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12 Lecture in physics
Homework
wave nature of light
Optical instruments
Theory of Relativity
Quantum Theory and Models of Atom
Quantum Mechanics of Atoms
Molecules and Solids
Nuclear Physics and Radioactivity
Homework is due 10
December 2014. It is
on the web site.
Presentations scores,
analysis.
The wave nature of light
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Huygens’ principle
Interference
Thin films interference
Atmosphere light scattering
Diffraction
CD diffraction
Dispersion
Polarization
Dispersive prism
In optics, a dispersive prism is a type of optical prism, usually having the shape of a
geometrical triangular prism. It is the most widely known type of optical prism,
although perhaps not the most common in actual use. Triangular prisms are used to
disperse light, that is, to break light up into its spectral components (the colors of the
rainbow). This dispersion occurs because the angle of refraction is dependent on the
refractive index of a certain material which in turn is slightly dependent on the
wavelength of light that is travelling through it. This means that different wavelengths
of light will travel at different speeds, and so the light will disperse into the colours of
the visible spectrum, with longer wavelengths (red, yellow) being refracted less than
shorter wavelengths (violet, blue). This effect can also be used to measure the
refractive index of the prism's material with high accuracy. In such a measurement,
the prism is placed on the central rotary platform of an optical spectrometer with the
incident light beam adjusted such that the refracted beam is at minimum deviation.
The refractive index can then be computed using the apex angle and the angle of
minimum deviation.
A good mathematical description single-prism dispersion is given by Born and Wolf
The case of multiple-prism dispersion is treated by Duarte.
Prism dispersion played an important role in understanding the nature of light,
through experiments by Sir Isaac Newton and others.
Optical instruments
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Cameras
f-stop = f/D
Telescopes
Microscopes
Lenses
Normal lens
Telephoto lenses
Wide-angle lens
Zoom lens
Single-lens reflex
Circles of confusion
Depth of field
Picture sharpness
Optical instruments (continued)
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Eye
Iris
pupil
Retina
Fovea
Cornea
Normal eye
Nearsightness
Farsightness
Astigmatism
Optical instruments (continued)
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Underwater vision
Magnifying glass
Angular magnification
Prism
Aberrations
Chromatic aberration
Circle of least confusion
Distortion
Optical instruments (continued)
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Resolution
Aperture
Rayleigh criterion
Hubble Space Telescope
Lambda limit
X-rays
Tomography
Bragg equation
Spying
Special Theory of Relativity
• 1. The laws of physics have the same form in all inertial
reference frames
• 2. Light propagates through empty space with a definite
speed c independent of the speed of the source or
observer
• Reference frames
• Relativity principle
• Ether
• Length contraction
• Time dilation
• Twin paradox
• 4-dimensional space-time
Special Theory of Relativity (continued)
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Relativistic momentum
Relativistic mass
Relativistic velocities addition
GPS
E = mc2
E2 = m2c4 + p2c2
Quantum physics
Quantum computers
Quantum cryptography
Early Quantum Theory and Models of Atom
Electron discovery
Cathode rays
Oil-drop experiment
The oil drop experiment was an experiment performed by Robert A.
Millikan and Harvey Fletcher in 1909 to measure the elementary
electric charge (the charge of the electron).
The experiment entailed balancing the downward gravitational force
with the upward drag and electric forces on tiny charged droplets of oil
suspended between two metal electrodes. Since the density of the oil
was known, the droplets' masses, and therefore their gravitational and
buoyant forces, could be determined from their observed radii. Using a
known electric field, Millikan and Fletcher could determine the charge
on oil droplets in mechanical equilibrium. By repeating the experiment
for many droplets, they confirmed that the charges were all multiples
of some fundamental value, and calculated it to be 1.5924(17)×10−19 C,
within 1% of the currently accepted value of 1.602176487(40)×10−19 C.
They proposed that this was the charge of a single electron.
Planck's Hypothesis
In 1900 Max Planck proposed a formula for the
intensity curve which did fit the experimental
data quite well. He then set out to find a set of
assumptions -- a model -- that would produce
his formula. Instead of allowing energy to be
continuously distributed among all frequencies,
Planck's model required that the energy in the
atomic vibrations of frequency f was some
integer times a small, minimum, discrete energy,
Emin = hf
Planck's Hypothesis (continued)
Molecular oscillations
are quantized: E=nhf,
f is natural frequency
of the oscillation
Black body
A black body is an idealized physical body that
absorbs all incident electromagnetic radiation,
regardless of frequency or angle of incidence. A
white body is one with a "rough surface [that]
reflects all incident rays completely and
uniformly in all directions."
Quantum
In physics, a quantum (plural: quanta) is the minimum
amount of any physical entity involved in an interaction.
Behind this, one finds the fundamental notion that a physical
property may be "quantized," referred to as "the hypothesis
of quantization". This means that the magnitude can take on
only certain discrete values.
A photon is a single quantum of light, and is referred to as a
"light quantum". The energy of an electron bound to an atom
is quantized, which results in the stability of atoms, and hence
of matter in general.
As incorporated into the theory of quantum mechanics, this is
regarded by physicists as part of the fundamental framework
for understanding and describing nature at the smallest
length-scales.
