Particles and antiparticlesBell Work

ObjectivesTo understand what happens when a

particle and antiparticle meet

To be able to calculate photon energies produced from annihilation and energies required for pair production

Particles and E=mc2

Einstein discovered that energy and mass are interchangeable at a particular level, hence his famous E=mc2 formula where E =energy m = mass and c = the speed of light.

When a particle and an antiparticle meet we know that annihilation occurs and two gamma photons are produced.

Using Einsteins ideas, this must mean that a gamma ray must be able to produce a particle and an antiparticle?IMPORTANT – When we talk about the energies of particles we talk about in terms of MeV (mega electron volts) not joules. The

conversion factor is 1.6 x 1013 J to every MeV

The electronvoltA joule (J) is a large unit of energy when dealing with tiny atoms. Scientists often use an alternative unit for small amounts of energy, called an electronvolt (eV).

How many electronvolts to one joule?

1 eV = 1.6 × 10-19 J

1 J = 1/(1.6 × 10-19) eV = 6.25 × 1018 eV

Use these two conversion rates to change between the two. Be careful to use joules in calculations with other SI units.

An electronvolt is equal to the amount of energy transferred to a single electron if it is accelerated through a potential difference of 1 V:

Energy of photons in light

Wave and photon calculations

Lets try some examples

Mass and EnergyIn the fission of a nucleus of Uranium-235 the nucleus splits into two lighter nuclei releasing energy. The mass at the end of the reaction is less than the mass at the beginning and the missing mass has been converted into energy.

Incoming

neutron

U-235 nucleus

Kr-90 nucleus

Ba-144 nucleus

Mass and Energy A high energy photon like a g-ray can vanish to form a

pair particle – anti-particle. This is the opposite of annihilation and we call it PAIR PRODUCTION.

e-e+

In what way is this reaction similar to the fission of Uranium-235 and in what way is it different?

We will visit this again later

Mini Review

Mass and Energy

• In both reactions energy and mass are involved.

• In the fission reaction mass is converted into energy.

• In the pair production energy is converted into mass.

So, mass and energy are an equivalent form of each other.

N.B. They are not the same but they can be turned into each other in certain reactions.

Mark your answers

Rest Mass

Every particle has a rest mass. This is the value of the mass when the particle is stationary.

Does this mean that moving particles have a different mass?

Yes, because they have kinetic energy, which is an equivalent form of mass.

Rest Energy

What is rest energy then?

It is the energy equivalent of the mass of the particle when it is stationary.

And in the case of the pair production the photon has to have an energy at least equal to the sum of the rest energy of the electron and the positron for the reaction to happen.

Particle rest energyEach particle has energy locked up in its mass. This energy can be calculated using Einstein’s relation E = mc2. The masses of sub-atomic particles are commonly quoted in energy terms using the unit MeV.

Particle Rest energy in MeV

Proton 938

Neutron 938

Electron 0.511

NOTE: For each of the above particle the is a corresponding anti particle, the mass of each antiparticle is the same (it is the the charge that differs)

Therefore the corresponding rest energy is also the same!

Annihilation

When an anti-particle is created it can be observed, but only for a very short time. This is because:

It will soon collide against its particleThe two destroy each otherTheir mass is converted in energy

This process is called ANNIHILATION.

Annihilation

When a particle and its corresponding antiparticle meet together annihilation occurs. Each particle has energy locked up in its mass E = mc2

All of their mass and kinetic energy is converted into two photons of equal frequency that move off in opposite directions.

Annihilation

Look at the annihilation of an electron and its anti-particle (positron)

e- e+

Annihilation

Why are two photons of energy produced and not just one? (Hint: any collision must obey all conservation laws)

g0001

01 2

ee• One photon only could conserve charge and mass/energy

• But to conserve momentum two photons moving in opposite directions must exist

Calculating energies AnnihilationAs energy must be conserved in this process,

the energy of the photon and the energies of the two particles produced can be equated. The minimum energy of a photon can be calculated using the below formula.

