General Physics (PHY 2140)
Lecture 20
 Modern Physics
Nuclear Energy and Elementary Particles
Fission, Fusion and Reactors
Elementary Particles
Fundamental Forces
Classification of Particles
Conservation Laws
Chapter
Chapter 2930
http://www.physics.wayne.edu/~alan/2140Website/Main.htm
General Physics (PHY 2140)
Lecture 21
 Modern Physics
Elementary Particles
Strange Particles – Strangeness
The Eightfold Way
Quarks
Colored Quarks
Electroweak Theory – The Standard Model
The Big Bang and Cosmology
Chapter
Chapter 2930
http://www.physics.wayne.edu/~alan/2140Website/Main.htm
Previously…
 Nuclear Physics
 Nuclear Reactions
 Medical Applications
 Radiation Detectors
Review Problem: A beam of particles passes undeflected through
crossed electric and magnetic fields. When the electric field is switched
off, the beam splits up in several beams. This splitting is due to the
particles in the beam having different
A. masses.
B. velocities.
C. charges.
D. some combination of the above
E. none of the above
r=mv/qB
Processes of Nuclear Energy
 Fission
 A nucleus of large mass number splits into
two smaller nuclei
 Fusion
 Two light nuclei fuse to form a heavier
nucleus
 Large amounts of energy are released in
either case
Processes of Nuclear Energy
 Fission
 A nucleus of large
mass number splits
into two smaller nuclei
 Fusion
 Two light nuclei fuse to
form a heavier nucleus
 Large amounts of
energy are released in
either case
Nuclear Fission
 A heavy nucleus splits into two smaller nuclei
 The total mass of the products is less than the
original mass of the heavy nucleus
 First observed in 1939 by Otto Hahn and Fritz
Strassman following basic studies by Fermi
 Lisa Meitner and Otto Frisch soon explained what
had happened
 Fission of 235U by a slow (low energy) neutron
236
n 235
U

92
92 U*  X  Y  neutrons
1
0
 236U* is an intermediate, short-lived state
 X and Y are called fission fragments
 Many combinations of X and Y satisfy the requirements of
conservation of energy and charge
Sequence of Events in Fission
 The 235U nucleus captures a thermal (slow-moving) neutron
 This capture results in the formation of 236U*, and the excess energy of this
nucleus causes it to undergo violent oscillations
 The 236U* nucleus becomes highly elongated, and the force of repulsion
between the protons tends to increase the distortion
 The nucleus splits into two fragments, emitting several neutrons in the
process
Energy in a Fission Process
 Binding energy for heavy nuclei is about 7.2 MeV per nucleon
 Binding energy for intermediate nuclei is about 8.2 MeV per nucleon
 Therefore, the fission fragments have less mass than the nucleons
in the original nuclei
 This decrease in mass per nucleon appears as released energy in
the fission event
 An estimate of the energy released
 Assume a total of 240 nucleons
 Releases about 1 MeV per nucleon
 8.2 MeV – 7.2 MeV
 Total energy released is about 240 MeV
 This is very large compared to the amount of energy released in
chemical processes
QUICK QUIZ
In the first atomic bomb, the energy released was equivalent to
about 30 kilotons of TNT, where a ton of TNT releases an energy
of 4.0 × 109 J. The amount of mass converted into energy in this
event is nearest to: (a) 1 g, (b) 1 mg, (c) 1 g, (d) 1 kg, (e)
20 kilotons
(c). The total energy released was E = (30 ×103
ton)(4.0 × 109 J/ton) = 1.2 × 1014 J. The mass
equivalent of this quantity of energy is:
E
1.2  1014 J
3
m 2 
 1.3  10 kg ~ 1g
8
2
c
(3.0  10 m/s)
Chain Reaction
 Neutrons are emitted when 235U undergoes fission
 These neutrons are then available to trigger fission in other nuclei
 This process is called a chain reaction
 If uncontrolled, a violent explosion can occur
 The principle behind the nuclear bomb, where 1 g of U can release
energy equal to about 30000 tons of TNT
Nuclear Reactor
 A nuclear reactor is a system designed to
maintain a self-sustained chain reaction
 The reproduction constant, K, is defined as the
average number of neutrons from each fission
event that will cause another fission event
 The maximum value of K from uranium fission is 2.5
 Two 235U reactions, one yields 3 the other 2 neutrons
 In practice, K is less than this
 A self-sustained reaction has K = 1
Basic Reactor Design
 Fuel elements consist of enriched
Cadmium
uranium (a few % 235U rest 238U)
 The moderator material helps to
slow down the neutrons
 The control rods absorb neutrons
 When K = 1, the reactor is said to
be critical
 The chain reaction is selfsustaining
 When K < 1, the reactor is said to
be subcritical
 The reaction dies out
 When K > 1, the reactor is said to
be supercritical
 A run-away chain reaction occurs
D2O, graphite
Schematic of a Fission Reactor
Nuclear Fusion
 When two light nuclei combine to form a heavier nucleus
 Is exothermic for nuclei having a mass less than ~20
 (Iron is the limit, Z=26, A=56)
 The sun is a large fusion reactor
 The sun balances gravity with fusion energy
Sun’s Proton Cycle
 First steps:
H + 11 H 
2
1
H + e+  ν e
H + 21 H 
3
2
He + γ
1
1
1
1
2% of sun’s
energyis carried
by neutrinos
 Followed by H – He or He – He fusion:
 or
1
1
3
2
H + 23 He 
He + 23 He 
4
2
He + e+  ν e
4
2
He + 11 H + 11 H
 Total energy released is 25 MeV
Net Result
 4 protons (hydrogen nuclei) combine to give
•
•
•
•
An alpha particle (a helium nucleus)
Two positrons
One or two neutrinos (they easily escape)
Some gamma ray photons (absorbed)
 The two positrons combine with electrons to
form more gamma photons
 The photons are usually absorbed and so
they heat the sun (blackbody spectrum)
Fusion Reactors
 Enormous energy in a small amount of fuel
 0.06g of deuterium could be extracted from 1 gal of water
 This represents the equivalent energy of ~6x109 J
 Fusion reactor would most likely use deuterium and tritium
2
1
H + 21 H 
3
2
He + 01 n, Q  3.27 MeV
H + 21 H  31 H + 11 H, Q  4.03 MeV
2
3
4
1
H
+
H