Photon
A photon is an elementary particle, the quantum of light and
all other forms of electromagnetic radiation, and the force
carrier for the electromagnetic force, even when static via
virtual photons. The effects of this force are easily observable
at both the microscopic and macroscopic level, because the
photon has zero rest mass; this allows long distance
interactions. Like all elementary particles, photons are
currently best explained by quantum mechanics and exhibit
wave–particle duality, exhibiting properties of both waves and
particles. For example, a single photon may be refracted by a
lens or exhibit wave interference with itself, but also act as a
particle giving a definite result when its position is measured.
Photoelectric effect
The photoelectric effect is the observation that many metals
emit electrons when light shines upon them. Electrons
emitted in this manner can be called photoelectrons
According to classical electromagnetic theory, this effect can
be attributed to the transfer of energy from the light to an
electron in the metal. From this perspective, an alteration in
either the amplitude or wavelength of light would induce
changes in the rate of emission of electrons from the metal.
Furthermore, according to this theory, a sufficiently dim light
would be expected to show a lag time between the initial
shining of its light and the subsequent emission of an
electron. However, the experimental results did not correlate
with either of the two predictions made by this theory
Compton scattering
Compton scattering is the inelastic scattering of
a photon by a quasi-free charged particle,
usually an electron. It results in a decrease in
energy (increase in wavelength) of the photon
(which may be an X-ray or gamma ray photon),
called the Compton effect. Part of the energy of
the photon is transferred to the recoiling
electron. Inverse Compton scattering also exists,
in which a charged particle transfers part of its
energy to a photon.
Pair production
Pair production is the creation of an elementary particle and its antiparticle,
for example an electron and its antiparticle, the positron, a muon and
antimuon, or a tau and antitau. Usually it occurs when a photon interacts
with a nucleus, but it can be any other neutral boson, interacting with a
nucleus, another boson, or itself. This is allowed, provided there is enough
energy available to create the pair – at least the total rest mass energy of the
two particles – and that the situation allows both energy and momentum to
be conserved. However, all other conserved quantum numbers (angular
momentum, electric charge, lepton number) of the produced particles must
sum to zero – thus the created particles shall have opposite values of each
other. For instance, if one particle has electric charge of +1 the other must
have electric charge of −1, or if one particle has strangeness of +1 then
another one must have strangeness of −1. The probability of pair production
in photon-matter interactions increases with photon energy and also
increases approximately as the square of atomic number.
Wave–particle duality
Wave–particle duality is the concept that every
elementary particle or quantic entity exhibits the
properties of not only particles, but also waves. It
addresses the inability of the classical concepts
"particle" or "wave" to fully describe the behavior
of quantum-scale objects. As Einstein wrote: "It
seems as though we must use sometimes the one
theory and sometimes the other, while at times we
may use either. We are faced with a new kind of
difficulty. We have two contradictory pictures of
reality; separately neither of them fully explains the
phenomena of light, but together they do".
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object;
having its root in the Latin nihil (nothing). A literal translation is "to make into
nothing".
In physics, the word is used to denote the process that occurs when a subatomic
particle collides with its respective antiparticle, such as an electron colliding with a
positron, illustrated here. Since energy and momentum must be conserved, the
particles are simply transformed into new particles. They do not disappear from
existence. Antiparticles have exactly opposite additive quantum numbers from
particles, so the sums of all quantum numbers of the original pair are zero. Hence, any
set of particles may be produced whose total quantum numbers are also zero as long
as conservation of energy and conservation of momentum are obeyed. When a
particle and its antiparticle collide, their energy is converted into a force carrier
particle, such as a gluon, W/Z force carrier particle, or a photon. These particles are
afterwards transformed into other particles.
During a low-energy annihilation, photon production is favored, since these particles
have no mass. However, high-energy particle colliders produce annihilations where a
wide variety of exotic heavy particles are created.
Complementarity
In physics, complementarity is a fundamental principle of
quantum mechanics, closely associated with the
Copenhagen interpretation. It holds that objects have
complementary properties which cannot be measured
accurately at the same time. The more accurately one
property is measured, the less accurately the
complementary property is measured, according to the
Heisenberg uncertainty principle. Further, a full
description of a particular type of phenomenon can only
be achieved through measurements made in each of the
various possible bases — which are thus complementary.
The complementarity principle was formulated by Niels
Bohr, a leading founder of quantum mechanics.
Spectral line
A spectral line is a dark or bright line in an otherwise
uniform and continuous spectrum, resulting from a
deficiency or excess of photons in a narrow frequency
range, compared with the nearby frequencies. Spectral
lines are often used as a sort of "atomic fingerprint," as
gases emit light at very specific frequencies when
exposed to electromagnetic waves, which are displayed in
the form of spectral lines. These "fingerprints" can be
compared to the previously collected fingerprints of
elements, and are thus used to identify the molecular
construct of stars and planets which would otherwise be
impossible.
Bohr model
In atomic physics, the Rutherford–Bohr model or Bohr model,
introduced by Niels Bohr in 1913, 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 attraction provided by electrostatic
forces rather than gravity. After the cubic model (1902), the
plum-pudding model (1904), the Saturnian model (1904), and
the Rutherford model (1911) came the Rutherford–Bohr
model or just Bohr model for short (1913). The improvement
to the Rutherford model is mostly a quantum physical
interpretation of it. The Bohr model has been superseded, but
the quantum theory remains sound.
