Space, time & Cosmos Lecture 7: Atom, nucleus and quantum theory

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Space, time & CosmosLecture 7:

Atom, nucleus and quantum theory

Dr. Ken Tsang

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Ancient (Philosophical) Atomism

• The earliest known theories were developed in ancient India in the 6th century BCE by Kanada, a Hindu philosopher.

• Leucippus and Democritus, Greek philosophers in the 5th century BCE, presented their own theory of atoms.

• Little is known about Leucippus, while the ideas of his student Democritus—who is said to have taken over and systematized his teacher's theory—are known from a large number of reports.

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Greek Atomism• These ancient atomists theorized that the two fundamental

and oppositely characterized constituents of the natural world are indivisible bodies—atoms—and void.

• The latter is described simply as nothing, or emptiness.• Atoms are solid and impenetrable bodies, and intrinsically

unchangeable; they can only move about in the void and combine into different clusters.

• Since the atoms are separated by void, they cannot fuse, but must rather bounce off one another when they collide.

• All macroscopic objects are in fact combinations of atoms. Everything in the macroscopic world is subject to change, as their constituent atoms shift or move away. Thus, while the atoms themselves persist through all time, everything in the world of our experience is transitory and subject to dissolution.

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Plato and Platonists

• Plato, a Greek philosopher, presented a different kind of physical theory based on indivisibles.

• In this theory, it is the elemental triangles composing the solids that are regarded as indivisible, not the solids themselves.

• The term elements (stoicheia) was first used by Plato in about 360 BC, in his dialogue Timaeus, which includes a discussion of the composition of inorganic and organic bodies and is a rudimentary treatise on chemistry.

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Plato’s 4 elements

Plato assumed that the minute particle of each element had a special geometric shape: tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).

Plato's Timaeus conjectures on the composition of the four elements which the ancient Greeks thought made up the universe: earth, water, air, and fire.

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Islamic Atomism

During the 11th century (in the Islamic Golden Age), Islamic atomists developed atomic theories that represent a synthesis of both Greek and Indian atomism.

The most successful form of Islamic atomism was in the Asharite school of philosophy, most notably in the work of the philosopher al-Ghazali (1058-1111).

In Asharite atomism, atoms are the only perpetual, material things in existence, and all else in the world is “accidental” meaning something that lasts for only an instant.

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Modern atomic theory• In the early years of the 19th century, John

Dalton developed the first useful atomic theory of matter around 1803 in which he proposed that each chemical element is composed of atoms of a single, unique type, and that though they are both immutable and indestructible, they can combine to form more complex structures (chemical compounds).

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John Dalton (1766-1844)

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Background of Dalton's Atomic Theory• Less than twenty years earlier, in the 1780's, Antoine

Lavoisier ushered in a new chemical era by making careful quantitative measurements which allowed the compositions of compounds to be determined with accuracy. He formulated the Law of conservation of mass in 1789, which states that the total mass in a chemical reaction remains constant (that is, the reactants have the same mass as the products). This law suggested to Dalton that matter is fundamentally indestructible.

• By 1799 enough data had been accumulated for Proust to establish the Law of Constant Composition ( also called the Law of Definite Proportions). This law states that if a compound is broken down into its constituent elements, then the masses of the constituents will always have the same proportions, regardless of the quantity or source of the original substance. He had synthesized copper carbonate through numerous methods and found that in each case the ingredients combined in the same proportions as they were produced when he broke down natural copper carbonate.

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• In 1803 Dalton noted that oxygen and carbon combined to make two compounds.  Of course, each had its own particular weight ratio of oxygen to carbon (1.33:1 and 2.66:1), but also, for the same amount of carbon, one had exactly twice as much oxygen as the other. This led him to propose the Law of Simple Multiple Proportions, which was later verified by the Swedish chemist Berzelius.

• In an attempt to explain how and why elements would combine with one another in fixed ratios and sometimes also in multiples of those ratios, Dalton formulated his atomic theory.

Background of Dalton's Atomic Theory

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Five main points of Dalton's Atomic Theory

• Chemical Elements are made of tiny particles called atoms

• All atoms of a given element are identical • The atoms of a given element are different from those of

any other element • Atoms of one element can combine with atoms of other

elements to form compounds. A given compound always has the same relative numbers of types of atoms.

• Atoms cannot be created, divided into smaller particles, nor destroyed in the chemical process. A chemical reaction simply changes the way atoms are grouped together.

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Additional work of Dalton

• In 1803 Dalton published his first list of relative atomic weights for a number of substances (though he did not publicly discuss how he obtained these figures until 1808).

• Dalton estimated the atomic weights according to the mass ratios in which they combined, with hydrogen being the basic unit.

