Israel Endeshaw, NK
Annihilation and Pair Production
Physics 203
October 13, 2009
Introduction:
Most people are familiar with Albert Einstein and the work he has done in the world of
science. For some the first thing that comes to our mind when hearing his name is his amazing
formula E = mc2. One of Einstein’s great insights was realizing that matter and energy are really
different forms of the same thing, just like ice and water are forms of H2O. Ice can be turned in
to liquid water by the process of melting and water can be turned in to Ice by the process of
freezing.
Einstein realized that matter can be turned in to energy and energy in to matter for a
moving object as well as for an object at rest. The interchange of matter and energy is very
broad and has different process; annihilation, pair production, nuclear decay, radioactivity
(nuclear binding energy), and kinetic energy are some of the process of the interchange.
E = mc2, the most famous equation of science, is the energy corresponding to mass m at
rest. When an object moves, kinetic energy, E = Δmc2; the mass of a moving a matter can be
given by
E = Δmc2…….and the mass m can be given by, m =
.
Where… mr is mass at rest, v is speed and c is speed of light.
The final equation for the energy of a moving object will be then:
K.E =
….where K.E is kinetic energy, m is mass, and v is speed.
The simple definition of matter is anything that occupies space. In physical physics for
every particle or matter there is antiparticle or antimatter. A particle and antiparticle are
identical almost in every way, they have the same mass but they have opposite charges. A good
example of a particle and antiparticle are electron and positron.
An electron is a negatively charged subatomic particle, with a charge of negative one.
According to, Chemistry and/or Physics that an electron along with the proton and neutron are
the basic building blocks of an atom. They make up the matter all around us. On the other
hand, the positron is an anti-electron which means it has the same mass like the electron and
its charge is positive one. Each electron and positron is matter and antimatter, and their
charges, positive one and negative one is the major differences.
A positron is an electron's anti-particle, and when the electron and positron come in contact
with each other to combine, they annihilate each other in a process called electron-positron
annihilation.
Annihilation:
In physics, Annihilation is a reaction in which a particle and its antiparticle collide and
disappear, causing energy to be released. The Annihilation process happens on two particles
which have the opposite matter and energy characteristics. The most common annihilation on
our planet occurs between an electron (particle) and a positron (antiparticle). (annihilation,
2009)
To illustrate the above sentence, consider a simple hydrogen atom, basically composed
of a single proton. The subatomic particle has a mass of 1.672 x 10-27kg, this is very tiny mass.
However, in everyday quantities of matter there are a lot of atoms. For instance, in one
kilogram of pure water, the mass of hydrogen atom is about one hundred eleven grams.
Einstein’s formula tells us the amount of energy this mass would be equivalent to, if it was
turned to energy, the multiple of the mass by the square of the speed of light (3.0 x 10 8m).
E = mc2
If this hydrogen matter can be changed to energy by the speed of light squared.
Therefore it would have been:
E = mc2
= 0.111kg x ((3.0 x 108)2)m
= 1.0 x 1016 Joules
Bill Wills (1999) interpreted the above number as, a joule is not a large unit of energy;
one joule is about the energy released when you drop a textbook to the floor. But, in this case,
1.0 x 1016 Joules is an incredible amount of energy. The amount of energy in thirty grams of
hydrogen atoms is equivalent to burning hundreds of thousands of gallons of gasoline.
Therefore, when consider the energy in one kilogram of water, which also contains oxygen
atoms, the total energy is close to ten million gallons of gasoline.
The only way for all this energy to be released is for the kilogram of water to be entirely
annihilated. This process involves the complete destruction of matter, and occurs only when
that matter meets an equal amount of antimatter. Antimatter has been created in the
laboratory, but it is short lived. It annihilates itself because it meets an equal quantity of
ordinary matter as soon as it encounters anything. For this reason, it has not yet been made in
measurable quantities, so our one kilogram of water can’t yet be turned into energy by mixing
it with ‘antiwater’. (Wills, B., 1999)
As said above the process of annihilation happens on two particles which have exactly
the opposite matter and energy characteristic: the annihilation process is illustrated as follows:
e- + e+ -> γ
For annihilation, the charge, the momentum and the energy of the system are
conserved. The electron, e- , possesses negative charge and the positron, e+, is positive charge;
both undergo annihilation process and transform into gamma rays, which is charge less. As a
result, the net charge of the system at both sides is zero. (Kong, K., 2007)
The process of Annihilation:
Annihilation process happens on two particles which have exactly the opposite matter
and energy properties, such as electron and positron. When both particles are attracted and
combined together, the matter and energy field is restructured and released to become light or
photon. (Kong, K., 2007). In short, annihilation can be defined as the reaction between particle
and its antiparticle in which the two bodies vanish or disappear and photons or other particles
are created.