Stationary state
In quantum mechanics, a stationary state is an
eigenvector of the Hamiltonian, implying the
probability density associated with the
wavefunction is independent of time.[1] This
corresponds to a quantum state with a single
definite energy (instead of a quantum superposition
of different energies). It is also called energy
eigenvector, energy eigenstate, energy
eigenfunction, or energy eigenket. It is very similar
to the concept of atomic orbital and molecular
orbital in chemistry, with some slight differences
Quantum number
Quantum numbers describe values of conserved quantities in the
dynamics of a quantum system. In the case of quantum numbers of
electrons, they can be defined as "The sets of numerical values which
give acceptable solutions to the Schrödinger wave equation for the
Hydrogen atom". Perhaps the most important aspect of quantum
mechanics is the quantization of observable quantities, since quantum
numbers are discrete sets of integers or half-integers, although they
could approach infinity in some cases. This is distinguished from
classical mechanics where the values can range continuously. Quantum
numbers often describe specifically the energy levels of electrons in
atoms, but other possibilities include angular momentum, spin, etc.
Any quantum system can have one or more quantum numbers; it is
thus difficult to list all possible quantum numbers.
Ground state
The ground state of a quantum mechanical system is its lowest-energy
state; the energy of the ground state is known as the zero-point energy
of the system. An excited state is any state with energy greater than
the ground state. The ground state of a quantum field theory is usually
called the vacuum state or the vacuum.
If more than one ground state exists, they are said to be degenerate.
Many systems have degenerate ground states. Degeneracy occurs
whenever there exists a unitary operator which acts non-trivially on a
ground state and commutes with the Hamiltonian of the system.
According to the third law of thermodynamics, a system at absolute
zero temperature exists in its ground state; thus, its entropy is
determined by the degeneracy of the ground state. Many systems,
such as a perfect crystal lattice, have a unique ground state and
therefore have zero entropy at absolute zero. It is also possible for the
highest excited state to have absolute zero temperature for systems
that exhibit negative temperature.
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy
state. In physics there is a specific technical definition for energy level which
is often associated with an atom being excited to an excited state.
In quantum mechanics an excited state of a system (such as an atom,
molecule or nucleus) is any quantum state of the system that has a higher
energy than the ground state (that is, more energy than the absolute
minimum). The temperature of a group of particles is indicative of the level of
excitation (with the notable exception of systems that exhibit Negative
temperature).
The lifetime of a system in an excited state is usually short: spontaneous or
induced emission of a quantum of energy (such as a photon or a phonon)
usually occurs shortly after the system is promoted to the excited state,
returning the system to a state with lower energy (a less excited state or the
ground state). This return to a lower energy level is often loosely described as
decay and is the inverse of excitation.
Matter wave
All matter can exhibit wave-like behaviour. For
example a beam of electrons can be diffracted just
like a beam of light or a water wave. Matter waves
are a central part of the theory of quantum
mechanics, an example of wave–particle duality.
The concept that matter behaves like a wave is also
referred to as the de Broglie hypothesis (/dəˈbrɔɪ/)
due to having been proposed by Louis de Broglie in
1924. Matter waves are often referred to as de
Broglie waves.
Electron microscope
Atomic models
Atomic spectra
Rydberg constant
• Balmer series
• Lyman series
• Paschen series
Photosynthesis chemical equation
6CO2 + 6H2O ------> C6H12O6 + 6O2
Sunlight energy
Where: CO2 = carbon dioxide
H2O = water
Light energy is required
C6H12O6 = glucose
O2 = oxygen
Tλ =
-3
3×10
mK
h=
-24
7×10
Js
E=hf
E=nhf
de Broglie wave length
λ = h/p
Compton effect
λ' = λ + (1 – cosA)h/(mc)
Exercises
• 41. The Sun’s surface temperature: Estimate the
surface temperature of our Sun, given that the
Sun emits light whose peak intensity occurs in the
visible spectrum at around 500 nm.
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• 42. Star color: Suppose a star has a surface
temperature of 32,500 K. What color would this
star appear?
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• 43. Calculate the energy of a photon of blue light
(λ = 450 nm) in the air or in vacuum.
Exercises (continued)
• 44. Estimate how many visible light photons a
100-W light bulb emits per second. The efficiency
of the bulb is 3%, the rest of the energy goes to
heat.
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• 45. Photon momentum and force: 1019 photons
emitted per second from 100-W light bulb are
focused on the peace of black paper and
absorbed. Calculate the momentum of one
photon and estimate the force all these photons
can exert on the paper.
Exercises (continued)
• 46. Photosynthesis: Nine photons are needed to
transform one molecule of CO2 to the
carbohydrate and O2. The light wavelength is 700
nm. The inverse chemical reaction releases
energy of 5 eV/ molecule of CO2. How efficient is
the photosynthesis process?
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• 47. X-ray scattering: X-rays of wavelength 0.140
nm are scattered from a very thin slice of carbon.
What will be the wavelengths of X-rays scattered
at (a) 0 degrees, (b) 90 degrees, (c) 180 degrees?
Exercises (continued)
• 48. Pair production: (a) What is the minimum energy of a
photon that can produce an electron-positron pair?
• (b) What is this photon’s wavelength?
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• 49. Wavelength of a ball: Calculate the de Broglie
wavelength of a 0.2 kg ball moving with a speed of 15 m/s.
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• 50. Wavelength of an electron: Determine the wavelength
of an electron that has been accelerated through the
potential difference of 100 V.
Exercises (continued)
• 51. As a particle travels faster, does its de
Broglie wavelength decrease, increase, or
remain the same?
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• 52. Wavelength of a Balmer line: Determine
the wavelength of light emitted when a
hydrogen atom makes a transition from n = 6
to n = 2 energy level according to the Bohr
model.