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Distinction of Atoms and Molecules

• In 1811, Avogadro published an article in Journal de physique that clearly drew the distinction between the molecule and the atom. He pointed out that Dalton had confused the concepts of atoms and molecules. That was why Dalton wrongly concluded water as HO, not H2O.

• Avogadro suggested that: equal volumes of all gases at the same temperature and pressure contain the same number of molecules which is now known as Avogadro's Principle. In other words, the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules regardless of the nature of the gas,and the mass of a gas's particles does not affect its volume.

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Avogadro's number• Avogadro's Principle allowed him to deduce the diatomic

nature of numerous gases by studying the volumes at which they reacted.

• For instance: since two litres of hydrogen will react with just one litre of oxygen to produce two litres of water vapor (at constant pressure and temperature). Thus two molecules of hydrogen can combine with one molecule of oxygen to produce two molecules of water.

• It meant a single oxygen molecule splits in two in order to form two particles of water. Thus, Avogadro was able to offer more accurate estimates of the atomic mass of oxygen and various other elements, and firmly established the distinction between molecules and atoms.

• Avogadro's number is the number of "elementary entities" (usually atoms or molecules) in one mole. For example. the number of atoms in exactly 12 grams of carbon-12 is 6.022X10^23.

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Brownian motion: molecules in motion

• In 1827, the British botanist Robert Brown observed that dust particles floating in water constantly jiggled about for no apparent reason.

• In 1905, Albert Einstein theorized that this Brownian motion was caused by the water molecules continuously knocking the grains about, and developed a hypothetical mathematical model to describe it.

• This model was validated experimentally in 1911 by French physicist Jean Perrin, thus providing additional validation for particle theory (and by extension atomic theory).

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Mendeleev's Periodic table of Elements

• SCIENTISTS HAD IDENTIFIED over 60 elements by Mendeleev's time (Today over 110 elements are known).

• In Mendeleev's day (1834-1907). the atom was considered the most basic particle of matter. The building blocks of atoms (electrons, protons, and neutrons) were discovered only later. What Mendeleev and chemists of his time could determine, however, was the atomic weight of each element: how heavy its atoms were in comparison to an atom of hydrogen, the lightest element.

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Mendeleev first trained as a teacher in the Pedagogic Institute of St. Petersburg before

earning an advanced degree in chemistry in 1856.

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Table from Mendeleev's 1869 paper

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Mendeleev’s work

AN OVERALL UNDERSTANDING of how the elements are related to each other and why they exhibit their particular chemical and physical properties was slow in coming.

Between 1868 and 1870, in the process of writing his book, The Principles of Chemistry, Mendeleev created a table or chart that listed the known elements according to increasing order of atomic weights.

When he organized the table into horizontal rows, a pattern became apparent--but only if he left blanks in the table. If he did so, elements with similar chemical properties appeared at regular intervals--periodically--in vertical columns on the table.

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Mendeleev’s contribution

• Mendeleev was bold enough to suggest that new elements not yet discovered would be found to fill the blank places. He even went so far as to predict the properties of the missing elements.

• Although many scientists greeted Mendeleev's first table with skepticism, its predictive value soon became clear.

• The discovery of gallium in 1875, of scandium in 1879, and of germanium in 1886 supported the idea underlying Mendeleev's table. Each of the new elements displayed properties that accorded with those Mendeleev had predicted, based on his realization that elements in the same column have similar chemical properties.

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Mendeleev said:

“I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and this soon convinced me that the properties of elements are in periodic dependence upon their atomic weights.” --Mendeleev, Principles of Chemistry, 1905, Vol. II

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WHAT MADE Mendeleev’sTABLE PERIODIC?

• The value of the table gradually became clear, but not its meaning. Scientists soon recognized that the table's arrangement of elements in order of atomic weight was problematic.

• The atomic weight of the gas argon, which does not react readily with other elements, would place it in the same group as the chemically very active solids lithium and sodium.

• In 1913 British physicist Henry Moseley confirmed earlier suggestions that an element's chemical properties are only roughly related to its atomic weight (now known to be roughly equal to the number of protons plus neutrons in the nucleus).

• What really matters is the element's atomic number-the number of electrons its atom carries, which Moseley could measure with X-rays. Ever since, elements have been arranged on the periodic table according to their atomic numbers.

• The structure of the table reflects the particular arrangement of the electrons in each type of atom. Only with the development of quantum mechanics in the 1920s did scientists work out how the electrons arrange themselves to give the element its properties.

