1. 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 30
Chapter 30

2. 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
v = E/B
r=mv/qB

3. 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

4. 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
Fission
Fusion

5. 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
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

6. 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

7. 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

8. 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:
Note: 1 gram TNT = 4184 J (exactly)

9. 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 tons of TNT

10. 11 Mt H-bomb

11. 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

12. Basic Reactor Design Cadmium D2O, graphite
Fuel elements consist of enriched 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 self-sustaining
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
SCRAM = Safety Control Rod Axe Man

13. Schematic of a Fission Reactor

14. 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

15. Sun’s Proton Cycle First steps: Followed by H – He or He – He fusion:
Total energy released is 25 MeV
2% of sun’s energyis carried by neutrinos

16. 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)

17. 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

18. 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

19. Plasma confinement Plasma ion density, n Plasma confinement time, 
In order to achieve a fusion reaction need to satisfy Lawson’s criterion:
Deuterium- tritium reactor
Deuterium- deuterium reactor
So need 108 K for 1 second

20. 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.

21. National Ignition Facility
the facility is very large, the size of a sports stadium
the target is very small, the size of a BB-gun 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

22. The beams are generated in the laser bay

23. and deliverd to the target bay.

24. The National Ignition Facility

25. The target chamber

26. Fusion Reactors - 2 Magnetic field confinement
Tokamak design – a toroidal magnetic field
First proposed by Russian scientists

27. Fusion Reactors – cont. Tokamak Fusion Test Reactor – ITER
International Thermonuclear Experimental Reactor
To be constructed in Cadarache in the South of France.

28. ITER’s proposed site layout

29. 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?

30. 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

31. 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.

32. More examples of Feynman diagrams

33. 30.5 The Fundamental Forces in Nature
Strong Force
Short range ~ 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

34. 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

35. 30.7 Mesons Part of an early theory to describe nuclear interactions
Mass between a electron and a proton
Flavors
Charged p meson: p+, p- ,mass MeV/c2
Netral p meson, p0 ,mass MeV/c2
Lifetimes 2.6x10-8 s for p+, p-
8.3x10-17 s for p0

36. More Mesons Also have heavier mesons Kaons ~500 MeV/c2
Eta’s 548 and 958 MeV/c2 (note, mass of  is greater than proton mass)