The international sign of radioactivity

Chapter 9 Nuclear Physics

Understanding the atoms was exclusively a pursuit of scientists for a long time. Over sixty years ago, scientists irrefutably demonstrated the power of these tiny particles (the atoms) to the world. The USA military dropped atomic bombs in Japan: Hiroshima (over 100,000 people were killed) and Nagasaki. Nuclear weapons have killed hundreds of thousands of people, and have the potential of destroying most life on earth. The threat of nuclear warfare is a serious problem.

On the other side, more and more countries are obtaining and developing nuclear weapons, these include of USA, Russia, France, UK, China (first atomic bomb in 1964, first Hydrogen bomb in 1967) India, Pakistan and Israel;

the suspected countries: North Korea, South Africa, Iran, Syria, Libya, Algeria.

Applications The nuclear energy:

advantage: it is potential of becoming the safest, cleanest, cheapest and most efficient type of energy; disadvantage: it carries the risk of a reactor meltdown and lots of harmful released radiation.

Medical imaging, such as CT scans and MRI, is used to determine the amount of radiation a person being exposed to. There have been quite a few different techniques and more are still being developed and improved presently.

Radioactive dating uses radioactive properties of certain elements to determine the age of something such as an ancient person.

Radiation detection involves different instruments used in order to detect radiation present somewhere.

The short history of the nuclear physics

1896, A. H. Becquerel discovered the radioactivity of 92U;1897, Mrs and Mr. P. & M. Curie discovered that the elements of 84Po and 88Ra have radioactive behaviors;1899, and rays, 1900, rays;1903, Rutherford found that ray is 2He++ and ray is electron;1911, Planet model of atoms;1919, man-made nuclear reactions;1932, J. Chadwick discovered neutron, Heisenberg: nucleus consists of protons and neutrons;

1934, Mrs. and Mr. F. & I. Joliot Curie discovered man-made radioactivity;

1939, O. Hahn, F. Strassmann, L. Meitner and O. Frisch, Fission of heavy elements;

1942, E. Feimi, hot neutron proliferation reactor;

1945, J. Oppenheimer at Los Alamos: atomic bomb

1952, E. Teller, Hydrogen bomb;

1954, Soviet set up a nuclear power plant;

1964, China, atomic bomb; 1967, hydrogen bomb.

§9.1 the basic properties of the nuclei

The atom and nucleus are two different levels of the matter:

The main contribution of nucleus is the mass and charge; The chemical and physical properties, and the properties of optical spectra are due to electron structure; The radioactivity is due to the characteristic of some isotopes.

§9.1 the basic properties of the nuclei

The components of atom: nuclei + electrons

Nuclei: neutrons + protons

nucleons

1 u = 1.66 x 10- 27 kg = 939 MeV/c 2

Mp = 1.008665 u, mn = 1.007277 u

The electrons, protons and neutrons which make up an atom have definite charges and

masses

Element: atoms with the same atomic number Z

Isotope: the same elements with different neutron number;

Nuclide: a type of atoms specified by its atomic number, atomic mass, and energy state.

At present it knows 112 elements. All of the elements heavier than 92U are man-made; approximately 270 stable isotopes and more than 2000 unstable isotopes.

Chart of Nuclide

Nuclide byland

Isotopic Abundances by Mass Spectrometry

The relative abundances of the isotopes of an element may be obtained with a mass spectrometer. For example, the relative abundances of krypton are shown below on an experimental spectrum adapted from Krane, Introductory Nuclear Physics.

78Kr 0.356%80Kr 2.27%82Kr 11.6%83Kr 11.5%84Kr 57.0%86Kr 17.3%

A weighted average of the isotopes above gives 83.8 u, the accepted atomic mass of krypton which appears in the periodic table. Other isotopes of krypton are known, but they do not appear in natural samples because they are unstable (radioactive).

§9.2 radioactivity

Radioactivity means atoms decay, which emit some kind of radiation. The reason for these decays is that they are instable.

The discovered 2000 nuclides, most of them are unstable, and can decay to another nuclide. An atomic nucleus is instable when it is too heavy or when a balance is missing between the protons and neutrons. Every atoms which has higher number of nucleons than 210 is instable.