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Discovery of subatomic particles

• Electron - J. J. Thomson 1896• Radioactivity - Henri Becquerel 1896• Alpha & beta particles - Ernest

Rutherford 1899• Nucleus - Ernest Rutherford 1907• Isotopes - J. J. Thomson 1913• Proton - Ernest Rutherford 1918• Neutron - James Chadwick 1932

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During the 1870s, English chemist and physicist Sir William Crookes developed the first cathode ray tube to have a high vacuum inside.[19] He then showed that the luminescence rays appearing within the tube carried energy and moved from the cathode to the anode. Furthermore, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged.

Experiments with Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the cross-shaped target is projected against the tube face at right by a beam of electrons.

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Joseph John Thomson, (1856 –1940) His discoveryof electron was made known in 1897, resulting in him being awarded a Nobel Prize in Physics in 1906.

In 1896, British physicist J. J. Thomson, with his colleagues John S. Townsend and H. A. Wilson, performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. Thomson made good estimates of both the charge e and the mass m, finding that cathode ray particles, which he called "corpuscles," had perhaps one thousandth of the mass of the least massive ion known: hydrogen.

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Contribution of J. J. Thomson • He showed that atoms could be further

subdivided into negative (which he named electrons) and positive components.

• He postulated a "Plum Pudding" model for atoms. He calculated the charge to mass ratio (e/m) for the electron by careful observations of the curvature of an electron beam in cathode ray tubes in a magnetic field.

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Measurement of Electronic charge

• Millikan calculated the charge on the electron with his famous oil drop experiment. He measured the static electrical charge on microscopic oil droplets by balancing droplets between charged plates.

• He was awarded the Nobel Prize in Physics (1923)

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Discovery of the nucleus

• They discovered that the particles bounced off of something dense in the foil.

• From this experiment Rutherford postulated that atoms are formed of a small dense positively charged nucleus "orbited" by negatively charged electrons. This led him to his theory that most of the atom was made up of 'empty space'.

• Ernest Rutherford (1871-1937) was Nobel Prize winner in 1908.

In a classic experiment by Hans Geiger and Ernest Marsden in 1907, under the direction of Ernest Rutherford at the Physical Laboratories of the University of Manchester, a thin sheet of gold foil was bombarded with alpha particles (He nuclei: 2 protons + 2 neutrons).

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Rutherford's scattering experiment

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Rutherford’s gold foil experimentTop: Expected results: alpha particles passing

through the plum pudding model of the atom with negligible deflection.

Bottom: Observed results: a small portion of the

particles were deflected, indicating a small,

concentrated positive charge.

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Discovery of isotopes

• In 1913, J. J. Thomson channeled a stream of neon ions through magnetic and electric fields, striking a photographic plate on the other side. He observed two glowing patches on the plate, which suggested two different deflection trajectories.

• Thomson concluded this was because some of the neon ions had a different mass; thus did he discover the existence of isotopes.

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J. J. Thomson had shown in 1897 that charged particles could be deflected by magnetic and electric fields and that the degree of the deflection depends upon the masses and electric charges of the particles. In the mass spectrometer, gas of an element enter the device and are ionized. The ions are then accelerated through a magnetic field which bends the ion paths into a semicircular shape. The radius of this path is dependent upon the mass of the particle. Thus isotopes of different masses can be separated.

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Radioactivity• In 1896, Henri Becquerel discovered

that a sample of uranium was able to expose a photographic plate even when the sample and plate were separated by black paper. He also discovered that the exposure of the plate did not depend on the chemical state of the uranium (what uranium compound was used) and therefore must be due to some property of the uranium atom itself.

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After Becquerel abandoned this work, it was continued by Pierre and Marie Curie who went on to discover other radioactive elements including polonium, radium and thorium. In 1903, Marie and Pierre Curie were awarded half the Nobel Prize in Physics. Henri Becquerel was awarded the other half for his discovery of spontaneous radioactivity.

She (Pierre was hit by a truck and killed in the middle of this work on 19 April 1906 ) further suggested that the uranium, and the new elements, were somehow disintegrating over time and emitting radiation that exposed the plate. She called this phenomenon "radioactivity". For the first time it became apparent that atoms might be composed of even smaller particles and might have a structure that could be analyzed.

Marie Curie was the first woman to win a Nobel prize and the first person to win two Nobel Prizes (Nobel Prize in Chemistry 1911).

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After determining that the radiation emitted from uranium was composed of two

different components, eventually Ernest Rutherford in 1899 , using two oppositely charged plates, he identified the components as positive particles (alpha particles) and lighter mass negative particles (beta particles).

Paul Villard in 1900 identified a third primary type of radioactivity, gamma rays, from a radium sample. Gamma rays have no mass and possess no charge. The behavior of the three types of particles as they pass through the electric field between two charged plates is shown below.