He
+
1
1
2
0 n, Q  17.59 MeV
2
1
Advantages of fusion power
 Fuel costs are relatively small
 Few radioactive by-products of fusion reaction
 (mostly helium-3 and helium-4)
Disadvantages of fusion power
 Hard to force two charged nuclei together
 Reactor is complex and expensive
 Need high temperatures and pressures to
achieve fusion (~108 K)
need a plasma
Plasma confinement
 Plasma ion density, n
 Plasma confinement time, 
 In order to achieve a fusion reaction need
to satisfy Lawson’s criterion:
n  10 s/cm
14
3
n  1016 s/cm3
Deuterium- tritium reactor
Deuterium- deuterium reactor
So need 108 K for 1 second
Fusion Reactors - 1
 Inertial confinement
 Inject fuel pellets and hit them with a laser (lots
of lasers) or ion beams to heat them
 Imploding pellet compresses fuel to fusion
densities
 Doesn’t require plasma confinement via
magnetic fields
 Requires large facility to house lasers and
target chamber.
National Ignition Facility
 the facility is very large, the size of a
sports stadium
 the target is very small, the size of a BBgun pellet
 the laser system is very powerful, equal to
1,000 times the electric generating power
of the United States
 each laser pulse is very short, a few
billionths of a second
The beams are generated in the laser bay
and deliverd to the target bay.
The National Ignition Facility
The target chamber
Fusion Reactors - 2
 Magnetic field
confinement
 Tokamak
design – a
toroidal
magnetic field
 First
proposed by
Russian
scientists
Fusion Reactors – cont.
 Tokamak Fusion Test Reactor – ITER
ITER’s proposed site layout
30.4 Elementary Particles
 First we studied atoms
 Next, atoms had electrons and a nucleus
 The nucleus is composed of neutrons and
protons
 What’s next?
Elementary particle interactions
The scattering of two electrons via a coulomb force
This virtual photon is said to mediate the electromagnetic
force. The virtual photon can never be detected because it
only lasts for a vanishing small time.
An simple example of a Feynman diagram
Interactions continued
 Can have similar diagrams with other
particles and other forces
 Strong force, weak force, gravity
 Basic idea of exchange of a virtual particle
is the common theme.
More examples of Feynman diagrams
30.5 The Fundamental Forces in Nature
 Strong Force
 Short range ~ 10-15 m (1 fermi)
 Responsible for binding of quarks into neutrons and protons
 Gluon
 Electromagnetic Force