The nucleus decays are quantum statistical behaviors. It is impossible to predict which nucleus will be the next one who decays. It is possible to predict how many nuclei will decay in a certain time.

dtNdN 0teNN 0

N: the number of nuclei; -dN: the number of nuclei decayed;: decay constant, the probability of nuclei decay in a unit time

Radioactive Half-Life

The radioactive half-life for a given radioisotope is the time for half the radioactive nuclei in any sample to undergo radioactive decay. After two half-lives, there will be one fourth the original sample, after three half-lives one eight the original sample, and so forth.

21

21 ln/ T21

002

1/TeNN

Examples of half life time

239Pu: 24,000 years,

238Ra: 6.7 years,

232Th: 14,000,000 years,

212Po: 0.0000003 s,

235U: 0.70 ×109 years,

238U: 4.5 × 109 years;

Proton: 1030 years.

Empirical results:

decay constant and half-life time T1/2 are characteristic of radioactivity, and they almost have no correlation with its circumstances:

temperature: 24k ~ 1500k, pressure: 0 ~ 2000 atm, magnetic field: 0 ~ 8.3T,

For 7Be: 70 days in sun, and 53 days in earth, 30% in change

Activity: the intensity of radioactive source

NeNdt

dNA t

0

1 Ci (Curie) = 3.7 × 1010 s-1, the activity of 1 g 216RaIn china: 1 Bq = 1 s-1, 1 Ci = 3.7 × 1010 Bq

The determination of the nuclides with long half life by measuring the activity.

The most common types of radiation are called , and radiations, and several

other varieties of radiation decays

Historically, the products of radioactivity were called alpha, beta, and gamma when it was found that they could be analyzed into three distinct species by either a magnetic field or an electric field.

Penetration of matter

Through the most massive and most energetic of radioactive emissions, the alpha particle is the shortest in range because of its strong interaction with matter. The electromagnetic gamma ray is extremely penetrating, even penetrating considerable thicknesses of concrete. The electron of beta radioactivity strongly interacts with matter and has a short range.

radioactivity

particle composes of two protons and two neutrons, the alpha particle is a nucleus of the element of helium.

decay:

YX A

ZAZ

42

ThU

PbPo23490

23892

20682

21084

For instance:

Alpha Barrier Penetration

The energy of emitted alpha particles was a mystery to early investigators because it was evident that they did not have enough energy, according to classical physics, to escape the nucleus. Once an approximate size of the nucleus was obtained by Rutherford scattering, one could calculate the height of the Coulomb barrier at the radius of the nucleus. It was evident that this energy was several times higher than the observed alpha particle energies. There was also an incredible range of half lives for the alpha particle which could not be explained by anything in classical physics.

Alpha Tunneling Model

Quantum mechanical tunneling gives a small probability that the alpha can penetrate the barrier. To evaluate this probability, the alpha particle inside the nucleus is represented by a free-particle wavefunction subject to the nuclear potential. Inside the barrier, the solution to the Schrodinger equation becomes a decaying exponential. Calculating the ratio of the wavefunction outside the barrier and inside and squaring that ratio gives the probability of alpha emission.

The illustration represents the barrier faced by an alpha particle in polonium-212, which emits an 8.78 MeV alpha particle with a half-life of 0.3 microseconds. The following characteristics of the nuclear environment can be calculated from a basic model of the nucleus:

Separation of centers of alpha and nucleus at edge of barrier

9.1 fm

Height of barrier26.4 Me

V

Radius at which barrier drops to alpha energy

26.9 fm

Width of barrier seen by alpha 17.9 fm

Alpha's frequency of hitting the barrier1.1 x 10^

21/s

Alpha Binding Energy

The mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together. This binding energy can be calculated from the Einstein relationship:

Nuclear binding energy = Δmc2

The nuclear binding energy of the alpha particle is extremely high, 28.3 MeV. It is an exceptionally stable collection of nucleons. This contrasts with a binding energy of only 8 MeV for helium-3, which forms an intermediate step in the proton-proton fusion cycle.