Quantum Mechanics of Atoms
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics,
or quantum theory) is a fundamental branch of physics which
deals with physical phenomena at nanoscopic scales where
the action is on the order of the Planck constant. It departs
from classical mechanics primarily at the quantum realm of
atomic and subatomic length scales. Quantum mechanics
provides a mathematical description of much of the dual
particle-like and wave-like behavior and interactions of energy
and matter. Quantum mechanics provides a substantially
useful framework for many features of the modern periodic
table of elements including the behavior of atoms during
chemical bonding and has played a significant role in the
development of many modern technologies.
Uncertainty principle
In quantum mechanics, the uncertainty principle is
any of a variety of mathematical inequalities
asserting a fundamental limit to the precision with
which certain pairs of physical properties of a
particle known as complementary variables, such as
position x and momentum p, can be known
simultaneously. For instance, in 1927, Werner
Heisenberg stated that the more precisely the
position of some particle is determined, the less
precisely its momentum can be known, and vice
versa.
Coordinate-Momentum Uncertainty Principle
xp > h/(2π)
Time-Energy Uncertainty Principle
Et > h/(2π)
Vacuum energy may be infinite
Quantum number
Quantum numbers describe values of conserved quantities in the
dynamics of a quantum system. In the case of quantum numbers of
electrons, they can be defined as "The sets of numerical values which
give acceptable solutions to the Schrödinger wave equation for the
Hydrogen atom". Perhaps the most important aspect of quantum
mechanics is the quantization of observable quantities, since quantum
numbers are discrete sets of integers or half-integers, although they
could approach infinity in some cases. This is distinguished from
classical mechanics where the values can range continuously. Quantum
numbers often describe specifically the energy levels of electrons in
atoms, but other possibilities include angular momentum, spin, etc.
Any quantum system can have one or more quantum numbers; it is
thus difficult to list all possible quantum numbers.
Principal quantum number
The principal quantum number, symbolized as n, is the first of a set of quantum numbers (which
includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum
number, and the spin quantum number) of an atomic orbital. The principal quantum number can only
have positive integer values. As n increases, the orbital becomes larger and the electron spends more
time farther from the nucleus. As n increases, the electron is also at a higher potential energy and is
therefore less tightly bound to the nucleus. This is the only quantum number introduced by the Bohr
model.
For an analogy, one could imagine a multistoried building with an elevator structure. The building has an
integer number of floors, and a (well-functioning) elevator which can only stop at a particular floor.
Furthermore the elevator can only travel an integer number of levels. As with the principal quantum
number, higher numbers are associated with higher potential energy.
Beyond this point the analogy breaks down; in the case of elevators the potential energy is gravitational
but with the quantum number it is electromagnetic. The gains and losses in energy are approximate
with the elevator, but precise with quantum state. The elevator ride from floor to floor is continuous
whereas quantum transitions are discontinuous. Finally the constraints of elevator design are imposed
by the requirements of architecture, but quantum behavior reflects fundamental laws of physics.
(Orbital) Azimuthal quantum number
The azimuthal quantum number is a quantum
number for an atomic orbital that determines its
orbital angular momentum and describes the shape
of the orbital. The azimuthal quantum number is
the second of a set of quantum numbers which
describe the unique quantum state of an electron
(the others being the principal quantum number,
following spectroscopic notation, the magnetic
quantum number, and the spin quantum number).
It is also known as the orbital angular momentum
quantum number, orbital quantum number or
second quantum number
Magnetic quantum number
In atomic physics, the magnetic quantum
number is the third of a set of quantum
numbers (the principal quantum number, the
azimuthal quantum number, the magnetic
quantum number, and the spin quantum
number) which describe the unique quantum
state of an electron and is designated by the
letter m. The magnetic quantum number
denotes the energy levels available within a
subshell.
Spin quantum number
In atomic physics, the spin quantum number is a
quantum number that parameterizes the intrinsic
angular momentum (or spin angular momentum, or
simply spin) of a given particle. The spin quantum
number is the fourth of a set of quantum numbers
(the principal quantum number, the azimuthal
quantum number, the magnetic quantum number,
and the spin quantum number), which describe the
unique quantum state of an electron and is
designated by the letter s. It describes the energy,
shape and orientation of orbitals.
Zeeman effect
The Zeeman effect (/ˈzeɪmən/; IPA: [ˈzeːmɑn]), named after the Dutch physicist Pieter
Zeeman, is the effect of splitting a spectral line into several components in the
presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a
spectral line into several components in the presence of an electric field. Also similar
to the Stark effect, transitions between different components have, in general,
different intensities, with some being entirely forbidden (in the dipole approximation),
as governed by the selection rules.
Since the distance between the Zeeman sub-levels is a function of the magnetic field,
this effect can be used to measure the magnetic field, e.g. that of the Sun and other
stars or in laboratory plasmas. The Zeeman effect is very important in applications
such as nuclear magnetic resonance spectroscopy, electron spin resonance
spectroscopy, magnetic resonance imaging (MRI) and Mössbauer spectroscopy. It may
also be utilized to improve accuracy in atomic absorption spectroscopy. A theory
about the magnetic sense of birds assumes that a protein in the retina is changed due
to the Zeeman effect.
When the spectral lines are absorption lines, the effect is called inverse Zeeman
effect.
Fine structure
In atomic physics, the fine structure describes the
splitting of the spectral lines of atoms due to quantummechanical (electron spin) and relativistic corrections.