While alpha particles were determined to have a larger charge than the beta particles (+2 vs. -1), they also have over 7000 times the mass of the beta particle. Therefore, their path is bent much less than that of the beta particle.

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Rutherford's discovery of the nucleus demonstrated that these positive charges were concentrated in a very small fraction of the atoms' volume. In 1919 Rutherford discovered that he could change one element into another by striking it with energetic alpha particles (which we now know are just helium nuclei). In the early 1920's Rutherford and other physicists made a number experiments, transmuting one atom into another. In every case, hydrogen nuclei were emitted in the process.

It was apparent that the hydrogen nucleus played a fundamental role in atomic structure, and by comparing nuclear masses to charges, it was realized that the positive charge of any nucleus could be accounted for by an integer number of hydrogen nuclei. He thus suggested that the hydrogen nucleus, which was known to have an atomic number of 1, was an elementary particle.

By the late 1920's physicists were regularly referring to hydrogen nuclei as 'protons'. The term proton itself seems to have been coined by Rutherford, and first appears in print in 1920.

Discovery of proton

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proton

electron

A schematic picture of the hydrogen atom. There is a single particle, proton, in the nucleus.

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As of 1930, only two known elementary particles had been identified, the proton and the electron. Protons were known to have a mass of 1 and a charge of +1, while electrons had essentially no mass and a charge of -1. Moseley had shown convincingly that the charge on the nucleus increases in steps of +1 as one traverses the periodic table. To account for this it was apparent that the nucleus of each atom contained a number of protons equal to its atomic number. In order to remain electrically neutral, it also contained an equivalent number of electrons.

The problem of the extra nuclear mass was solved in 1932 when James Chadwick

identified the neutron. While studying the radiation resulting from the bombardment of beryllium with alpha particles, Chadwick noted a particle with approximately the same mass as a proton being released. He determined that, as the particle was not bent by electrical fields and was highly penetrating, it was electrically neutral.

Discovery of neutron

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After the discovery of neutron, scientist know there are three smaller particles that make up individual atoms. These are called subatomic particles as they are below the level of the atom in size.

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The protons and neutrons are clumped together in the middle of an atom to form the nucleus and the electrons orbit around the outside. While this seems to contradict the idea that like charges repel, scientists have established that though protons (+) do indeed repel each other, once they are very close to each other another force, called the Strong Force, takes over and glues them together.

As an example, for a Helium atom the structure is like this:

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Isotopes – same atomic number but different mass number (same element, with different nuclei)

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Isotopes of elements

Carbon-12: 6 protons + 6 neutrons

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The atomic nuclei of all chemical elements consist of protons (p) and of neutrons (n). These two fundamental particles, which are summarised by

the term nucleons, have almost the same mass (p: 1.00727 amu; n: 1.00866 amu), but only the protons are electrically charged (+1 e). In an

atom, the number of protons indicates the atomic number (symbolised

Z) of the corresponding element, while its mass number (symbolised A) is equal to the sum of protons and neutrons.

1 atomic mass unit = 1.66053886 × 10^(-27) kilograms

Structure of atomic nuclei

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Graph of the number of neutrons versus the number of protons for all stable naturally occurring nuclei. Nuclei that lie to the right of this band of stability are neutron poor; nuclei to the left of the band are neutron-rich. The solid line represents a neutron to proton ratio of 1:1.

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Properties of stable nuclides• The stable nuclides lie in a very narrow band of neutron-to-

proton ratios. • The ratio of neutrons to protons in stable nuclides gradually

increases as the number of protons in the nucleus increases.

• Light nuclides, such as 12C, contain about the same number of neutrons and protons. Heavy nuclides, such as 238U, contain up to 1.6 times as many neutrons as protons.

• There are no stable nuclides with atomic numbers larger than 83.

• This narrow band of stable nuclei is surrounded by a sea of instability.

• Nuclei that lie above this line have too many neutrons and are therefore neutron-rich.

• Nuclei that lie below this line don't have enough neutrons and are therefore neutron-poor.

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Larger nucleus need more neutrons to maintain stability. However, there is no stable nucleus beyond Z>83, no matter how many neutrons are inside the nucleus.

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The alpha particles discovered by Rutherford are identified to be just the nucleus of helium.

The beta particles are proved to be electrons.

Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting particles and radiation to reach a more stable nuclear configuration. This decay results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.

The origin of radioactivity

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Three Types of Radioactive Decay: Alpha Decay

usually restricted to the heavier elements in the periodic table

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Beta Decay is the process

in which an electron is ejected or emitted from the nucleus

When this happens, the charge on the nucleus increases by one

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Gamma DecayThe daughter nuclides produced by alpha-decay or beta-decay are often left in an excited state. The excess energy associated with this excited state is released when the nucleus emits a photon in the gamma-ray portion of the electromagnetic spectrum.