Warning

Because of its very large mass (more than 7000 times the mass of the beta particle) and its charge, it has a very short range. The alpha particle is not suitable for radiation therapy since its range is less than a tenth of a millimeter inside the body. Its main radiation hazard comes when it is ingested into the body; it has great destructive power within its short range. In contact with fast-growing membranes and living cells, it is positioned for maximum damage.

Beta Radioactivity

Beta particles are just electrons from the nucleus, the term "beta particle" being an historical term used in the early description of radioactivity. Beta emission is accompanied by the emission of an electron antineutrino which shares the momentum and energy of the decay.The emission of the electron's antiparticle, the positron, is also called beta decay.

The radiation hazard from betas is greatest if they are ingested.

Beta decay can be seen as the decay of one of the neutrons to a proton via the weak interaction. The use of a weak interaction

Feynman diagram can clarify the process.

eepn

The beta decay:

eA

ZAZ eYX

1

The energy released in decay, Q:

QcmcMcM eYX 222

Q = 1.71 Mev for 32P 32S

e

e

eHeH

eSP

32

31

3216

3215

Positron and Neutrino

The emission of a positron or an electron is referred to as beta decay. The positron is accompanied by a neutrino, a massless(?) and chargeless particle. Positrons are emitted with the same kind of energy spectrum as electrons in negative beta decay because of the emission of the neutrino.

Beta Energy SpectrumIn the process of beta decay, either an electron or a positron is emitted. There is a spectrum of energies for the electron or positron, depending upon what fraction of the reaction energy Q is carried by the massive particle. The shape of this energy curve can be predicted from the Fermi theory of beta decay.

From the Fermi theory of beta decay, the shape of the energy distribution for this "allowed" transition is given approximately by the expression:

where F(Z',KEe) is called the Fermi function. It accounts for the nuc

lear coulomb interaction which shifts this distribution toward lower energies because of the coulomb attraction between the daughter nucleus and the emitted electron. (It shifts the distribution upward for positrons.) Q represnts the energy yield of the transition and as such is the upper bound on the kinetic energy of the electron, KEe. The a

pparent complexity of the expression is partly because it is necessary to use relativistic momentum for the electron.

eeeeeee

e

KEZFcmKEKEQcmKEKEC

KEN

,'2 2222

Gamma Radioactivity

)()(* energylowerXstateexcitedX ZA

ZA

Gamma radioactivity is composed of electromagnetic rays.

Gama radioactivity is distinguished from x-rays only by the fact that it comes from the nucleus. Most gamma rays are somewhat higher in energy than x-rays and therefore are very penetrating.

It is the most useful type of radiation for medical purposes, but at the same time it is the most dangerous because of its ability to penetrate large thickness of material.

Gamma RadioactivityBinding energiesfor 203Tl

K 85.529 keV

LI 15.347 keV

LII 14.698 keV

LIII 12.657 keV

M 3.704 keV

Electron emissions from the Hg-203 to Tl-203 decay, measured by A. H. Wapstra, et al., Physica 20, 169 (1954).

Other Radioactive Processes

Electron capture: A parent nucleus may capture one of its own electrons and emit a neutrino. Most commonly, it is a K-shell electron which is captured, and this is referred to as K-capture. A typical example is

Internal conversion is the use of electromagnetic energy from the nucleus to expel an orbital electron from the atom. It is another electromagnetic process which can occur in the nucleus and which competes with gamma emission.

This process is not the same as emitting a gamma ray which knocks an electron out of the atom. It is also not the same as beta decay, since the emitted electron was previously one of the orbital electrons, whereas the electron in beta decay is produced by the decay of a neutron.

Radioactive Decay Paths

Radioactivity involves the emission of particles from the nuclei. In the case of gamma emission, the nucleus remaining will be of the same chemical element, but for alpha, beta, and other radioactive processes, the nucleus will be transmuted into the nucleus of another chemical element. Each decay path will have a characteristic half-life, but some radioisotopes have more than one competing decay path.

