Bell Work Objectives To 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 Emc ID: 462997
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Slide1
Particles and antiparticles
Bell WorkSlide2
Objectives
To understand what happens when a particle and antiparticle meetTo be able to calculate photon energies produced from annihilation and energies required for pair productionSlide3
Particles and E=mc
2Einstein 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 10
13 J to every MeVSlide4
The
electronvolt
A 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:Slide5
Energy of photons in lightSlide6
Wave and photon calculations
Lets try some examples
Slide7
Mass and Energy
In 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 nucleusSlide8
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 ReviewSlide9
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 answersSlide10
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.Slide11
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.Slide12
Particle rest energy
Each 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
!Slide13
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 particle
The two destroy each otherTheir mass is converted in energy This process is called
ANNIHILATION.Slide14
Annihilation
When a particle and its corresponding antiparticle meet together annihilation occurs.
Each particle has energy locked up in its mass E = mc
2
All of their mass and kinetic energy is converted into
two photons
of equal frequency that move off in opposite directions.Slide15
Annihilation
Look at the annihilation of an electron and its anti-particle (positron)
e-
e
+Slide16
Annihilation
Why are two photons of energy produced and not just one? (Hint: any collision must obey
all
conservation laws)
One photon only could conserve charge and mass/energy
But to conserve momentum two photons moving in opposite directions must existSlide17
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 energySlide18
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+Slide19
Pair production
The energy of
one photon
can be used to create a particle and its corresponding antiparticle.
The photon ceases to exist afterwardsSlide20
Pair Production
In what way would a third particle, e.g. nucleus or electron, get involved in this reaction? (Hint: again
all
conservation laws must apply)
The third particle recoils and carries away some of the energy of the photon
The recoil ensures that the momentum is also conservedSlide21
Calculating energies pair production
In 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 energySlide22
Annihilation & Pair productionSlide23
Annihilation and pair productionSlide24
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 ParticlesSlide25
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 positronSlide26
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 chamberTheir paths are inferred from the tracks that are visible.
Slide27
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 particle
Each 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?Slide28
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
photon
Answer:
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 = 0.590MeVSlide29
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
photon
antiproton
Answer
:
energy of the photon = 2x proton rest energy
= 2 x 938.257 = 1876.5 MeV Slide30
Annihilation calculation
Calculate the minimum energies of the photons produced by the annihilation of a proton and antiproton.
Answer:
The minimum energies occur when the pair of particles have initially insignificant kinetic energy. (in other words treat the
kinectic
energy as zero)
rest energy of a proton in MeV = 938MeV
rest energy of an antiproton also = 938MeV
= total mass converted into electromagnetic radiation in the form of two photons = 1876 MeV
therefore each photon has an energy of 938 MeVSlide31
AQA AS Specification, where are we up to?
Lessons
Topics
1-2
Constituents of the atom
Proton, 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 nuclei
The 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
photons
Candidates 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 / λ
Knowledge of annihilation and pair production processes and the respective energies involved. The use of
E = mc
2
is not required in calculations.
10 to 15
Particle interactions
Concept 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-proton
collisions; 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.Slide32
Homework
Visit the below website. Answer the questions as directedhttp://www.particledetectives.net/html/hidden_antimatter.html