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Alpha radiation consists of helium-4 nucleus and is readily stopped by a sheet of paper. Beta radiation, consisting of electrons, is halted by an aluminum plate. Gamma radiation is eventually absorbed as it penetrates a dense material. Lead is good at absorbing gamma radiation, due to its density.

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Radiation therapy• Even radioactivity can induce cancer in a living organism, controlled

application of nuclear radiations are successfully employed in the treatment of certain cancers.

• Radiation therapy is the use of a certain type of (ionizing) radiation to kill cancer cells and shrink tumors that cannot be safely or completely removed by surgery. It is also used to treat cancers that are not affected by chemotherapy.

• Radiation therapy injures or destroys cells in the area being treated (the “target tissue”) by damaging their genetic material, making it impossible for these cells to continue to grow and divide.

• Radiation damages both cancer cells and normal cells. However, most normal cells can recover from the effects of radiation and function properly. The goal of radiation therapy is to damage as many cancer cells as possible, while limiting harm to nearby healthy tissue.

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An image of a patient undergoing radiation therapy for a tumor in her head. Her head is stabilized by a steel frame while a linear accelerator hidden behind the wall fires radiation at the tumor.

Dec. 24, 1936: Radiation Used to Treat Disease for the First Time, marking the birth of nuclear medicine.

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Veterinary Technicians prepare a patient (dog) for radiation therapy. The Cobalt-60 radiation source is located in the mechanical arm above the patient.

Radiation therapy with radioactive isotope

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Dating By Radioactive Decay • Just after World War II, Willard F. Libby proposed a way to

use Radioactive Decay of C14 to estimate the age of carbon-containing substances. The C14 dating technique for which Libby received the Nobel prize was based on the following assumptions. – C14 is produced in the atmosphere at a more or less constant rate. – Carbon atoms circulate between the atmosphere, the oceans, and

living organisms at a rate very much faster than they decay. As a result, there is a constant concentration of 14C in all living things.

– After death, organisms no longer pick up 14C.

• By comparing the activity of a sample with the activity of living tissue we can estimate how long it has been since the organism died.

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Introduction to quantum mechanics• 1900 - Max Planck's landmark paper on black body

radiation.• 1905 - Albert Einstein extended Planck's theory to explain

the photoelectric effect.• 1913 - Niels Bohr introduced his model of the atom,

incorporating Planck's quantum hypothesis.• 1924 - Louis de Broglie proposed the matter-wave

hypothesis• 1925, Heisenberg introduced matrix mechanics &

Heisenberg's Uncertainty Principle• 1926 - Erwin Schrödinger analyzed how an electron would

behave if it were assumed to be a wave surrounding a nucleus (Schrödinger's equation).

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Light : Wave–particle duality• In the 1600s, competing theories of light were

proposed by Christiaan Huygens and Isaac Newton: light was thought either to consist of waves (Huygens) or of particle (Newton).

• Light was believed to be a wave, after Thomas Young's double-slit interference experiment and effects such as diffraction had clearly demonstrated the wave-like nature of light.

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Animation of interference of waves coming from two point sources.

If light is a kind of wave, light will exhibit interference phenomena as well.

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Interference pattern produced with a Michelson interferometer. Bright bands are the result of constructive interference while the dark bands are the result of destructive interference.

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Double-slit experiment with a laser beam

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Double-slit diffraction and interference pattern

Single-slit diffraction pattern

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Thomas Young's sketch of two-slit diffraction, which he presented to the Royal Society in 1803

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The intensity pattern formed on a screen by diffraction from a square aperture

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Thin Film interference (soap film)

This demonstration shows the interference effects of thin films. If the film survives to a point where it is less then 1/4 of a wavelength of light, no light will be reflected which is characterized by a black part (see picture).

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So light is a form of wave!

• In the late 1800s, James Clerk Maxwell explained light as the propagation of electromagnetic waves according to the Maxwell equations. These equations were verified by experiment by Heinrich Hertz in 1887, and the wave theory became widely accepted.

• During the late nineteenth century, no one ever doubled that light is a form of wave.

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The Ultraviolet catastropheHowever, in late 19th century/early 20th century classical

physics led to the prediction that an ideal black body at thermal equilibrium will emit radiation with infinite power. This error is embodied in the Rayleigh–Jeans law for the energy emitted by an ideal black-body at short wavelengths.

In 1901, Max Planck published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object. To accomplish this, Planck had to make a mathematical assumption of quantized energy of the oscillators (atoms of the black body) that emit radiation.

It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized, and not the energy of radiating atoms.

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As the temperature decreases, the peak of the

black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.