For annihilation, the charge for the system is conserved (Energy and Momentum are
conserved). The electron, e- whose possesses negative charge and the positron, e+ whose is
positive charge, both undergo annihilation process and transform into gamma rays, whose is
chargeless. As described in the above equation, the net charge of the system at both sides is
zero.
In annihilation, two particles structure are combined and restructured to become the
wave structure. Kok-Haw Kong (2007) illustrates the stages and the transformation from
particles to photon with the graphics below.
http://www.greatians.com/physics/mass/pair%20production_files/figure%20mc.1.1.GIF
Stage 1 shows the structure of the positron (p) and electron (e). Both have the magnetic
(B) and electric (E) field as the nucleus. The positron and electron attract to each other due to
the electrostatic and magnetic force and transform to the next stage.
Stage 2 shows the combination of the annihilation process. The combination causes the
change in magnetic and electric fields.
Stage 3 the dot product in the Faraday’s and Maxwell’s law of induction between the
change of magnetic and electric flux and the magnetic and electric field produced is always
perpendicular. Therefore, the induced photon always travels at the direction perpendicular to
the change of magnetic and electric flux. (Kong, K., 2007)
According to Kok-Haw Kong (2009), “In this annihilation process, the combination process also
implies the nuclear reaction process where the interaction of the nucleus of particles takes
place. It is also observed that the photon and particle have the same ingredients, which are the
Matter & Energy field.”
Pair Production:
In the above section, process of annihilation, matter is changed to energy. From the
famous Einstein formula E = mc2, if one solve for the mass from this equation, mass will be the
energy divided by the light of speed squared. That is:
E = mc2 ………
.……equation 1
m = E / c2…….
.……equation 2
We can change liquid water into ice by the process of melting; we can also reverse the
process of melting and change liquid water to ice by the process of freezing.
From equation 1, we can change matter in to energy by the process of annihilation; we can
reverse the process of annihilation and from equation 2 we can change energy in to matter by
the process of pair production. Simply the analogy is that if melting is for annihilation, then
freezing will be for pair production.
Pair production is the converse of annihilation. It is a phenomenon of nature where energy is
converted in to mass.
The process of Pair Production:
The process of pair production can be described as the formation of electron and
positron from very high energy electromagnetic radiation traveling through matter. It is a direct
conversion of radiant energy into matter in accord with the equation E = mc2. It is one of the
principal ways in which high-energy gamma rays are absorbed in matter. The positrons quickly
disappear by being reconverted into photons in the reverse process of annihilation with other
electrons. Pair production may sometimes refer to the formation of other particle/antiparticle
pairs as well. (pair production, 2006 & Pair Production)
For Pair production process can simply described as, with respect to time, a process where the
kinetic-time-energy is converted to the potential-time-energy.
Kok-Haw Kong (2007) illustrates the stages of the transformation from photons to
particles in the graphics below.
http://www.greatians.com/physics/mass/pair%20production_files/figure%20mc.2.4.GIF
Stage 1 of the figure shows the change of the Kong vector (Kong vector is the velocity of
photon). When the gamma photon enters into the magnetic and electric field of the atom
hydrogen before it reaches the origin point, the magnetic and electric field of gamma photon is
twisted or deformed. The deformed magnetic and electric field of the photon reduces the
velocity of photon from the speed of light.
Stage 2 shows that when the photon enters deeper into the center of the atom
hydrogen, the deformed angle increases and the velocity of the photon become slower and
almost stagnant. When the gamma photon reaches the center of the atom hydrogen, the
electric field of the photon is fully squeezed into a point and become a point charge where the
deformed electric field becomes spherical.
Stage 3 the squeezed photon then becomes the charge particles. The charge particles
are separated perpendicular to the direction of the incident photon and the electron and
positron travel in opposite direction. (Kong, K., 2007)
It's not possible, however, to collect these newly created particles and assemble them
into atoms, molecules and bigger (less microscopic) structures that we associate with 'matter'
in our daily life. This is partly because in a technical sense, you cannot just create matter out of
energy: there are various 'conservation laws' of electric charges, the number of leptons
(electron-like particles) etc., which means that you can only create matter / anti-matter pairs
out of energy. Anti-matter, however, has the unfortunate tendency to combine with matter
and turn itself back into energy. Even though physicists have managed to safely trap a small
amount of anti-matter using magnetic fields, note that this is not easy to do.