The gross structure of line spectra is the line spectra
predicted by the quantum mechanics of non-relativistic
electrons with no spin. For a hydrogenic atom, the gross
structure energy levels only depend on the principal
quantum number n. However, a more accurate model
takes into account relativistic and spin effects, which
break the degeneracy of the energy levels and split the
spectral lines.
Selection rule
In physics and chemistry, a selection rule, or
transition rule, formally constrains the possible
transitions of a system from one quantum state
to another. Selection rules have been derived for
electronic, vibrational, and rotational transitions
in molecules. The selection rules may differ
according to the technique used to observe the
transition.
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that says
that two identical fermions (particles with half-integer spin) cannot occupy
the same quantum state simultaneously. In the case of electrons, it can be
stated as follows: it is impossible for two electrons of a poly-electron atom to
have the same values of the four quantum numbers (n, ℓ, mℓ and ms). For two
electrons residing in the same orbital, n, ℓ, and mℓ are the same, so ms must
be different and the electrons have opposite spins. This principle was
formulated by Austrian physicist Wolfgang Pauli in 1925.
A more rigorous statement is that the total wave function for two identical
fermions is anti-symmetric with respect to exchange of the particles. This
means that the wave function changes its sign if the space and spin coordinates of any two particles are interchanged.
Integer spin particles, bosons, are not subject to the Pauli exclusion principle:
any number of identical bosons can occupy the same quantum state, as with,
for instance, photons produced by a laser and Bose–Einstein condensate.
Fluorescence
Fluorescence is the emission of light by a substance that has absorbed
light or other electromagnetic radiation. It is a form of luminescence.
In most cases, the emitted light has a longer wavelength, and
therefore lower energy, than the absorbed radiation. The most striking
examples of fluorescence occur when the absorbed radiation is in the
ultraviolet region of the spectrum, and thus invisible to the human
eye, and the emitted light is in the visible region.
Fluorescence has many practical applications, including mineralogy,
gemology, chemical sensors (fluorescence spectroscopy), fluorescent
labelling, dyes, biological detectors, cosmic-ray detection, and, most
commonly, fluorescent lamps. Fluorescence also occurs frequently in
nature in some minerals and in various biological states in many
branches of the animal kingdom.
Phosphorescent
Metastability
Aggregated systems of subatomic particles
described by quantum mechanics (quarks inside
nucleons, nucleons inside atomic nuclei, electrons
inside atoms, molecules or atomic clusters) are
found to have many distinguishable states. Of
these, one (or a small degenerate set) is indefinitely
stable: the ground state or global minimum.
All other states besides the ground state (or those
degenerate with it) have higher energies.
Laser
A laser is a device that emits light through a process of optical amplification based on
the stimulated emission of electromagnetic radiation. The term "laser" originated as
an acronym for "light amplification by stimulated emission of radiation".[1][2] A laser
differs from other sources of light because it emits light coherently. Spatial coherence
allows a laser to be focused to a tight spot, enabling applications like laser cutting and
lithography. Spatial coherence also allows a laser beam to stay narrow over long
distances (collimation), enabling applications such as laser pointers. Lasers can also
have high temporal coherence which allows them to have a very narrow spectrum,
i.e., they only emit a single color of light. Temporal coherence can be used to produce
pulses of light—as short as a femtosecond.
Lasers have many important applications. They are used in common consumer devices
such as optical disk drives, laser printers, and barcode scanners. Lasers are used for
both fiber-optic and free-space optical communication. They are used in medicine for
laser surgery and various skin treatments, and in industry for cutting and welding
materials. They are used in military and law enforcement devices for marking targets
and measuring range and speed. Laser lighting displays use laser light as an
entertainment medium.
Holography
Holography is a technique which enables threedimensional images (holograms) to be made. It involves
the use of a laser, interference, diffraction, light intensity
recording and suitable illumination of the recording. The
image changes as the position and orientation of the
viewing system changes in exactly the same way as if the
object were still present, thus making the image appear
three-dimensional.
The holographic recording itself is not an image; it
consists of an apparently random structure of either
varying intensity, density or profile.
Moseley's law
Moseley's law is an empirical law concerning the characteristic x-rays
that are emitted by atoms. The law was discovered and published by
the English physicist Henry Moseley in 1913. It is historically important
in quantitatively justifying the conception of the nuclear model of the
atom, with all, or nearly all, positive charges of the atom located in the
nucleus, and associated on an integer basis with atomic number. Until
Moseley's work, "atomic number" was merely an element's place in
the periodic table, and was not known to be associated with any
measureable physical quantity. Moseley was able to show that the
frequencies of certain characteristic X-rays emitted from chemical
elements are proportional to the square of a number which was close
to the element's atomic number; a finding which supported van den
Broek and Bohr's model of the atom in which the atomic number is the
same as the number of positive charges in the nucleus of the atom.
Operators of physical
quantities, not
physical quantities
Wave function
A wave function or wavefunction (also named a state function) in quantum
mechanics describes the quantum state of a system of one or more particles,
and contains all the information about the system considered in isolation.
Quantities associated with measurements, such as the average momentum of
a particle, are derived from the wavefunction by mathematical operations
that describe its interaction with observational devices. Thus it is a central
entity in quantum mechanics. The most common symbols for a wave function
are the Greek letters ψ or Ψ (lower-case and capital psi). The Schrödinger
equation determines how the wave function evolves over time, that is, the
wavefunction is the solution of the Schrödinger equation. The wave function
behaves qualitatively like other waves, like water waves or waves on a string,
because the Schrödinger equation is mathematically a type of wave equation.
