Space, time & Cosmos
Lecture 7:
Atom, nucleus and quantum
theory
Dr. Ken Tsang
1
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.
2
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.
3
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.
4
Plato’s 4 elements
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.
Plato assumed that the minute particle of each element had a special geometric shape:
tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).
5
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 (10581111).
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.
6
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).
7
John Dalton
(1766-1844)
8
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. 9
Background of Dalton's Atomic
Theory
• 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.
10
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.
11
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.
12
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.
13
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.
14
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).
15
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.
16
Mendeleev first trained as a teacher in the
Pedagogic Institute of St. Petersburg before
earning an advanced degree in chemistry in 1856.
17
Table from Mendeleev's 1869 paper
18
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.
19
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.
20
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
21
22
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.
23
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
24
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 crossshaped target is
projected against
the tube face at right
by a beam of
electrons.
25
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.
26
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.
27
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)
28
Discovery of the nucleus
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).
• 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.
29
Rutherford's scattering experiment
30
Rutherford’s
gold foil experiment
Top: 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.
31
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.
32
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.
33
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.
34
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).
35
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.
36
Discovery of proton
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.
37
A schematic picture of the hydrogen atom.
There is a single particle, proton, in the
nucleus.
electron
proton
38
Discovery of neutron
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.
39
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.
40
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:
41
Isotopes – same atomic number but different mass
number (same element, with different nuclei)
42
Isotopes of elements
Carbon-12: 6 protons + 6 neutrons
43
Structure of atomic nuclei
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
44
45
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.
46
Properties of stable nuclides
• The stable nuclides lie in a very narrow band of neutron-toproton 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.
47
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.
48
The origin of radioactivity
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 alpha particles discovered by Rutherford are identified to be just
the nucleus of helium.
The beta particles are proved to be electrons.
49
Three Types of Radioactive
Decay: Alpha Decay
usually restricted to the heavier elements in the periodic table
50
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
51
Gamma Decay
The 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.
52
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.
53
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.
54
Dec. 24, 1936: Radiation Used to Treat Disease for the
First Time, marking the birth of nuclear medicine.
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.
55
Radiation therapy with radioactive isotope
Veterinary Technicians
prepare a patient (dog) for
radiation therapy. The
Cobalt-60 radiation source is
located in the mechanical
arm above the patient.
56
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.
57
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).
58
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.
59
Animation of interference of waves
coming from two point sources.
If light is a kind of
wave, light will
exhibit interference
phenomena as well.
60
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.
61
Double-slit experiment with a laser beam
62
Single-slit diffraction
pattern
Double-slit diffraction and
interference pattern
63
Thomas Young's sketch of two-slit diffraction,
which he presented to the Royal Society in 1803
64
The intensity pattern formed on a screen by
diffraction from a square aperture
65
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).
66
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.
67
The Ultraviolet catastrophe
However, 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.
68
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.
69
Planck's constant
Classical 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)
70
Photoelectric effect
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.
71
Photons
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.
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.
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.
72
Photons & Photoelectric effect
The 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 or photovoltaic cell is a device that converts
sunlight directly into electricity by the photovoltaic
effect. A solar cell made from a monocrystalline silicon wafer
A CCD image sensor on a flexible circuit board
Silicon image sensors, such as charge-coupled devices,
widely used for photographic imaging, are based on a
variant of the photoelectric effect.
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Bohr’s Atomic model
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.
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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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Emission spectrum of
hydrogen atom
Electronic energy level diagram for a 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 and Transmission
Electron Microscope (TEM)
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.
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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Quantum wave function of
hydrogen atom
N=3, l=2
Bohr model for hydrogen
atom
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Hydrogen molecule
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.
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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/chemvi
z/index.html)
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Superposition principle of wave
Superposition 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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Superposition in probability
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:
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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Wave-particle duality - Light too!
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).
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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 decoherence. 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 Cat
Schrödinger 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-andalive 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
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.
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.
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Scanning tunneling microscope
Image of reconstruction on a
clean Gold(100) surface.
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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 - finance
Inspired 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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Influence of QM – quantum
computer
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.
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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.
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