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Planck's constantClassical physics predicted that a black-body radiator would

emit an infinite amount of energy. Not only was this prediction absurd, but the observed emission spectrum of a black-body rose from zero at one end, peaked at a frequency related to the temperature of the radiator, and then declined to zero.

In 1900, Max Planck developed an empirical equation that could account for the observed emission spectra of black bodies assuming that the energy E of any one oscillator was proportional to some integral multiple of its frequency f,

where n =1, 2, 3,... h is a fundamental physical constant first proposed by Planck and now named Planck's constant in his honor. (h is exceedingly small, about 6.6260693 × 10-34 joule-seconds)

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When a metallic surface is exposed to electromagnetic radiation above a certain threshold frequency (typically visible light), the light is absorbed and electrons are emitted. In 1902, Philipp Eduard Anton von Lenard observed that the energy of individual emitted electrons increased with the frequency, or color, of the light. This was at odds with James Clerk Maxwell's wave theory of light, which predicted that the electron energy would be proportional to the intensity (amplitude) of the radiation.

Photoelectric effect

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In 1905, Einstein proposed the simple description of "light quanta“, introduced by Max Planck in 1900, or photons, and showed how they explained the photoelectric effect.

Photons

Einstein was awarded the 1921 Nobel Prize in Physics, "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". He got the Nobel Prize not for his theories of Relativity.

Electrons can absorb energy from photons when irradiated, but they follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding.

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Photons & Photoelectric effectThe photons of a light beam have a characteristic energy determined by the frequency of the light. In the photoemission process, if an electron within some material absorbs the energy of one photon and thus has more energy than the work function (the electron binding energy) of the material, it is ejected. If the photon energy is too low, the electron is unable to escape the material. Increasing the intensity of the light beam increases the number of photons in the light beam, and thus increases the number of electrons emitted, but does not increase the energy that each electron possesses. Thus the energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy of the individual photons.

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A solar cell made from a monocrystalline silicon wafer

A solar cell or photovoltaic cell is a device that converts sunlight directly into electricity by the photovoltaic effect.

Silicon image sensors, such as charge-coupled devices, widely used for photographic imaging, are based on a variant of the photoelectric effect.

A CCD image sensor on a flexible circuit board

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In 1913, Niels Bohr depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity.

Bohr’s Atomic model

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Bohr proposed a model for the hydrogen atom that explained the spectrum of the

hydrogen atom.

The Bohr model was based on the following assumptions. • The electron in a hydrogen atom travels around the nucleus in a

circular orbit. • The energy of the electron in an orbit is proportional to its distance

from the nucleus. The further the electron is from the nucleus, the more energy it has.

• Only a limited number of orbits with certain energies are allowed. In other words, the orbits are quantized.

• The only orbits that are allowed are those for which the angular momentum of the electron is an integral multiple of Planck's constant divided by 2pi.

• Light is absorbed when an electron jumps to a higher energy orbit and emitted when an electron falls into a lower energy orbit.

• The energy of the light emitted or absorbed is exactly equal to the difference between the energies of the orbits.

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Bohr won the Nobel Prize in Physics (1922) for his atomic model.

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Emission Spectrum of Hydrogen

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When a sample composed of a pure chemical element emits light by heating or other agency, the spectrum of the emitted light, called the emission spectrum, is peculiar to that element and the temperature to which it is heated. Unlike the spectrum of white light, an emission spectrum is not a wide band composed of all the colours from indigo to red, but instead consists of narrow bands, each of a single colour and separated from other bands by darkness. Such a display is called a line spectrum.

The bright-line spectrum of hydrogen & nitrogen

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83Electronic energy level diagram for a hydrogen atom

Emission spectrum of hydrogen atom

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De Broglie (matter) wave In 1924, Louis-Victor de Broglie formulated the de

Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature; he related wavelength (denoted as λ), and momentum (denoted as p):

De Broglie's formula was confirmed three years later for electrons (which differ from photons in having a rest mass) with the observation of electron diffraction in two independent experiments.

De Broglie was awarded the Nobel Prize for Physics in 1929 for his hypothesis.

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Electron diffraction of solids is usually performed in a Transmission Electron Microscope (TEM) where the electrons pass through a thin film of the material to be studied.

Electron diffraction and Transmission Electron Microscope (TEM)

Typical electron diffraction pattern obtained in a TEM with a parallel electron beam

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Transmission electron microscope

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A TEM image of the polio virus. The polio virus is between 30 and 230 nm in size.

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Wave-particle duality

• Light – Wave? Particle?

• Electron, proton … - Wave? Particle?

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Full quantum mechanical theory• De Broglie’s matter-wave hypothesis (1924)

quickly led to a more sophisticated and complete variant of atomic theory called the "new quantum mechanics" with important contributors like: Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger.