This explains the name "wave function", and gives rise to wave–particle
duality. The wave of the wave function, however, is not a wave in physical
space; it is a wave in an abstract mathematical "space", and in this respect it
differs fundamentally from water waves or waves on a string.
Probability
Eigenvalues
Electron can be in many places at the same time
No trajectories
No mechanical spin
Schrödinger's cat
Schrödinger's cat is a thought experiment, sometimes
described as a paradox, devised by Austrian physicist Erwin
Schrödinger in 1935. It illustrates what he saw as the problem
of the Copenhagen interpretation of quantum mechanics
applied to everyday objects. The scenario presents a cat that
may be both alive and dead, this state being tied to an earlier
random event. Although the original "experiment" was
imaginary, similar principles have been researched and used
in practical applications. The thought experiment is also often
featured in theoretical discussions of the interpretations of
quantum mechanics. In the course of developing this
experiment, Schrödinger coined the term Verschränkung
(entanglement).
Schrödinger equation
In quantum mechanics, the Schrödinger equation is a partial
differential equation that describes how the quantum state of a
physical system changes with time. It was formulated in late 1925, and
published in 1926, by the Austrian physicist Erwin Schrödinger.
In classical mechanics, the equation of motion is Newton's second law,
(F = ma), used to mathematically predict what the system will do at
any time after the initial conditions of the system. In quantum
mechanics, the analogue of Newton's law is Schrödinger's equation for
a quantum system (usually atoms, molecules, and subatomic particles
whether free, bound, or localized). It is not a simple algebraic
equation, but in general a linear partial differential equation,
describing the time-evolution of the system's wave function (also
called a "state function").
Schrödinger equation (continued)
The concept of a wavefunction is a fundamental postulate of quantum
mechanics. Schrödinger's equation is also often presented as a separate
postulate, but some authors assert it can be derived from symmetry
principles. Generally, "derivations" of the SE demonstrate its mathematical
plausibility for describing wave–particle duality.
In the standard interpretation of quantum mechanics, the wave function is
the most complete description that can be given to a physical system.
Solutions to Schrödinger's equation describe not only molecular, atomic, and
subatomic systems, but also macroscopic systems, possibly even the whole
universe. The Schrödinger equation, in its most general form, is consistent
with either classical mechanics or special relativity, but the original
formulation by Schrödinger himself was non-relativistic.
The Schrödinger equation is not the only way to make predictions in quantum
mechanics - other formulations can be used, such as Werner Heisenberg's
matrix mechanics, and Richard Feynman's path integral formulation.
Dirac equation
In particle physics, the Dirac equation is a
relativistic wave equation derived by British
physicist Paul Dirac in 1928. In its free form, or
including electromagnetic interactions, it describes
all spin-½ massive particles, for which parity is a
symmetry, such as electrons and quarks, and is
consistent with both the principles of quantum
mechanics and the theory of special relativity, and
was the first theory to account fully for special
relativity in the context of quantum mechanics.
Dirac equation (continued)
It accounted for the fine details of the hydrogen spectrum in a
completely rigorous way. The equation also implied the
existence of a new form of matter, antimatter, hitherto
unsuspected and unobserved, and actually predated its
experimental discovery. It also provided a theoretical
justification for the introduction of several-component wave
functions in Pauli's phenomenological theory of spin; the
wave functions in the Dirac theory are vectors of four complex
numbers (known as bispinors), two of which resemble the
Pauli wavefunction in the non-relativistic limit, in contrast to
the Schrödinger equation which described wave functions of
only one complex value. Moreover, in the limit of zero mass,
the Dirac equation reduces to the Weyl equation.
Dirac equation (continued)
Although Dirac did not at first fully appreciate the
importance of his results, the entailed explanation
of spin as a consequence of the union of quantum
mechanics and relativity—and the eventual
discovery of the positron—represent one of the
great triumphs of theoretical physics. This
accomplishment has been described as fully on a
par with the works of Newton, Maxwell, and
Einstein before him. In the context of quantum field
theory, the Dirac equation is reinterpreted to
describe quantum fields corresponding to spin-½
particles.
Exercises
• 53. An electron moves in a straight line with a constant
speed
• v = 1.1×106 m/s which has been measures with a precision
of 0.1%. What is the maximum precision with which its
position could be simultaneously measured?
•
• 54. An electron’s position is measured with accuracy of
5×10-11 m. Find the minimum uncertainty in its momentum
and velocity.
•
• 55. Position uncertainty of a football: What is the position
uncertainty imposed by the uncertainly principle, on a 500g football kicked at (30 ± 1) m/s?
Exercises (continued)
• 56. An electron has n = 4, l = 2. What valued of ml are possible?
•
• 57. What are the energy and angular momentum of the electron in
a hydrogen atom with n = 6, l = 4?
•
• 58. Which of the following electron configurations are possible and
which are not
• (a) 1s22s22p63s3; (b) 1s22s22p63s23p64s2; (c) 1s22s22p62d1?
•
• 59. Write the complete ground state configuration for lithium.
•
• 60. Estimate the wavelength for an n = 2 to n = 1 transition in
molybdenum (Z = 42). What is the energy of such a photon?
Exercises (continued)
• 61. High energy photons are used to bombard
an unknown material. The strongest peak is
found for X-rays emitted with energy of 66
keV. Guess what the material is.