Eo = hfmin

where h = Plancks Constant (6.62607004 × 10-34 m2 kg / s)

and f = frequency and Eo= rest energy

Pair Production A high energy photon like a g-ray can vanish to form a pair particle –

anti-particle. This is the opposite of annihilation and we call it PAIR PRODUCTION.

e-e+

Pair production

The energy of one photon can be used to create a particle and its corresponding antiparticle.The photon ceases to exist afterwards

Pair ProductionIn what way would a third particle, e.g. nucleus or electron, get involved

in this reaction? (Hint: again all conservation laws must apply)

ee 0

101

00g

• The third particle recoils and carries away some of the energy of the photon

• The recoil ensures that the momentum is also conserved

Calculating energies pair productionIn pair production a photon produces a

particle and antiparticle. Therefore the two energies can be equated as below

hfmin = 2Eo

where h = Plancks Constant (6.62607004 × 10-34 m2 kg / s) and f = frequency and Eo= rest energy

Annihilation & Pair production

Annihilation and pair production

Both the cloud chamber and the bubble chamber are used to detect the path of charged particles

A bubble chamber is filled with superheated liquid hydrogen; when a charged particle passes through, it leaves a trail of ionised particles around which small bubbles form.

A cloud chamber is filled with alcohol saturated gas; when a charged particle passes through, it causes the alcohol to condense producing a trail.In both the cloud chamber and the bubble chamber, there is a strong magnetic field which curves the path of the particles.

Detecting Particles

Detecting particles

Interpreting particle tracks

There is a strong magnetic field into the page

fast positive particle

slow positive particle

fast negative particle

negative heavy particle

Particles with greatest momentum deflected the least

positive particle losing momentum / slowing down

Heavier particles cause thicker tracks

fast particle decays into a negative particle and a neutral particle (dotted line) which itself decays into an electron and a positron

Bubble chambers The charge on the particles can be

found from the direction in which they curve in the magnetic field.

Faster moving particles have more curved paths.

The dashed tracks indicate uncharged particles (neutron and neutrinos)

Uncharged particles produce no ionisation trails in the bubble chamber

Their paths are inferred from the tracks that are visible.

 

 

 

  

 

 

Annihilation calculation (example)

Answer:Since energy is conserved,Energy of the two photons = energy of the electron & positron = 2x energy of each photon = 2x the rest mass of each particleEach photon must have 0.511Mev of energy

electron positron

photon

photon

An electron which has a rest mass of 0.511MeV annihilate a positron to produce two photons.What is the energy of each photon?

Annihilation calculation (another example)

A positron created in a cloud chamber in an experiment has 0.158 MeV of kinetic energy. It collides with an electron at rest, creating two photons of equal energies as a result.What is the energy of each photon?(the electron has a rest mass of 0.511MeV )

Stationary electron

Positron with KE of 0.158MeV

photon

photonAnswer:Total energy before annihilation == (Rest mass of electron) + (rest mass of positron + kinetic energy of positron)= 0.511 + 0.511 + 0.158 = 1.180MeV

The energy of each photon must be 1.180/2 = 0.590MeV

Pair production calculation (example)

A photon creates a proton and an antiproton and vanishes in the process.What is the minimum photon energy required to produce a proton-antiproton pair?

proton

photonantiproton

Answer:

energy of the photon = 2x proton rest energy = 2 x 938.257 = 1876.5 MeV

AQA AS Specification, where are we up to?

Lessons Topics

1-2 Constituents of the atomProton, neutron, electron. Their charge and mass in SI units and relative units. Specific charge of nuclei and of ions. Atomic mass unit is not required. Proton number Z, nucleon number A, nuclide notation, isotopes.

3 to 4 Stable and unstable nucleiThe strong nuclear force; its role in keeping the nucleus stable; short-range attraction to about 3 fm, very-short range repulsion below about 0.5 fm;Equations for alpha decay and β - decay including the neutrino.

5 to 10 Particles, antiparticles and photonsCandidates should know that for every type of particle, there is a corresponding antiparticle. They should know that the positron, the antiproton, the antineutron and the antineutrino are the antiparticles of the electron, the proton, the neutron and the neutrino respectively.Comparison of particle and antiparticle masses, charge and rest energy in MeV.Photon model of electromagnetic radiation, the wave equation the Planck constant,E = hf = hc / λKnowledge of annihilation and pair production processes and the respective energies involved. The use of E = mc2 is not required in calculations.

10 to 15 Particle interactionsConcept of exchange particles to explain forces between elementary particles.The electromagnetic force; virtual photons as the exchange particle.The weak interaction limited β - , β + decay, electron capture and electron-protoncollisions; W+ and W- as the exchange particles.Simple Feynman diagrams to represent the above reactions or interactions in terms of particles going in and out and exchange particles.

HomeworkVisit the below website. Answer the

questions as directed

http://www.particledetectives.net/html/hidden_antimatter.html