• In 1925, Werner Heisenberg (won the Nobel Prize in Physics in 1932) developed the matrix mechanics formulation of quantum mechanics.

• In 1926 Erwin Schrödinger published the Schrödinger equation and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. He won the Nobel Prize in Physics in 1933.

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Matrix mechanics & Schrödinger's equation

• Matrix mechanics was the first complete and correct definition of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices that evolve in time.

• Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics.

• In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger's equation describe not only atomic and subatomic systems, electrons and atoms, but also macroscopic systems.

• Schrödinger's equation can be mathematically transformed into Heisenberg's matrix mechanics.

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Wave functions

A wave function is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (i.e. the Schrödinger equation) describe how the wave function evolves over time. The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states.

It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where | ψ | 2 is equal to the chance of finding the subject at a certain time and position.

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Eigen-state & eigen-energy of the Schrödinger equation

Time-independent Schrödinger equation in quantum mechanics:

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The wavefunctions associated with the bound states of an electron in a hydrogen atom

Electron orbitals - The regions around the nucleus of the atoms where the electron "probability wave" resides. These replace Rutherford's or Bohr’s model of electron orbits.

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The electron wavefunctions for the first few hydrogen atom eigen-states

N=1, l=0 N=2, l=1

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N=3, l=2

Bohr model for hydrogen atom

Quantum wave function of hydrogen atom

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As two atoms of hydrogen come together the positively charged atomic centers begin to attract both electrons (their own and the one in the other atom). At a certain distance apart, the orbitals overlap and merge into a single, larger molecular orbital in which the pair of electrons distribute themselves over the pair of atomic centers.

Hydrogen molecule

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Quantum chemistry• Properties of all chemical compound can be

obtained from solution of the time-independent Schrödinger equation.

• For example: ChemViz (Chemistry Visualization) is an interactive chemistry program which incorporates computational chemistry simulations and visualizations for use in the chemistry classroom. The chemistry simulations support the chemistry principles teachers are trying to convey, and the visualizations allow students to see how matter interacts at an atomic level. (http://education.ncsa.illinois.edu/products/chemviz/index.html)

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Superposition principle of waveSuperposition of almost plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water.

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In probability theory with a finite number of states, the probabilities can always be multiplied by a positive number to make their sum equal to one. For example, if there is a three state probability system:

Superposition in probability

where the probabilities x,y,z are positive numbers and

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Quantum Superposition

Quantum Superposition is a principle of quantum theory that describes a challenging concept about the nature and behavior of matter at the sub-atomic level.

The principle of superposition claims that while we do not know what the state of any object (e.g. an electron) is, it is actually in all possible states simultaneously, as long as we don't look to check. It is the measurement itself that causes the object to be limited to a single possibility.

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Double-slit experiment for electron

This experiment is fundamental to all of modern physics. It cannot be explained by any classical means.

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If the electrons were classical particles, the 2-slit experiment would be like shooting a machine gun at an iron plate with two slots in it. If there were a concrete wall behind the iron plate, what kind of pattern do you think the bullets would make?

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In the experiment, electrons are emitted from a source and travel past a doubly-slit wall region on their way to a screen. The apparatus is shielded against light. If one believes that the emitted electron is a little three-dimensional particle, much like a tiny baseball, then it should go through one of the slits and not the other. It would then hit the screen at one of the two spots indicated as the expected distribution, with a little scatter from those that chip the edge of the slit a bit. Electrons which do not hit the holes but strike the wall are absorbed.    We do not get this expected pattern. Instead, the pattern is essentially the same as the one we would get if each electron were a wavefront passing through both slits at once. However, each electron still strikes the screen in only one point; the distribution of these points fits the actual distribution pattern shown.

In this case the electron wavefunction is the sum of 2 states, i.e. i = 1 or 2, representing 2 possible states that the electron either passing slit-1 or slit-2.

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Two-slit experiments reveal that photons, the quantum entities giving rise to light and other forms of electromagnetic radiation, act both like particles and like waves. A single photon will strike the screen in a particular place, like a particle (left)- But as more photons strike the screen, they begin to create an interference pattern (center). Such a pattern could occur only if each photon had actually gone through both slits, like a wave (right).

Wave-particle duality - Light too!

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Copenhagen interpretation of quantum mechanics

• In quantum mechanics, the state of every particle (e.g. electron) is described by a wavefunction, which is just a mathematical tool used to calculate the probability for it to be found in a state (of motion) that can be measured by experiment.

• Before the measurement, the wavefunction is a superposition of all possible states that is consistent with the constraint of the system.

• The act of measurement causes the wavefunction to "collapse" to the state defined by the result of the measurement.