10-2 as strong as strong force
1/r2 force law
Binding of atoms and molecules
Photon
 Weak force
 ~ 10-6 times as strong as the strong force
 Responsible for beta decay, very short range ~10-18 m
 W+, W- and Z0 bosons
 Gravitational Force
 10-43 times as strong as the strong force
 Also 1/r2 force law
 Graviton
30.6 Positrons and Antiparticles
 Dirac proposed the positron to solve a
negative energy problem (Dirac sea)
 The general implication is that for every
particle there is an antiparticle (symmetry)
 Other antiparticles:
 antiproton, antineutrino
 Usually denoted with a bar over symbol
 Some particles are their own antiparticles
 photon, neutral pion: , 0
30.7 Mesons
 Part of an early theory to describe nuclear
interactions
 Mass between a electron and a proton
 Flavors
 Charged  meson: ,  ,mass 139.6 MeV/c2
 Netral  meson, 0 ,mass 135.0 MeV/c2
 Lifetimes 2.6x10-8 s for , 
8.3x10-17 s for 0
More Mesons
 Also have heavier mesons
 Kaons ~500 MeV/c2
 Etas 548 and 958 MeV/c2 (note, mass of
 is greater than proton mass)
30.8 Particle Classification
(Classify the animals in the particle zoo)
Hadrons (strong force interaction, composed of quarks)
 We already met the mesons (middle weights)
 Decay into electrons, neutrinos and photons
 Baryons, i.e. the proton and neutron (the
heavy particles)
 Still other more exotic baryons:
 L, S, X,  all are heavier than the proton
 Decay into end products that include a proton
Particle Classification – cont.
 Leptons
 Small or light weight particles
 Are point like particles – no internal structure
(yet)
 6 leptons (and their antiparticles
6 more)
 Electron e, muon , tau 
 and their associated neutrinos: ne, n, n
 Neutrinos have tiny mass, ~3 eV/c2
Some members of the Zoo
Particle Physics Conservation Laws
So far in Physics we have conservation of energy,
momentum (linear and angular), charge, spin.
Now we add more to help balance particle
reactions
 Baryon number:
 B = +1 for baryons, -1 for anti-baryons
 Eg. Proton, neutron have B = +1
 p, n , antiparticles have B = -1
 B = 0 for all other particles (non-baryons)
More Conservation Laws
 Lepton number
 L = +1 for leptons, -1 for anti-leptons
 L = 0 for non-leptons
 Example for electrons:
 Electron e, electron neutrino ne have Le = +1
 Anti electron and antineutrino have Le = -1
 Other leptons have Le = 0 BUT have their own lepton
numbers, L, L
 Refer to table 30.2
Example neutron decay
 Consider the decay of the neutron
n  p + e + νe
+
-
 Before: B = +1, Le = 0
 After: B = +1, Le = +1 -1 = 0
Quiz 30.2
 Which of the following cannot occur?
 (a)
p+p  p+p+p
 (b)
n  p + e + ne
 (c)
μ  e + n e + νμ
 (d)
π  μ +νμ
-
-
-
-
Quiz 30.2 - answer
 The disallowed reaction is (a) because
 Charge is not conserved:
 Q = +2  Q = +1
 Baryon number is also not conserved:
 B = +2  B = +2-1 = +1
p+p  p+p+p
Strangeness
 Several particles found to have unusual
(strange) properties:
 Always produced in pairs
- + p+  K0 + L0 but not - + p+  K0 + n
 Decay is slow (indicative of weak interaction
rather than strong) Half-lives of order of 10-10
to 10-8 sec
 Members of the strange club: K, L, S
More Strangeness
 Explanation lies in the addition of a new
conservation law – Strangeness, S
 One of the pair of strange particles gets
S=+1 the other S=-1. All other particles
get S=0. So in the previous reaction,
strangeness is conserved:
 Before S=0; After S=+1-1 = 0
 Second reaction violates strangeness
Example 30.6: Strangeness Conservation
Consider:
- + n  K+ + S-
 Before: S=0+0=0 (no strange particles)
 After: K+ has S=+1, S- has S = -1 thus the
net strangeness S = +1-1 = 0
 So reaction does not violate law of
conservation of strangeness, the reaction
is allowed
The Eightfold Way
Consulting table 30.2, Take the first 8
baryons and plot Strangeness vs. Charge.
We get an interesting picture. A hexagonal
pattern emerges.
If we do the same for the spin 0 mesons we
also get a hexagonal pattern.
The Eightfold Way
The Original Quark Model (in B/W)
 Gell-Mann (1961) proposed hadrons have