Molecules and Solids
Covalent bond
A covalent bond is a chemical bond that involves the sharing of
electron pairs between atoms. The stable balance of attractive and
repulsive forces between atoms when they share electrons is known as
covalent bonding. For many molecules, the sharing of electrons allows
each atom to attain the equivalent of a full outer shell, corresponding
to a stable electronic configuration.
Covalent bonding includes many kinds of interactions, including σbonding, π-bonding, metal-to-metal bonding, agostic interactions, and
three-center two-electron bonds. The term covalent bond dates from
1939. The prefix co- means jointly, associated in action, partnered to a
lesser degree, etc.; thus a "co-valent bond", in essence, means that the
atoms share "valence", such as is discussed in valence bond theory.
Ionic bonding
Ionic bonding is a type of chemical bond that
involves the electrostatic attraction between
oppositely charged ions. These ions represent
atoms that have lost one or more electrons
(known as cations) and atoms that have gained
one or more electrons (known as an anions). In
the simplest case, the cation is a metal atom and
the anion is a nonmetal atom, but these ions
can be of a more complex nature
van der Waals force
In physical chemistry, the van der Waals force
(or van der Waals' interaction), named after
Dutch scientist Johannes Diderik van der Waals,
is the sum of the attractive or repulsive forces
between molecules (or between parts of the
same molecule) other than those due to
covalent bonds, or the electrostatic interaction
of ions with one another, with neutral
molecules, or with charged molecules.
Metallic bonding
Metallic bonding occurs as a result of electromagnetism and describes
the electrostatic attractive force that occurs between conduction
electrons (in the form of an electron cloud of delocalized electrons)
and positively charged metal ions. It may be described as the sharing
of free electrons among a lattice of positively charged ions (cations). In
a more quantum-mechanical view, the conduction electrons divide
their density equally over all atoms that function as neutral (noncharged) entities. Metallic bonding accounts for many physical
properties of metals, such as strength, ductility, thermal and electrical
resistivity and conductivity, opacity, and luster.
Metallic bonding is not the only type of chemical bonding a metal can
exhibit, even as a pure substance. For example, elemental gallium
consists of covalently-bound pairs of atoms in both liquid and solid
state—these pairs form a crystal lattice with metallic bonding between
them.
Conduction band
The conduction band quantifies the range of energy required to free an electron from
its bond to an atom. Once freed from this bond, the electron becomes a 'delocalized
electron', moving freely within the atomic lattice of the material to which the atom
belongs. Various materials may be classified by their band gap: this is defined as the
difference between the valence and conduction bands.
In insulators, the conduction band is much higher in energy than the valence band and
it takes large energies to delocalize their valence electrons. Insulating materials have
wide band gaps.
In semiconductors, the band gap is small. This explains why it takes a little energy (in
the form of heat or light) to make semiconductors' electrons delocalize and conduct
electricity, hence the name, semiconductor.
In metals, the Fermi level is inside at least one band. These Fermi-level-crossing bands
may be called conduction band, valence band, or something else depending on
circumstance.
Electrons within the conduction band are mobile charge carriers in solids, responsible
for conduction of electric currents in metals and other good electrical conductors.
Valence band
In solids, the valence band is the highest range of
electron energies in which electrons are normally
The valence electrons are bound to individual atoms, as
opposed to conduction electrons (found in conductors
and semiconductors), which can move freely within the
atomic lattice of the material. On a graph of the
electronic band structure of a material, the valence band
is located below the conduction band, separated from it
in insulators and semiconductors by a band gap. In
metals, the conduction band has no energy gap
separating it from the valence band. present at absolute
zero temperature.
Semiconductor
A semiconductor material has an electrical conductivity value between a conductor, such as copper, and an insulator,
such as glass. Semiconductors are the foundation of modern electronics. The modern understanding of the properties
of a semiconductor relies on quantum physics to explain the movement of electrons and holes in a crystal lattice. An
increased knowledge of semiconductor materials and fabrication processes has made possible continuing increases in
the complexity and speed of microprocessors and memory devices.
The electrical conductivity of a semiconductor material increases with increasing temperature, which is behaviour
opposite to that of a metal. Semiconductor devices can display a range of useful properties such as passing current
more easily in one direction than the other, showing variable resistance, and sensitivity to light or heat. Because the
electrical properties of a semiconductor material can be modified by controlled addition of impurities, or by the
application of electrical fields or light, devices made from semiconductors can be used for amplification, switching, and
energy conversion.
Current conduction in a semiconductor occurs through the movement of free electrons and "holes", collectively known
as charge carriers. Adding impurity atoms to a semiconducting material, known as "doping", greatly increases the
number of charge carriers within it. When a doped semiconductor contains mostly free holes it is called "p-type", and
when it contains mostly free electrons it is known as "n-type". The semiconductor materials used in electronic devices
are doped under precise conditions to control the location and concentration of p- and n-type dopants. A single
semiconductor crystal can have many p- and n-type regions; the p–n junctions between these regions are responsible
for the useful electronic behaviour.
Some of the properties of semiconductor materials were observed throughout the mid 19th and first decades of the
20th century. Development of quantum physics in turn allowed the development of the transistor in 1948. Although
some pure elements and many compounds display semiconductor properties, silicon, germanium, and compounds of
gallium are the most widely used in electronic devices.