• Interpretation first suggested by Bohr and Heisenberg in the course of their collaboration in Copenhagen around 1927.

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Dissatisfaction with Copenhagen interpretation

• God doesn't play dice -- Albert Einstein• Schrödinger's Cat -- Shows that our

consciousness and knowledge are somehow mixed up in the process of observation.

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Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum de-coherence. If an internal Geiger counter detects radiation then the flask is shattered, releasing the poison which kills the cat. Close the box and wait 10 minutes (half life of the Radioactive source). We then ask: Is the cat alive or dead? The answer according to quantum mechanics is that it is 50% dead and 50% alive. Yet, when we look in the box, we see the cat either alive or dead, not a mixture of alive and dead.

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Schrödinger's CatSchrödinger intended to use this thought experiment to highlight the strange nature of quantum superposition. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the box is opened.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse: the thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation—the prevailing orthodoxy in 1935—the Schrödinger cat thought experiment remains a topical touchstone for all interpretations of quantum mechanics; how each interpretation deals with Schrödinger's cat is often used as a way of illustrating and comparing each interpretation's particular features, strengths and weaknesses.

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Heisenberg’s Uncertainty principle• In quantum mechanics, a particle is

described by a wave. The position is where the wave is concentrated and the momentum is the wavelength. The position is uncertain to the degree that the wave is spread out, and the momentum is uncertain to the degree that the wavelength is ill-defined.

•The general form of this principle states that there are certain "complementary" quantities of particles such as position and momentum. These quantities are correlated so that the product of the errors of measurement must be greater than Planks constant.

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Heisenberg's microscope

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If one wants to be clear about what is meant by "position of an object," for example of an electron..., then one has to specify definite experiments by which the "position of an electron" can be measured; otherwise this term has no meaning at all. --Heisenberg, in uncertainty paper, 1927

Heisenberg's microscope

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Quantum tunneling

Schematic representation of quantum tunneling through a barrier. The energy of the tunneled particle is the same, only the quantum amplitude (and hence the probability of the process) is decreased.

By 1928, George Gamow had solved the theory of the alpha decay of a nucleus via tunneling. Classically, the particle is confined to the nucleus because of the high energy requirement to escape the very strong potential. Under this system, it takes an enormous amount of energy to pull apart the nucleus. In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape. It was later applied to other situations, such as the cold emission of electrons, and perhaps most importantly semiconductor and superconductor physics.

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Image of reconstruction on a clean Gold(100) surface.

Scanning tunneling microscope

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Influence of QM - Philosophy of physics or metaphysics

Interpretations of quantum mechanics are attempts to explain how quantum mechanics change our understanding of nature. Even quantum mechanics has received thorough experimental testing, many of these experiments are open to different interpretations. There exist a number of contending schools of thought, differing over whether quantum mechanics can be understood to be deterministic, which elements of quantum mechanics can be considered "real", and other related matters.

Observation/measurement will interact with and change the physical world. In other words, reality is being affected by the observer. Is there an objective physical world existed independent of the observer?

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Influence of QM - financeInspired by Heisenberg's rule about quantum

particles, George Soros proclaims a human uncertainty principle which suggests our understanding is often incoherent and always incomplete. From his case study, one notices that uncertainty continually besets Mr. Soros in managing his hedge fund, which has the same name as the particles subject to Heisenberg's uncertainty principle. He named the fund he created the Quantum Fund.

Quantum Finance - Quantum theory is used to model secondary financial markets.

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A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition, to perform operations on data. The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data.

Influence of QM – quantum computer

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Influence of QM –Psychology & Neurosciences

Materialistic world-view (scientific materialism) QM Relationship between the conscious of observer and the physical world ??

Sigmund Freud (1856-1939) – brought Psychology into the realm of scientific studies, “The Interpretation of

Dreams” 1900, introduced the concept of conscious and unconscious mind

Carl Jung (1875-1961) – developed Analytical psychology, and the theory of unconscious mind

Quantum psychology – a multidimensional model of self http://www.quantumconsciousness.org/overview.html

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Glossary

• A.D. - "Abbreviation for the term Anno Domini Nostri Jesu Christi (or simply Anno Domini) which means ""in the year of our Lord Jesus Christ.""  Years are counted from the traditionally recognized year of the birth of Jesus.  In academic, historical, and archaeological circles,  A.D. is generally replaced by the term Common Era (C.E.).“

• B.C. - Abbreviation for the term Before Christ.  Years are counted back from the traditionally recognized year of Christ's birth. In academic, historical, and archaeological circles, this term is now generally  replaced by Before Common Era (B.C.E.).

• B.C.E. - Before Common Era.  See B.C.