Radioactive Decay Paths

§9.3 Nuclear reactions

Many kinds of nuclear reactions occur in response to the absorption of particles such as neutrons or protons. Other types of reactions may involve the absorption of gamma rays or the scattering of gamma rays.

Specific nuclear reactions can be written down in a manner similar to chemical reaction equations. If a target nucleus X is bombarded by a particle a and results in a nucleus Y with emitted particle b, this is commonly written in one of two ways.

Reaction energy

We can characterize the energy of the reaction with a reaction energy Q, defined as the energy released in the reaction. The Q is positive if the total mass of the products is less than that of the projectile and target, indicating that the total nuclear binding energy has increased. The probability of a given type of nuclear reaction taking place is often stated as a "cross section".

A commonly used unit is the barn:1 barn = 10-28 m2

Some Nuclear Reactions

Nuclear Binding Energy curve

Nuclear binding energy = Δmc2

Iron limit

Nuclear Fission

If a massive nucleus like uranium-235 breaks apart (fissions), then there will be a net yield of energy because the sum of the masses of the fragments will be less than the mass of the uranium nucleus.

In one of the most remarkable phenomena in nature, a slow neutron can be captured by a uranium-235 nucleus, rendering it unstable toward nuclear fission. A fast neutron will not be captured, so neutrons must be slowed down by moderation to increase their capture probability in fission reactors.

Uranium Fuel Natural uranium is composed of 0.72% U-235 (the fissionable isotope), 99.27% U-238, and a trace quantity 0.0055% U-234 . The 0.72% U-235 is not sufficient to produce a self-sustaining critical chain reaction in U.S. style light-water reactors, although it is used in Canadian CANDU reactors. For light-water reactors, the fuel must be enriched to 2.5-3.5% U-235.

Uranium is found as uranium oxide which when purified has a rich yellow color and is called "yellowcake". After reduction, the uranium must go through an isotope enrichment process. Even with the necessity of enrichment, it still takes only about 3 kg of natural uranium to supply the energy needs of one American for a year.

Light Water Reactors

The nuclear fission reactors used in the United States for electric power production are classified as "light water reactors" in contrast to the "heavy water reactors" used in Canada. Light water (ordinary water) is used as the moderator in U.S. reactors as well as the cooling agent and the means by which heat is removed to produce steam for turning the turbines of the electric generators. The use of ordinary water makes it necessary to do a certain amount of enrichment of the uranium fuel before the necessary criticality of the reactor can be maintained. The two varieties of the light water reactor are the pressurized water reactor (PWR) and boiling water reactor (BWR).

Heavy Water Reactors

Nuclear fission reactors used in Canada use heavy water as the moderator in their reactors. Since the deuterium in heavy water is slightly more effective in slowing down the neutrons from the fission reactions, the uranium fuel needs no enrichment and can be used as mined. The Canadian style reactors are commonly called CANDU reactors.

Fissionable Isotopes While uranium-235 is the naturally occuring fissionable isotope, there are other isotopes which can be induced to fission by neutron bombardment. Plutonium-239 is also fissionable by bombardment with slow neutrons, and both it and uranium-235 have been used to make nuclear fission bombs. Plutonium-239 can be produced by "breeding" it from uranium-238. Uranium-238, which makes up 99.3% of natural uranium, is not fissionable by slow neutrons. U-238 has a small probability for spontaneous fission and also a small probability of fission when bombarded with fast neutrons, but it is not useful as a nuclear fuel source. Some of the nuclear reactors at Hanford, Washington and the Savannah-River Plant (SC) are designed for the production of bomb-grade plutonium-239. Thorium-232 is fissionable, so could conceivably be used as a nuclear fuel. The only other isotope which is known to undergo fission upon slow-neutron bombardment is uranium-233.

History of U-235 Fission

In the 1930s, German physicists/chemists Otto Hahn and Fritz Strassman attempted to create transuranic elements by bombarding uranium with neutrons. Rather than the heavy elements they expected, they got several unidentified products. When they finally identified one of the products as Barium-141, they were reluctant to publish the finding because it was so unexpected. When they finally published the results in 1939, they came to the attention of Lise Meitner, an Austrian-born physicist who had worked with Hahn on his nuclear experiments.