structure, i.e. composed of a more
fundamental type of particle.
Quarks have fractional charge e/3 or 2e/3
Three types u, d, s: up, down, strange
Mesons were made of 2 quarks: q, q¯
Baryons were made of 3 quarks
But that wasn’ enough!
 Soon after, experimental discrepancies
required the addition of three more quarks
 Top, bottom and charm: t, b, c
 And three more conservation laws: C, B, T for
charm, bottomness and topness
Properties of Quarks and Antiquarks
Fundamental Particles: Properties
Quarks
Particle
Rest Energy
Charge (e)
u
360 MeV
+2/3
d
360 MeV
-1/3
c
1500 MeV
+2/3
s
540 MeV
-1/3
t
173 MeV
+2/3
b
5 GeV
-1/3
Fundamental Particles Properties
continued
Leptons
Particle
Rest Energy
Charge
e-
511 keV
-e
-
107 MeV
-e
-
1784 MeV
-e
ne
< 30 eV
0
n
< 0.5 MeV
0
n
< 250 MeV
0
Quarks in Mesons and Baryons
We should still
be in B/W!
Color
 Because of the Pauli exclusion principle
(all quarks are spin ½ particles) can’t have
three of the same particles occupying the
same state.
 Example: - is (sss) so need three
different yet strange quarks
 So colored quarks were proposed
Color continued
 Three color charges were added
 Red, green blue: r, g, b
 And…three anti-colors
¯ g,
¯ b¯
 antired, antigreen and antiblue: r,
 Mesons have a color anticolor pair
 Spin is either zero or 1 so can have ↑↑ or ↑↓
 Baryons must have three different colors
 Spin is ½ so have ↑↑↓ or ↓↓↑
Quarks combinations with color
Total spin is 0 or 1
Total spin is ½ or 3/2
Quantum Chromodynamics
 In analogy with photons and the electromagnetic





force, an interaction between colored quarks is
the result of color force – 8 colored gluons.
The general theory is complex but explains
experimental results better.
Numerical results can be very hard to calculate
Opposite colors attract, red-antired, in analogy
with electromagnetism.
Different colors also attract though less strongly
Residual color force is responsible for nuclear
force that bind protrons and neutrons.
Interactions in the Yukawa pion and
quark-gluon models
Yukawa’s pion model
Quark QCD model
In both cases a proton-neutron
pair scatter off each other and
exchange places.
The Standard Model
History of the Universe
and of the four forces
Energy: 1028
Time:
0
1024
10-40
10-35
1021
1017
1013
1011
10-11
eV
sec
Time
Big Bang Model
A broadly accepted theory for the origin and
evolution of our universe.
It postulates that 12 to 14 billion years ago, the
portion of the universe we can see today was only
a few millimeters across. It has since expanded
from this hot dense state into the vast and much
cooler cosmos we currently inhabit.
In the beginning, there was a Big Bang, a
colossal explosion from which everything in
the Universe sprung out.
Experimental Evidence of the Big Bang

Expansion of the universe


Abundance of the light elements H, He, Li


Edwin Hubble's 1929 observation that galaxies were generally
receding from us provided the first clue that the Big Bang theory
might be right.
The Big Bang theory predicts that these light elements should have
been fused from protons and neutrons in the first few minutes after
the Big Bang.
The cosmic microwave background (CMB) radiation

The early universe should have been very hot. The cosmic
microwave background radiation is the remnant heat leftover from
the Big Bang.
Cosmic Microwave Background
99.97% of the radiant energy of the
Universe was released within the first
year after the Big Bang itself and now
permeate space in the form of a
thermal 3 K radiation field.
COBE CMB Measurement
• CMB spectrum is that of a nearly perfect blackbody with a temperature
of 2.725 +/- 0.002 K.
• Observation matches predictions of the hot Big Bang theory
extraordinarily well.
• Deviation from perfect black body spectrum less than 0.03 %
• Nearly all of the radiant energy of the Universe was released within the
first year after the Big Bang.
How did we get from there…
… to here?
Let there be light:
400,000-700,000 years