculate the energy released
- Max kinetic energy is equal to energy released
- Velocity of electro calculated using mc^2(γ-1)=KE
43
When does β+ decay occur/is possible?
Nuclides with N / Z ratio too small for stability can emit a positron
Occurs when the mass of the original neutral atom is bigger than that
of the final atom plus the *double electron* mass (neglecting the mass of ne)
44
What happens in β+ decay ?
The e charge of the nucleus Z decreases by 1, the number of neutrons N increases by 1, while the nucleon number A does not change.
(conservation law: lepton number should be conserved)
45
What is electron capture?
Orbital electron can
combine with a proton in a nucleus to form a neutron with the emission of the
electron neutrino
46
When does electron capture occur?
Occurs when the mass of the original neutral atom is bigger
| than that of the final atom (neglecting the mass of the neutrino).
47
What happens in electron capture?
Z decreases by 1, N increases by 1, whereas A remains constant
48
What is gamma decay?
The de-excitation of the nucleus
49
What occurs in gamma decay?
Nothing, the nucleus does not change in gamma-decay
50
What is a series of successive decay?
When a radioactive nucleus decays, the resulting (daughter) nucleus may also be
unstable.
51
What is the most abundant radioactive nuclide?
The most frequent: U-238, U-235 (0.72% of natural uranium), Th-232. Also
K-40 (a single decay)
52
How do radio-isotopes occur?
Naturally occurring or cosmogenically produced
53
What is the decay chain of U-238?
```
238U ⎯α⎯→ 234Th
234Th β−⎯⎯→ 234Pa
234Pa* ⎯γ⎯→ 234Pa
In total 14 decays: 8 alpha-decays and
6 beta-decays.
```
54
What is the radioactive decay rate equation?
N(t) = N0e^−λt=N0e^−t/t0
55
What is a half life?
The time required for the number of radioactive nuclei
| to decrease to one-half of the original number N
56
What is the relationship between the half life, t0 and λ?
t1/ 2 = 0.693/λ = 0.693t0
57
What is activity, what is it related to the unit of activity?
The activity: -dN/dt
The activity is related to the number of atoms
-dN/dt=λN
1 Bq = 1 decay/s
1 Ci = 3.70´x 10^10 Bq.
1 Ci is approximately equal to the
activity of 1 g of radium.
58
What is radioactive dating?
The dating of archaeological and
| geological specimens by measuring the concentration of radioactive isotopes.
59
What is carbon dating?
Measurement of carbon-14.
| By measuring the proportion of 14C in the remains, we can determine how long ago the organism died.
60
What is the half life of carbon?
5730 years
61
What is radon?
- Radon-222 is a product of Ra-226 decay
(in the U-238 decay chain).
- Rn-222 has a half-life of 3.82 days and
emits an alpha-particle
62
Why is radon harmful?
It is radioactive.
It is a highly penetrating gas, can diffuse through the walls, floor and be
accumulated in the rooms.
63
What are the radiation hazards?
Alphas and betas - ionisation by interacting with electrons, breaking
molecular bonds, creating ions.
Gamma-rays and X-rays - photoelectric effect, also Compton scattering
and electron-positron pair production for high-energy gamma-rays.
Neutrons - collisions with nuclei and absorption with subsequent
radioactive decay of the resulting nuclei.
Cause the destruction of tissue cells, in severe cases destruction of the
components of bone marrow that produce red blood cells.
64
What is radiation dosimetry?
Quantitative description of the effect of radiation on living tissue.
65
What is absorbed dose?
What is the energy in Joules received by the sample?
```
The energy delivered to tissue per unit mass:
1 gray (Gy) = 1 J/kg, 1 rad = 0.01 Gy = 0.01 J/kg
```
Energy = Absorbed dose/mass in kg
66
```
What is relative
biological effectiveness (RBE) AKA quality factor (QF)?
```
Variation in biological effect
```
RBE = Equivalent dose (Sv) /
Absorbed dose (Gy)
```
Photons with E = 200 keV (hard X-rays or gamma rays) are defined to have RBE = 1 and effects of other types of particles are defined relative to this one.
67
What is the biologically equivalent dose?
The product of the absorbed dose and
the RBE of the radiation
```
Equivalent dose (sievert or Sv) = RBE
x Absorbed dose (Gy)
```
68
What are the other units for the biological effects?
1 rem = 0.01 Sv.
| RBE units: 1 Sv/Gy = 1 rem/rad
69
What are the radiation hazards?
A whole-body dose >5 Sv (short term) is fatal.
| A localised dose of 100 Sv causes complete destruction of exposed tissues
70
What are the safety limits for effective dose?
Limits on effective dose to the whole-body: 20 mSv/year.
Special cases: 100 mSv in 5 years with no more
than 50 mSv in any single year
71
What is the application of radiation?