Upon Hitler's invasion of Austria, she had been forced to flee to Sweden where she and Otto Frisch, her nephew, continued to work on the neutron bombardment problem. She was the first to realize that Hahn's barium and other lighter products from the neutron bombardment experiments were coming from the fission of U-235. Frisch and Meitner carried out further experiments which showed that the U-235 fission yielded an enormous amount of energy, and that the fission yielded at least two neutrons per neutron absorbed in the interaction. They realized that this made possible a chain reaction with an unprecedented energy yield.

§9.4 Radioactive dating in Archeology

湖南马王堆汉墓辛追

Dating in Geography

Radioactive dating

Because the radioactive half-life of a given radioisotope is not affected by temperature, physical or chemical state, or any other influence of the environment outside the nucleus, then radioactive samples continue to decay at a predictable rate. If determinations or reasonable estimates of the original composition of a radioactive sample can be made, then the amounts of the radioisotopes present can provide a measurement of the time elapsed.

carbon dating (in Archeology) is limited to the dating of organic (once living) materials. It is a variety of radioactive dating which is applicable only to matter which was once living and presumed to be in equilibrium with the atmosphere, taking in carbon dioxide from the air for photosynthesis.

The longer-lived radioisotopes in minerals provide evidence of long time scales in geological processes. While original compositions cannot be determined with certainty, various combination measurements provide self-consistent values for the the times of formations of certain geologic deposits. These clocks-in-the-rocks methods (in Geography) provide data for modeling the formation of the Earth and solar system.

Carbon Dating

Cosmic ray protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen, the major constituent of the atmosphere. This neutron bombardment produces the radioactive isotope carbon-14. The radioactive carbon-14 combines with oxygen to form carbon dioxide and is incorporated into the cycle of living things.

The carbon-14 forms at a rate which appears to be constant, so that by measuring the radioactive emissions from once-living matter and comparing its activity with the equilibrium level of living things, a measurement of the time elapsed can be made.

Carbon dating

Carbon-14 decays with a halflife of about 5730 years by the emission of an electron of energy 0.016 MeV. This changes the atomic number of the nucleus to 7, producing a nucleus of nitrogen-14. At equilibrium with the atmosphere, a gram of carbon shows an activity of about 15 decays per minute. The low activity of the carbon-14 limits age determinations to the order of 50,000 years by counting techniques. That can be extended to perhaps 100,000 years by accelerator techniques for counting the carbon-14 concentration.

Clocks in the rocks

The clocks-in-the-rocks methods provide data for modeling the formation of the Earth and solar system.

The following radioactive decay processes have proven particularly useful in radioactive dating for geologic processes:

Parent half-life(billion yrs.) daughter materials

Zircon, uraninite, pitchblende, Muscovite, biotite, hornblende, volcanic rock, glauconite, K-feldspar Zircon, uraninite, pitchblende K-micas, K-feldspars, biotite, metamorphic rock, glauconite

Potassium-Argon Method

eCaK

AreK4020

4019

4018

4019 11.2%

88.8%

T1/2 = 1.26 billion

,112.0

1ln1

40

40

K

Art

It is hard to determine how much Calcium was initially present.

Potassium-Argon dating has the advantage that the argon does not react chemically, so any found inside a rock is very likely the result of radioactive decay of potassium. Since the argon will escape if the rock is melted, the dates obtained are to the last molten time for the rock. The radioactive transition which produces the argon is electron capture.

Disadvantage: very tiny air bubbles is usually trapped in the rock.

Rubidium-Strontium

The rubidium-strontium pair is often used for dating and has a non-radiogenic isotope, strontium-86, which can be used as a check on original concentrations of the isotopes. This process is often used along with potassium-argon dating on the same rocks. The ratios of rubidium-87 and strontium-87 to the strontium-86 found in different parts of a rock sample can be plotted against each other in a graph called an isochron which should be a straight line. The slope of the line gives the measured age. The oldest ages obtained from the Rb/Sr method can be taken as one indicator of the age of the earth.

