Chapter 30: Nuclear Energy and Elementary Particles

Nuclear FissionHomework : Read and understand the lecture note.

What is nuclear fission?• Nuclear fission occurs when a heavy nucleus, such as , splits, or fissions, into two smaller nuclei.

• The fission of by slow (low-energy) neutron can be represented symbolically by : : an intermediate excited and short-lived state X, Y : fission fragments that satisfy conservation of energy and charge

• A typical reaction of this type is :

U23592

neutrons*23692

23592

10 YXUUn

*23592 U

U23592

nKrBaUUn 10

9236

14156

*23692

23592

10 3

Nuclear fission (in some detail)

Nuclear Fission

• Sequence of events in the nuclear fission neutrons*23692

23592

10 YXUUn

- The nucleus captures a thermal (slow-moving) neutron.- An excited state is formed and the excess energy cause oscillation of the nucleus.- The nucleus highly elongated, and the repulsive force among protons enhances the deformation.- The nucleus splits into to fragments, emitting several neutrons.

*23592 U

*23592 U

U23592

Nuclear fission (cont’d)

Nuclear Fission

• Energy released in the nuclear fission neutrons*23692

23592

10 YXUUn

- The binding energy per nucleon for heavy nuclei (mass~240) :~7.2 MeV- The binding energy per nucleon of intermediate mass :~8.2 MeV- Nuclei of intermediate mass are more tightly bound than heavy nuclei.- For a total of 240 nucleons, the energy released (Q-value) in a fission: Q=240 nucleons/(8.2 MeV/nucleon – 7.2 MeV/nucleon) = 240 MeV

Nuclear Fission Example 30.1 : Fission of uranium

• How many neutrons are produced in the fission process ?)x(1

09438

14054

23592

10 nSrXeUn

2941402351 xx

Example 30.2 : A fission-powered world• Calculate the total energy released if 1.00 kg of undergoes fission, taking the disintegration energy per event to be Q = 208 MeV?

U235

nuclei 102.56g) 1000.1(g/mol 235

nuclei/mol 1002.6 24323

NNumber of nuclei in

1.0 kg of uranium

MeV 105.32s)MeV/nucleu 208nuclei)( 1056.2( 2624 NQETotal energy released

• How many kilograms would provide for world’s annual energy needs (4x1020 J)?

Total energy released from Nkg kg of uranium

J 104 20 totkgkg ENE

kg 105J/eV) 100eV/kg)(1.6 1032.5(

J 104 619-32

20

kg

totkg E

EN

Nuclear Reactors Nuclear chain reaction

• Neutrons emitted when undergoes fission can in turn trigger other nuclei to undergoes with the possibility of a chain reaction.• Calculations show that without control the chain reaction goes out of control and results in the sudden release of enormous amount of energy (1 kg of would produce energy equivalent to 20 ktons of TNT).

U235

U235

Nuclear Reactors Nuclear reactors

• A nuclear reactor is designed to control nuclear reactions and maintain a self-sustained chain reaction.

D2O

cadmium

- Moderator slows down neutrons so that they can be absorbed by uranium more easily.- Control rods absorb very efficiently neutrons to control the reaction rate.- The reproduction constant K, defined as the average number of neutrons from each fission event that will cause another event. A self-sustained chain reaction is achieved when K=1.

Nuclear Fusion Nuclear fusion

• The binding energy of light nuclei (mass number <20) is much smaller than that of heavier nuclei.• When two light nuclei combine to form a heavier nucleus, the process is called nuclear fusion.• Because the mass of the final nucleus is less than the masses of the original nuclei, there is extra energy released.

Nuclear fusion in Sun (thermal nuclear fusion reactions)

eeDHH 21

11

11

HeDH 32

21

11

)(2or 11

42

32

32

42

32

11 HHeHeHeeHeHeH e

• proton-proton chain: to sustain the nuclear fusion - the temperature needs to be high enough to overcome the repulsive Coulomb force between protons - the density of nuclei must be high enough to ensure a high rate of collisions

The liberated energy is carried bygamma rays, positrons and neutrinos.

Nuclear Fusion Fusion reactors

• Scientists and engineers have been trying to create similar conditions to those in the interior of Sun to achieve self-sustained nuclear fusion reactions on Earth.

• Most promising reactions as fusion reactors are:

MeV) 27.3( 10

32

21

21 QnHeDD

MeV) 03.4( 11

31

21

21 QHTDD

MeV) 59.17( 10

42

31

21 QnHeTD

• Deuterium is abundant on Earth but tritium is radio active with T1/2= 12.3 yr and undergoes beta decay to 3He. So tritium is rare on Earth.

• One of the major problems to achieve fusion reactors is to give to the nuclei enough kinetic energy to overcome the repulsive Coulomb force.

