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 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 v = E/B 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

Fusion Fission

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 235 U by a slow (low energy) neutron 0 1 n  235 92 U  236 92 U *  X  Y  neutrons   236 U* 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 235 U nucleus captures a

thermal

(slow-moving) neutron This capture results in the formation of 236 U*, and the excess energy of this nucleus causes it to undergo violent oscillations The 236 U* 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 × 10 9 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 × 10 3 ton)(4.0 × 10 9 J/ton) = 1.2 × 10 14 J. The mass equivalent of this quantity of energy is:

m



E c

2  1 .

2  10 14 J ( 3 .

0  10 8 m/s) 2  1 .

3  10  3 kg ~ 1g Note: 1 gram TNT = 4184 J (exactly)

Chain Reaction

   Neutrons are emitted when 235 U 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

11 Mt H-bomb

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 235 U 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

Cadmium Fuel elements consist of enriched uranium (a few % 235 U rest 238 U) The

moderator material

slow down the neutrons helps to 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 D 2 O, graphite SCRAM = S afety C ontrol R od A xe M an

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: 1 1 1 H + H 1  2 H + e 1 +  ν e 2% of sun’s 1 1 2 H + H 1  3 He + γ 2 energyis carried by neutrinos Followed by H – He or He – He fusion: 1 1 3 H + He 2  4 He + e 2 +  ν e  or 2 3 3 He + He 2  4 2 1 1 He + H + H 1 1  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 ~6x10 9 J  Fusion reactor would most likely use deuterium and tritium 2 1 2 H + H 1  3 2 1 He + n, 0

Q

 3.27 MeV 2 1 2 1 2 H + H 1 3 H + H 1   3 H + H, 1 1 1

Q

4 2 1 He + n, 0

Q

  4.03 MeV 17.59 MeV

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 (~10 8 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

  14 10 s/cm 3

n

  16 10 s/cm 3 Deuterium- tritium reactor Deuterium- deuterium reactor

So need 10 8 K for 1 second

Fusion Reactors - 1

 Inertial confinement  Inject fuel pellets and hit them with a of lasers) or ion beams to heat them

laser

(

lots

 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 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

The beams are generated in the laser bay

and deliverd to the target bay.

The

N

ational

I

gnition

F

acility

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 International Thermonuclear Experimental Reactor To be constructed in Cadarache in the South of France.

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/r 2 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 W + , W and Z 0 bosons m Gravitational Force  10 -43 times as strong as the strong force   Also 1/r 2 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 Netral  meson:   ,   , mass 139.6 MeV/c 2  meson ,  0 ,mass 135.0 MeV/c 2 Lifetimes 2.6x10

-8 s for   ,   8.3x10-17 s for  0

More Mesons

   Also have heavier mesons Kaons ~500 MeV/c 2 Eta’s 548 and 958 MeV/c 2 (note, mass of  is greater than proton mass)