,8738

8737 eeSrRb

T1/2 = 48.8 billion yrs

From an example by Jelley, the following five chondritic meteorites are reported to have the following proportions of the rubidium and str

ontium isotopes:

Meteorites 87Rb/86Sr 87Sr/86Sr

Modoc 0.86Sr 0.757

Homestead 0.8Sr 0.751

Bruderheim 0.72Sr 0.747

Kyushu 0.6Sr 0.739

Buth Furnace 0.09Sr 0.706

Uranium-Lead Dating

The Uranium-Lead method is the oldest-used dating method (since 1907) and more complicated. Common lead contains a mixture of four isotopes. None of the lead isotopes is produced directly from U and Th with a series of intermediate products.

radiogenicnotPbPbTh

PbUPbU

:,

,20482

20882

23290

20682

23892

20782

23592

204Pb, which is not produced by radioactive decay provides a measure of what was "original" lead. It is observed that for most minerals, the proportions of the lead isotopes is very nearly constant, so the 204Pb can be used to project the original quantities of 206Pb and 207Pb.

This method has proved to be less reliable. Yet, three dating systems all in one, which it is easily to determine whether the system has been disturbed or not.

Age of the Earth"The oldest rocks on earth that have been dated thus far include 3.4 billion year old granites from the Barberton Mountain Land of South Africa, 3.7 billion year old granites of southwestern Greenland, ..." Levin, 1983

But later in 1983: "Geologists working in the mountains of western Australia have discovered grains of rock that are 4.1 to 4.2 billion years old, by far the oldest ever found on the Earth" This dating was done on grains of zircon, a mineral so stable that it can retain its identity through volcanic activity, weathering, and sedimentation. It is a compound of zirconium, silicon and oxygen which in its colorless form is used to make brilliant gems.

Samples more than 3.5 billion years old have been found in eight or more locations, including Wisconsin, Minnesota, South Africa, Greenland, and Labrador.

Meteorite Dating

Meteorites, which many consider to be remnants of a disrupted planet that originally formed at about the same time as the earth, have provided uranium-lead and rubidium-strontium ages of about 4.6 billion years. From such data, and from estimates of how long it would take to produce the quantities of various lead isotopes now found on the earth, geochronologists feel that the 4.6-billion-year age for the earth can be accepted with confidence." Levin

Moon Rock Dating

The ages of rocks returned to Earth from the Apollo missions range from 3.3 to about 4.6 billion years. The older age determinations are derived from rocks collected on the lunar highland, which may represent the original lunar crust.

§9.5 Radioactive Detection

Nuclear radiation and x-rays are ionizing radiation and they can be detected from the ionizing events they produced.

Ionization Counters

Radiation detection can be accomplished by stretching a wire inside a gas-filled cylinder and raising the wire to a high positive voltage. The total charge produced by the passage of an ionizing particle through the active volume can be collected and measured.

Different names are used for the devices based on the amount of voltage applied to the center electrode and the consequent nature of the ionizing events.

ionization chamber: The voltage is high enough for the primary electron-ion pair to reach the electrodes but not high enough for secondary ionization. The collected charge is proportional to the number of ionizing events, and such devices are typically used as radiation dosimeters.

proportional counter: At a higher voltage, the number of ionizations associated with a particle detection rises steeply because of secondary ionizations. A single event can cause a voltage pulse proportional to the energy loss of the primary particle.

Geiger counters: At a still higher voltage, an avalanche pulse is produced by a single event in the devices.

Scintillation CountersRadiation detection can be accomplished by the use of a scintillator: a substance which emits light when struck by an ionizing particle.

phosphor screens (in the Geiger-Marsden experiment): which emitted a flash of light when struck by an alpha particle. single crystals of NaI doped with thallium (for modern scintillation counters): use electrons from the ionizing event are trapped into an excited state of the thallium activation center and emit a photon when they decay to the ground state.

Photomultiplier tubes are used to intensify the signal from the scintillations. The decay times are on the order of 200 ns and the magnitude of the output pulse from the photomultiplier is proportional to the energy loss of the primary particle.

Organic scintillators such as a mixture of polystyrene and tetraphenyl butadine. They have the advantage of faster decay time (about 1 ns) and can be molded into experimentally useful configurations.