Particle Physics

Model of Atoms

electrons e-

nucleus

Old view

Semi-modern view

Modern view

nucleusquarks

prot

on

What is the world made of?

Pion + : ud

Particle PhysicsBuilding Blocks of Matter

Discoveries of too many “elementary” particles and anti-particles lead to more fundamental model the Standard Model. Anti-particlehas the same property as particle except that charge is opposite to that of particle.

Proton p : uudNeutron n : udd

-

Particles made of quarks are calledhadrons and among them theyinteract through strong force.

What is matter made of?

Hadrons

Leptonsneutrinos : feel only weak forcecharged lepton : feel electromagnetic e-,-, and weak force

2MeV/c 3.938pm2MeV/c 6.939nm

2MeV/c 6.139m

2MeV/c 511.0em2MeV/c 7.105m

2MeV/c 1777m

+(2/3)e

-(1/3)e

+e

0

ele

ctri

c ch

arg

e

but tiny 0m

Particle Physics

Fundamental Forces

There are four know fundamental forces:

An example:Free neutron decay

How many kinds of forces are there?

Particle Physics

Fundamental Forces

Examples of weak interaction

Free neutron decay: n -> p + e-e

-

Muon decay: -> e-e + -

Particle Physics

Unification of Forces

Grand Unified Theories (GUTs)

Strong

Electric

Magnetic

Electromagnetic

Weak

Electroweak

Gravitational

GU

Ts

hard

19th c.

20th c.

21st c.?

GUTs predict:

Nucleon decays (not yet found)

Neutrino mass/oscillation (found)

What is our dream?

.,,0 etcKvep

Particle Physics

Neutrino Oscillation

There are three kinds of neutrinos: e

If neutrinos have mass, they can change their identities (flavours)

e

A simple example:

=

2

cos

+ cos

- sin

sin =

1

1

2

neutrinos with definite mass

Probability

1-Probability

Pro

babi

lity

Neutrino pathlength (km)

It depends onneutrino energy,masses, anddistance it travels

What is neutrino oscillation?

(flavours)

~Earth’s diameter 12,000 km

Atmospheric Neutrinos

Source of atmospheric neutrinos

Earth’s atmosphere is constantlybombarded by cosmic rays.

Energetic cosmic rays (mostlyprotons) interact with atoms inthe air.

These interactions produce manyparticles-air showers.

Neutrinos are produced in decaysof pions and muons.

Physicists are having fun on a boat in Super-Kamiokande

50,000 tons of pure water equipped with 12,000 50 cm photomultipliersand 2,800 20 cm photomultipliers (PMTs).

Atmospheric Neutrinos

Water Cherenkov Detector: Kamiokande,IMB,Super-Kamiokande,SNO

Water is cheap and easy to handle!

When the speed of a chargedparticle exceeds that of lightIN WATER, electric shockwaves in form of light are generated similar to sonic boomsound by super-sonic jet plane .

These light waves form a coneand are detected as a ring bya plane equipped by photo-sensors.

How does a water Cherenkov detector work?

Atmospheric Neutrinos

How do we detect atmospheric muon and electron neutrinos ?

electron-like ring

muon-like ring

+ n -> p +

e

+ n -> p +

e-

Major interactions:

Most of time invisible

Atmospheric Neutrinos

How do we see neutrino oscillation in atmospheric neutrinos?

Pro

babi

lity

(

N

eutr

ino

path

leng

th

cos (zenith angle)

downward-goingupward-going

Actual probability for measured zenith angledue to measurement errors

a

b

cos = a/b

Atmospheric NeutrinosEvidence of neutrino oscillation/mass

low energye

high energye

low energy

high energy

with oscillation

without oscillation

First crack in the Standard Model!!!

Solar Neutrinos How does the Sun shine?

Nuclear fusions generate: - energy/heat/light - neutrinos

1 MeV = 1x106 eV

Kamiokande

Solar Neutrinos How does the neutral current confirm neutrino oscillation?

Elastic scattering

-This reaction is available only for e .

-Available for both water and heavy water.

+ e- -> + e-

Solar Neutrinos

Solar neutrinos

background

Seeing the Sun underground

Image of Sun by Super-Kamiokande

How do we see the Sun underground?

e

e

Solar Neutrinos How do we see neutrino oscillation with solar neutrinos?

Super-Kamiokande : 0.465+-0.005+0.016-0.015

Flux: measured/expected

Neutrino deficit!!!

is not visible to allexperiments above

Supernova

Background level

Birth of a supernova witnessed with neutrinos

How do we know detected neutrinos are from a supernova?

Kamiokande

Num

ber

of p

hoto

mul

tipl

iers

fir

edA few hours before optical observation

Taken by Hubble Telescope ( 1990)