Doping (semiconductor)
In semiconductor production, doping intentionally
introduces impurities into an extremely pure (also
referred to as intrinsic) semiconductor for the purpose of
modulating its electrical properties. The impurities are
dependent upon the type of semiconductor. Lightly and
moderately doped semiconductors are referred to as
extrinsic. A semiconductor doped to such high levels that
it acts more like a conductor than a semiconductor is
referred to as degenerate.
In the context of phosphors and scintillators, doping is
better known as activation.
Diode
In electronics, a diode is a two-terminal electronic component with
asymmetric conductance; it has low (ideally zero) resistance to current
in one direction, and high (ideally infinite) resistance in the other. A
semiconductor diode, the most common type today, is a crystalline
piece of semiconductor material with a p–n junction connected to two
electrical terminals. A vacuum tube diode has two electrodes, a plate
(anode) and a heated cathode. Semiconductor diodes were the first
semiconductor electronic devices. The discovery of crystals' rectifying
abilities was made by German physicist Ferdinand Braun in 1874. The
first semiconductor diodes, called cat's whisker diodes, developed
around 1906, were made of mineral crystals such as galena. Today,
most diodes are made of silicon, but other semiconductors such as
selenium or germanium are sometimes used.
p–n junction
A p–n junction is a boundary or interface between two types of
semiconductor material, p-type and n-type, inside a single crystal of
semiconductor. It is created by doping, for example by ion implantation,
diffusion of dopants, or by epitaxy (growing a layer of crystal doped with one
type of dopant on top of a layer of crystal doped with another type of
dopant). If two separate pieces of material were used, this would introduce a
grain boundary between the semiconductors that would severely inhibit its
utility by scattering the electrons and holes.
p–n junctions are elementary "building blocks" of most semiconductor
electronic devices such as diodes, transistors, solar cells, LEDs, and integrated
circuits; they are the active sites where the electronic action of the device
takes place. For example, a common type of transistor, the bipolar junction
transistor, consists of two p–n junctions in series, in the form n–p–n or p–n–p.
The discovery of the p–n junction is usually attributed to American physicist
Russell Ohl of Bell Laboratories.
A Schottky junction is a special case of a p–n junction, where metal serves the
role of the p-type semiconductor.
Rectifier
A rectifier is an electrical device that converts alternating
current (AC), which periodically reverses direction, to
direct current (DC), which flows in only one direction. The
process is known as rectification. Physically, rectifiers
take a number of forms, including vacuum tube diodes,
mercury-arc valves, copper and selenium oxide rectifiers,
semiconductor diodes, silicon-controlled rectifiers and
other silicon-based semiconductor switches. Historically,
even synchronous electromechanical switches and
motors have been used. Early radio receivers, called
crystal radios, used a "cat's whisker" of fine wire pressing
on a crystal of galena (lead sulfide) to serve as a pointcontact rectifier or "crystal detector".
Transistor
A transistor is a semiconductor device used to amplify and switch electronic
signals and electrical power. It is composed of semiconductor material with at
least three terminals for connection to an external circuit. A voltage or
current applied to one pair of the transistor's terminals changes the current
through another pair of terminals. Because the controlled (output) power can
be higher than the controlling (input) power, a transistor can amplify a signal.
Today, some transistors are packaged individually, but many more are found
embedded in integrated circuits.
The transistor is the fundamental building block of modern electronic devices,
and is ubiquitous in modern electronic systems. Following its development in
1947 by American physicists John Bardeen, Walter Brattain, and William
Shockley, the transistor revolutionized the field of electronics, and paved the
way for smaller and cheaper radios, calculators, and computers, among other
things. The transistor is on the list of IEEE milestones in electronics, and the
inventors were jointly awarded the 1956 Nobel Prize in Physics for their
achievement.
Exercises
• 53. An electron moves in a straight line with a constant
speed
• v = 1.1×106 m/s which has been measures with a precision
of 0.1%. What is the maximum precision with which its
position could be simultaneously measured?
•
• 54. An electron’s position is measured with accuracy of
5×10-11 m. Find the minimum uncertainty in its momentum
and velocity.
•
• 55. Position uncertainty of a football: What is the position
uncertainty imposed by the uncertainly principle, on a 500g football kicked at (30 ± 1) m/s?
Exercises (continued)
• 56. An electron has n = 4, l = 2. What valued of ml are possible?
•
• 57. What are the energy and angular momentum of the electron in
a hydrogen atom with n = 6, l = 4?
•
• 58. Which of the following electron configurations are possible and
which are not
• (a) 1s22s22p63s3; (b) 1s22s22p63s23p64s2; (c) 1s22s22p62d1?
•
• 59. Write the complete ground state configuration for lithium.
•
• 60. Estimate the wavelength for an n = 2 to n = 1 transition in
molybdenum (Z = 42). What is the energy of such a photon?
Exercises (continued)
61. High energy photons are used to bombard
an unknown material. The strongest peak is
found for X-rays emitted with energy of 66 keV.
Guess what the material is.
Nuclear Physics and Radioactivity
Structure and properties of the nucleolus
Proton
Neutron
Atomic mass number
Isotope
Abandancy
Q=
2
MPc
– (MD + mα
2
)c
(30-2)
14
6
𝐶→
14
7
𝑁 + e- + a neutrino
n→p+
e
+ a neutrino
Exercises
• 62. Calculate the disintegration energy when
232
228
𝑈
(mass
=
232.037146
u)
decays
to
92
90𝑇ℎ
(228.028731 u) with the emission of an α
particle.
•
• 63. How much energy is released when 146𝐶
decays to 147𝑁 by β emission?