Particle Track Devices

Radiation detection can take the form of devices which visualize the track of the ionizing particle.

Cloud chambers can show the track of a passing particle which can be photographed.

D. A. Glaser's invention of the bubble chamber in 1952 largely replaced the cloud chamber. Placed in an intense magnetic field, the curvature of the tracks of the primary particles and their products give information about their charge and momentum.

Spark chambers can also visualize the tracks of particles and has the advantage that the paths can be recorded electronically.

§9.6 Fundamental forces

The Electromagnetic Force

The electric force between charges may be calculated using Coulomb's law.

The electric force is straightforward, being in the direction of the electric field if the charge q is positive:

The Electromagnetic Forcethe magnetic force on a moving charge, the direction of the magnetic part of the force is given by the right hand rule:

The Electromagnetic Force

The electromagnetic force are summarized in the Lorentz force law.

The electromagnetic force is a force of infinite range which obeys the inverse square law:

Fundamentally, both magnetic and electric forces are manifestations of an exchange force involving the exchange of photons . The quantum approach to the electromagnetic force is called quantum electrodynamics or QED.

The electromagnetic force holds atoms and molecules together. In fact, the forces of electric attraction and repulsion of electric charges are so dominant over the other three fundamental forces that they can be considered to be negligible as determiners of atomic and molecular structure. Even magnetic effects are usually apparent only at high resolutions, and as small corrections.

Gravity force

Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large scale structure of galaxies, stars, etc.

The gravitational force between two masses m1 and m2 is given by the relationship:

This is often called the "universal law of gravitation" and G the universal gravitation constant. It is an example of an inverse square law force. The force is always attractive and acts along the line joining the centers of mass of the two masses. The forces on the two masses are equal in size but opposite in direction, obeying Newton's third law. Viewed as an exchange force, the massless exchange particle is called the graviton (not yet observed).

TidesThe Earth experiences two high tides per day because of the difference in the Moon's gravitational field at the Earth's surface and at its center:

Moon as Dominant Tidal Source

The tidal effect of the sun is smaller than that of the Moon because tides are caused by the difference in gravity field across the Earth. The Earth's diameter is such a small fraction of the Sun-Earth distance

The Strong Force

The strong force is the strongest of the four fundamental forces, which can hold a nucleus together against the enormous forces of repulsion of the protons is strong indeed. However, it is not an inverse square force like the electromagnetic force and it has a very short range. The range of a particle exchange force is limited by the uncertainty principle. At the most fundamental level the strong force is an exchange force between quarks mediated by gluons, as modeled by Yukawa. As an exchange force in which the exchange particles are pions and other heavier particles. Feynman diagram to visualize the strong interactions involves with quarks and gluons.

The characteristics of the strong force

A short range force; ~1fm, much stronger than Coulomb force; at the distance of atom size (~0.1nm) essentially zero, so that each nucleon just interacts with its nearest neighbors, and the total binding energy is proportional to the number of nucleus.

An attractive force with a repulsive core; nuclei are held together but they do not collapse; the density of all nuclei is about the same, the nucleons bound in the nucleus are tend to maintain the same average separation

Not all particles experiences the nuclear forces;

the division of the matter into two classes of fundamental particles, quarks and leptons.

a) the quarks are bound together by the strong forces into hadrons, like the protons, pion, etc.

b) the leptons do not participate in the strong interactions.

The nucleon-nucleon force is the same and irresponsive to whether the nucleons are protons or neutrons;

The exchange force

All four of the fundamental forces involve the exchange of one or more particles. In 1935, Hideki Yukawa reasoned that the electromagnetic force was infinite in range because the exchange particle was massless. He proposed that the short range strong force came about from the exchange of a massive particle which he called a meson.

Such exchange forces may be either attractive or repulsive, but are limited in range by the nature of the exchange force. The maximum range of an exchange force is dictated by the uncertainty principle since the particles involved are created and exist only in the exchange process - they are called "virtual" particles.

