Particle Physics Tutorial 6 - Energy, Particles and Anti-Particles

 

Particle physics is concerned with fundamental particles.  It used to be thought that protons, neutrons and electrons were the fundamental particles of matter, which could not be broken down into anything smaller.  However it has been found that nucleons are made up of smaller particles, so nucleons are now not fundamental.  To make sense of quantities involved, we need to look at the units used in particle physics for mass and energy.   We have come across them in passing in previous tutorials

 

Units in Particle Physics

You will often see some strange looking units when reading about particles.  Joules and kilograms are far too big and clumsy at the particle level.  In the last tutorial you will have seen that the rest energy of a Higgs boson was 126 GeV.

 

The main unit you will see is the electron-volt.  It is not a voltage, but a unit of energy.  It is the amount of energy that a single electron has when it is accelerated by a potential difference of 1 volt.  You have already looked at rest energies in electron-volts in previous tutorials.  The electron volt is defined as:

 

The amount of energy that a single electron has when it is accelerated by a potential difference of 1 volt.
 

1 eV = 1.6 × 10-19 J

 

You will also see multiples like keV, MeV, and GeV:

 

Worked Example

A photon has frequency of 1.0 × 1018 Hz. What is its energy in J and eV?

Answer
E = hf = 6.63 × 10-34 J s × 1 × 1018 Hz = 6.63 × 10-16 J.

E = 6.63 × 10-16 J ÷ 1.6 × 10-19 J eV-1 = 4.14 keV
 

 

 

Question 1

What is the energy in joules of the following electron energies?   

(a) 100 eV

(b) 100 MeV

(c) 10 GeV              

Answer

 

Atomic Mass Unit

You will also see the atomic mass unit, u (it will not be examined at AS, but will be at A-level):

 

1 u = 1.661 × 10-27 kg

 

The atomic mass unit is defined:

Having exactly 1/12th the mass of a carbon-12 atom.
 

A particle of 1 u has a rest energy:
 

E = 1.661 × 10-27 kg × (3.0 × 108 m s-1)2 = 1.495 × 10-10 J

 

Convert this to eV by dividing by 1.6 × 10-19 J eV-1:

 

E = 1.495 × 10-10 J ÷ 1.6 × 10-19 J eV-1 = 933 × 106 eV = 930 MeV (2 significant figures)

 

 

Rest Mass and Rest Energy

You will also come across an odd expression rest energy.  At the subatomic level, mass and energy are one and the same thing.  Mass can be turned into energy, and energy can be made into mass.  They are linked by Einstein’s famous simple equation:

 

E = mc2

 

The rest energy is expressed in MeV.  Rest mass is given in MeV/c2 where c2 is the square of the speed of light (9.0 × 1016 m2 s-2).  It can be shown that J/ m2 s-2 = kg.

 

The rest energy (mass) of an electron is 0.511 MeV/c2 = 9.11 × 10-31 kg.

 

The rest energy of a muon = 105.7 × 106 eV × 1.6 × 10-19 C = 1.88 × 10-28 kg

                                                            9 × 1016 m2 s-2

 

In this unit we will talk about rest energy, but it’s the same as rest mass.  In some syllabuses, the rest mass is used, so the units are MeV/c2.

 

1 MeV/c2 = (1.60 × 10-19 eV × 1 × 106) ÷ 9.0 × 1016 m2 s-2 =1.78 × 10-30 kg.
 

 

Question 2

What is the speed of an electron at:

100 eV;

10 GeV?
 

Answer

Question 3

(a) The mass of a proton is 1.67 × 10-27 kg. What is this in MeV/c2?

 

(b) The rest energy of a Higgs Boson is 126 GeV.  What is its mass in kg?

 

(c) Compare your answer to the mass of a proton (mass = 1.67 × 10-27 kg).

Answer

 

 

Particles and antiparticles

Each particle has an antiparticle.  However, antiparticles are not found in normal matter, but arise in:

 

We should note the following:

For example:

The symbol for the electron is e- and for the positron is e+.  For other particles, the antiparticle has a bar over the symbol, for example if the proton has the symbol p, the antiproton has the symbol:

This is pronounced "pee-bar".

 

Note:

In this web-editor, placing a bar over a letter gives results that are most unsatisfactory.  The line often flies off to a completely different part of the page.  If I need to refer to an antiparticle in the text, I will write it like this:

p
 

i.e. white text on a black background

 

Annihilation

When particles and antiparticles meet, they annihilate each other, releasing their combined mass as energy in the form of gamma photons. 

 

 

Consider the collision between an electron and a positron. 

 

e-   +   e+ → g      +     g

 

 

If there is sufficient energy, other particles may be created as well.  For example, the collision between an electron and a positron may give rise to two muons:

 

e-   +   e+ → m+      +     m-

 

Question 4

An electron of rest energy 0.511 MeV collides with a positron.
a. What happens?
b. 3 identical photons are produced. Calculate their energy in eV and joules.
c. Calculate the wavelength of the photons.

Answer

Question 5

State and explain the sequence of events in an annihilation.

Answer

 

 

Pair Production

The reverse process can apply as well.  Electrons and positrons can be formed when a gamma ray passes through matter.  A gamma photon can give rise to an electron and a positron, provided the energy of the photon is more than twice the rest mass of an electron, and that it is near a nucleus. This pair production is a good illustration of how mass and energy can be changed from one to another.

PowerPoint Animation

 

Two gamma photons meeting will not interact.  They just superpose and pass through each other.  No pair production happens.

A single gamma photon (with energy greater than 1.02 MeV) will form a positron and an electron, but it has to be in the presence of a nucleus.  The gamma photon must have the same energy as the rest energies of the electron and the positron added together.

 


 

The photon is pure energy, but it can turn into matter.  So there is a chance that the photon of sufficient energy becoming a positron and an electron.  However they will immediately annihilate back into the gamma photon.  So we wouldn't know that that has happened.  To conserve momentum, physicists say that the electron and the positron are in virtual states.  Near a nucleus, a virtual photon from the nucleus, mediating the electromagnetic force, may separate the electron and the positron.  The electric field within the nucleus repels the positron and attracts the electron.  Therefore they fly apart and do not annihilate.  The positron will annihilate on interaction with another electron, of which there are plenty.

 

Question 6

a. An electron and a positron each have a rest energy of 0.511 MeV. Show that the minimum energy required for pair production is 1.022 MeV
b. Calculate the wavelength of a gamma photon of energy 1.022 MeV
c. Show that a rest energy of 0.511 MeV is equivalent to about 9 × 10-31 kg

Answer

 

Antiparticles can be made in large quantities in accelerators, resulting from high-energy collisions.  They have short lifetimes, about 10-10 s because when they meet their equivalent particle, they annihilate each other in a burst of energy.  It is even possible to make simple anti-atoms

 

It is thought that there is more matter than antimatter in the Universe.  It is possible that antimatter exists in large quantities somewhere, and that there are antimatter stars and planets.  None have yet been detected.