It takes a huge amount of energy to create matter in this way. For instance, if the process in the
example above is reversed, that is converting 111g of hydrogen in to energy will result in about
hundreds of thousands of gallons of gasoline. Hence, if we reverse the process that is to create
only 111g of hydrogen, we will end up burning hundreds of thousands of gallons of gasoline.
Although it’s very difficult to create matter from energy in a laboratory, the universe
that we exist in was created from energy, by the process of pair production. The Big Bang
theory states that before there was the universe that we exist in, energy was condensed into a
very dense point. At some time there was an explosion of this energy, and the very dense point
expanded outwards to form matter/the universe. The aggression of the process caused
molecules and atoms to collide and stick together or shear off, creating new energy. And this
new energy is again changed into matter by the process of pair production.
Applications of E = mc2
Applications of E=mc2 are widely experienced within the current society: For instance,
the most important applications of Einstein’s great insight are the smoke detectors in our
homes; the radio-isotopes used in medical imaging and radiotherapy; the atomic bomb in
Hiroshima is also the direct application of the equation. From all the applications, the most
useful one is the PET scanner. (Tyson, P, 2005)
PET (Positron Emission Tomography) scanner is the major diagnostic imaging modality
used mainly in determining the existence and/or severity of cancers, cardiovascular disease,
and neurological conditions. It offers significant advantages over other forms of imaging such as
CT (computerized tomography) or MRI (magnetic resonance imaging) scans in detecting disease
in many patients.
(perfusion) et a described PET as, “A PET scanner consists of an array of detectors that
surround the patient. Using the gamma ray signals given off by the injected radionuclide, PET
measures the amount of metabolic activity at a site in the body and a computer reassembles the
signals into images. Cancer cells have higher metabolic rates than normal cells, so they show up
as denser areas on a PET scan. PET is useful in diagnosing certain cardiovascular and
neurological diseases because it highlights areas with increased, diminished or no metabolic
activity, thereby is pinpointing problems.”
The PET scanner looks like the image given below:
http://www.ccsb.org/upload/Image/Machines/PET-Scanner.jpg
Conclusion
Albert Einstein realized that matter can be changed into energy, and energy can be
changed into matter. From this he concluded that matter can be changed into energy with the
speed of light squared. This interchange can happen by the process of annihilation, pair
production, nuclear decay, radioactivity, and kinetic energy. The universe that we exist in, as
suggested by the Big Bang theory, is created by the concept of changing energy into matter.
Annihilation and Pair Production are the process of changing matter into energy, and
changing energy into matter, respectively. By changing matter into energy and vice versa, the
world that we live in have been simpler. For instance, every time a person undergoes a PET
scan he/she is paying direct respect to Einstein’s great formula.
E = mc2, interchange between matter and energy, is responsible for the creation of the universe
and everything in it, including human beings.
Works Cited
Kong, K. (2007, March 15). ANNIHILATION AND PAIR PRODUCTION. Retrieved October 7, 2009,
from http://www.greatians.com/physics/mass/pair%20production.htm#MC.1.0
Pair Production . (n.d.). Retrieved October 7, 2009, from
http://abyss.uoregon.edu/~js/glossary/pair_production.html
pair production. (2006.). Retrieved October 15, 2009, from
http://www.credoreference.com/entry/ebconcise/pair_production
The phenomenon of pair production. (n.d.). Retrieved October 2, 2009, from
www.ryuc.info/creativityphysics/energy/pair_production.htm
Tyson, P. (2005.). NOVA | Einstein's Big Idea | The Legacy of E = mc2 | PBS. Retrieved October
10, 2009, from http://www.pbs.org/wgbh/nova/einstein/legacy.html
Wills, B. (1999.). E=mc2 Explained. Retrieved October 2, 2009, from
www.worsleyschool.net/science/files/emc2/emc2.html
annihilation. (2009.). Retrieved October 7, 2009, from
http://www.britannica.com/EBchecked/topic/26347/annihilation
(perfusion), m. b., heart, m. r., flow, p. u., blockages, s. a., muscle, d. l., & attack), w. h. (n.d.).
What Is PET. Retrieved October 12, 2009, from
http://interactive.snm.org/index.cfm?PageID=972