Range of Forces

If a force involves the exchange of a particle, in the sense that it must fit within the constraints of the uncertainty principle. A particle of mass m and rest energy E = mc2 can be exchanged if it does not go outside the bounds of the uncertainty principle in the form:

22

tmctE

A particle which can exist only within the constraints of the uncertainty principle is called a "virtual particle", and the time in the expression above represents the maximum lifetime of the virtual exchange particle. The maximum range of the force would then be on the order of

mctcRange

2

Pion Range of Strong ForceAn estimate of the range of the strong force can be made by assuming that it is an exchange force involving neutral pions. When the range expression is used as followings:

With a pion mass of

20 /0.135264 cMeVmmass e

61010730 15 .. mRange Classical proton radius

mctcRange

2

quarksSince the protons and neutrons which make up the nucleus are themselves considered to be made up of quarks, and the quarks are considered to be held together by the color force, the strong force between nucleons may be considered to be a residual color force. In the standard model, therefore, the basic exchange particle is the gluon which mediates the forces between quarks.

Quark Symbol Spin ChargeBaryonNumber

S C B T Mass*

Up U 1/2 +2/3 1/3 0 0 0 0 360 MeV

Down D 1/2 -1/3 1/3 0 0 0 0 360 MeV

Charm C 1/2 +2/3 1/3 0 +1 0 0 1500 MeV

Strange S 1/2 -1/3 1/3 -1 0 0 0 540 MeV

Top T 1/2 +2/3 1/3 0 0 0 +1 174 GeV

Bottom B 1/2 -1/3 1/3 0 0 +1 0 5 GeV

Elementary particles

Leptons and quarks are the basic building blocks of matter, i.e., they are seen as the "elementary particles". There are six leptons in the present structure, the electron, muon, and tau particles and their associated neutrinos. The different varieties of the elementary particles are commonly called "flavors", and the neutrinos here are considered to have distinctly different flavor.

Feynman Diagrams

Feynman diagrams are graphical ways to represent exchange forces. Developed by Feynman to describe the interactions in quantum electrodynamics (QED), the diagrams have found use in describing a variety of particle interactions.

Particles are represented by lines with arrows to denote the direction of their travel, with antiparticles having their arrows reversed. Virtual particles are represented by wavy or broken lines and have no arrows.

They are space-time diagrams, ct vs x. The time axis points upward and the space axis to the right. (Particle physicists often reverse that orientation.) Each point at which lines come together is called a vertex, and at each vertex one may examine the conservation laws which govern particle interactions. Each vertex must conserve charge, baryon number and lepton number.

Electromagnetic interactions

All electromagnetic interactions can be described with combinations of primitive diagrams like this one.

Other electromagnetic process can be represented, as in the examples below. A backward arrow represents the antiparticle, in these cases a positron.

Feynman diagram for strong interaction

Gluon-mediated interaction between two quarks

The Weak Force

the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z. Since the mass of these particles is on the order of 80 GeV, the uncertainty principle dictates a range of about 10-18 meters which is about 0.1% of the diameter of a proton.

It was in radioactive decay such as beta decay that the existence of the weak interaction was first revealed. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton - the so-called "flavor changes".

The weak force

The weak interaction acts between both quarks and leptons, whereas the strong force does not act between leptons. "Leptons have no color, so they do not participate in the strong interactions; neutrinos have no charge, so they experience no electromagnetic forces; but all of them join in the weak interactions."(Griffiths)

It is crucial to the structure of the universe in that

1. The sun would not burn without it since the weak interaction causes the transmutation p -> n so that deuterium can form and deuterium fusion can take place.2. It is necessary for the buildup of heavy nuclei.

the decay of the muon

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Feynman diagram for weak force

A free neutron will decay by emitting a W-, which produces an electron and an antineutrino.

A neutron or proton can interact with a neutrino or antineutrino by the exchange of a Z0.

Feynman diagram for weak force

This interaction is the same as the one at left since a W+ going right to left is equivalent to a W- going left to right.

When a neutrino interacts with a neutron, a W- can be exchanged, transforming the neutron into a proton and the neutrino into an electron.

the weak interaction with quarks

Feynman diagram for the four fundamental forces

Fundamental forces