```
Diagnostics:
– X-ray scanning;
– Positron emission tomography (PET);
– I-131 for thyroid studies.
– Tc-99 as a radioactive tracer.
Treatment:
– Tumour destruction.
Security:
– X-ray scanning
```
72
What are nuclear reactions subjected to?
Conservation laws:
Charge;
– Energy (including rest energy);
– Momentum;
– Angular momentum (not considered here);
– Number of nucleons or mass number (baryon number - Particle Physics);
– Lepton number
73
What is reaction energy?
Reaction energy is the difference between the rest energies of ‘particles’
(nuclei) in the initial and final states
74
What is the equation for reaction energy?
: Q = (MA+MB - MC - MD)c^2.
(uses the masses
of neutral atoms rather than nuclei, although reaction happens with nuclei)
75
What is an exoergic/exothermal reaction?
When the reaction energy is positive.
The total mass decreases and the total kinetic energy
increases
76
What is an endoergic/endothermal reaction?
When the reaction energy is negative.
| The mass increases and the kinetic energy decreases
77
When does endoergic/exothermal reactions not occur?
Cannot occur at all
| unless the initial kinetic energy in the center-of-mass reference frame is at least as great as |Q|
78
What is threshold energy?
The minimum kinetic energy to make an endoergic reaction go
79
How do you calculate the threshold energy in
| the centre of mass system?
Endothermal: Q is negative then threshold energy = 0
Exothermal: Q is positive then threshold energy = |Q|
80
How do you calculate the threshold energy in
| the laboratory system?
Exothermic:
| MQ/M+m
81
What is Nuclear Fission?
Decay process in which a nucleus splits into two fragments
| of comparable mass.
82
What are the two types of fission?
Induced fission
| Spontaneous fission
83
What is Induced fission?
caused by neutron absorption (capture)
84
What is Spontaneous fission?
Nuclei that split into two fragments
| without absorbing a neutron(spontaneously)
85
What is the mass
| distribution of fragments from U235 fission?
```
The masses of nuclear
fragments will be around 95 and
140, adding up to the mass of the
original nucleus plus initial
neutron minus several emitted
neutrons.
```
86
What is the consequences of fission fragments having too may neutrons?
- Emission of several neutrons during fission.
| - Subsequent b-decay of unstable nuclear fragments
87
What does the shell model predict in relation to fission?
The existence of quasi-stable nuclei
88
How can we understand fission using the liquid drop model?
A 235U nucleus
absorbs a neutron becoming a 236U* nucleus with excess energy. This excess energy causes violent oscillations, during which a neck
between two lobes develops. The electrical repulsion of these two
lobes stretches the neck farther and finally two smaller fragments
are formed that move rapidly apart.
89
Why some nuclei undergo fission and others don’t?
* hypothetical potential-energy function graph
If excitation energy is greater than UB,
fission occurs immediately.
90
How can we explain spontaneous fission through tunnelling?
through the potential energy
barrier. The probability depends on the width
and height
91
How are chain reaction proceeded?
Controlled chain reaction - nuclear power plant.
| – Uncontrolled reaction - explosion, A-bomb, nuclear weapon.
92
What is a nuclear reactor
A system in which a controlled nuclear chain reaction is used
to liberate energy
93
How is energy generated in a nuclear reactor?
The fission energy appears as kinetic energy of
the fission fragments, and its immediate result is to increase the internal energy
of the fuel elements and the surrounding moderator. This increase in internal
energy is transferred as heat to generate steam to drive turbines, which spin the
electrical generators.
94
What does the moderator do?
Cause higher-energy neutrons to slow down by collisions with
nuclei in the surrounding material (water or graphite)
95
What do control rods do?
The rate of the reaction is controlled by inserting or
withdrawing control rods made of elements (such as boron or cadmium) whose
nuclei absorb neutrons without undergoing any additional reaction
96
How do you enhance the efficiency of a chain reaction?
Natural
uranium (0.7% of U-235) is
enriched up to 3-5% of U-235.
97
What is nuclear fusion?
When two or more light nuclei collide to form a
| heavier nucleus
98
How does fusion produce energy?
The binding energy of initial nuclei is
smaller than the binding energy of the final nucleus or, the sum of masses of
the initial nuclei is bigger than the mass of the final nucleus. The difference is
released as an energy
99
What is thermonuclear fusion?
Another type of nuclear reactions which releases huge
| energy: fusion of light nuclei into a heavier one.
100
What do fusion reactors require?
- Need to contain nuclei within a small volume and at high temperatures.
- Magnetic confinement of plasma is one of the solutions.
- radioactive.
- Choice of materials for walls without long-lived isotopes produced via neutron absorption.
Special Relativity and Subatomic Physics
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