# Wave-Particle Duality_3_ by pptfiles

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```									Wave Properties of Light
In modern physics, light or electromagnetic radiation may be viewed in one of two complementary ways: 1. as a wave in an abstract electromagnetic field, or 2. as a stream of massless particles called photons.

Light as a Wave
• The quantity that is "waving" is the electromagnetic field, an esoteric but quite measurable entity • your lights shine and your microwave runs and your radio plays because the electromagnetic field exists. • As illustrated in the adjacent image, a wave has a wavelength associated with it.

Units of Wavelength
Unit Symbol Length

centimeter Angstrom nanometer micrometer micron

cm Å nm μm

10-2 meters 10-8 centimeters 10-9 meters 10-6 meters

Wavelength, Energy, and Frequency
• The speed of light in a vacuum is commonly given the symbol c. • It is a universal constant that has the value c = 2.9979 x 108m/s

A wave can be characterized by • its wavelength • the frequency • the energy that it carries For light waves the relationship among the wavelength (usually denoted by Greek "lambda"), the frequency (usually denoted by Greek "nu"), and the energy E are

where c is the speed of light and h is another universal constant called Planck's Constant that has the values h = 6.626 x 10-34 J-s • h = 4.135 x 10-15 eV-sec = 6.625 x 10-27 erg-sec

Electric and magnetic fields oscillate together but perpendicular to each other and the electromagnetic wave moves in a direction perpendicular to both of the fields.

• Light, electricity, and magnetism are manifestations of the same thing called electromagnetic radiation. • The energy you see coming out of the computer screen you are using to read this page is made of fluctuating electric and magnetic energy fields. • The electric and magnetic fields oscillate at right angles to each other and the combined wave moves in a direction perpendicular to both of the electric and magnetic field oscillations. • This energy also comes in many forms that are not detectable with our eyes such as infrared (IR), radio, X-rays, ultraviolet (UV), and gamma rays.

• we feel infrared light as heat • radios pick up messages encoded in radio waves • Ultraviolet light has high enough energy to damage our skin cells • ``black lights'' produce UV - used by hospitals to kill bacteria, amoebas, and other micro-organisms • X-rays are produced by very hot things in space have more energy than UV can pass through skin, muscles, and organs blocked by bones picture that results is the shadow image of the X-rays that passed through your body have high energy, can damage or kill cells • Gamma rays are the most energetic form of electromagnetic radiation and are produced in nuclear reactions.

• consider light as a stream of minute packets of energy, photons, which create a pulsating electromagnetic disturbance • A single photon differs from another photon only by its energy. In empty space (vacuum) all photons travel with the same speed or velocity. • Photons are slowed down when they pass through different media such as water, glass or even air. This slowing down accounts for the refraction or bending of light by optical lenses. • The energy of the photon is not changed, but the wavelength is. Different energy optical photons are slowed by different amounts in glass or water leading to the dispersion of light and the appearance of rainbows.

Continuous Spectrum

EMISSION SPECTRUM FOR A FEW GASES

Discrete Spectrum

Wave-Particle Duality
• debate about whether light was composed of particles or waves • a wave-particle dual nature soon was found to be characteristic of electrons as well • evidence for the description of light as waves was well established at the turn of the 19th century when the photoelectric effect introduced firm evidence of a particle nature as well • the particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer established the wave nature of the electron.

DeBroglie Wavelengths

DeBroglie Wavelengths

Davisson-Germer Experiment

Davisson-Germer Experiment
• designed and built a vacuum apparatus for the purpose of measuring the energies of electrons scattered from a metal surface. • Electrons from a heated filament were accelerated by a voltage and allowed to strike the surface of nickel metal. The electron beam was directed at the nickel target, which could be rotated to observe angular dependence of the scattered electrons. • Their electron detector (called a Faraday box) was mounted on an arc so that it could be rotated to observe electrons at different angles. • It was a great surprise to them to find that at certain angles there was a peak in the intensity of the scattered electron beam. This peak indicated wave behavior for the electrons, and could be interpreted by the Bragg law to give values for the lattice spacing in the nickel crystal.

Davisson-Germer Experiment
• experiment demonstrated the wave nature of the electron • confirmed the earlier hypothesis of deBroglie • put wave-particle duality on a firm experimental footing • it represented a major step forward in the development of quantum mechanics. • The Bragg law for diffraction had been applied to x-ray diffraction, but this was the first application to particle waves.

The Photoelectric Effect
• electrons were emitted immediately - no time lag! • Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! • Red light will not cause the ejection of electrons, no matter what the intensity! • A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

The Photoelectric Effect
• It was known that if one shines a beam of light on a clean surface of a metal, electrons will be ejected from the metal. • The light has to exceed a certain energy, to remove electrons from the metal surface. • If the light has more than the minimum energy required, then the extra energy will be given to the ejected electrons as kinetic energy of motion.

The Photoelectric Effect
• Light of a single wavelength behaves as if it consists of separate particles, photons, all with the same energy, with each ejected electron being the result of a collision between one photon and one electron in the metal. • Greater intensity of light means only that more photons are hitting the metal per second and more electrons are being ejected, not that there is more energy per photon. • The energy of the outgoing electrons depended on the frequency of light used. • Max Planck first proposed this relationship between energy and frequency in 1900.

Louis de Broglie The Nobel Prize in Physics 1929
• developed the general theory of wave mechanics, a theory which has totally transformed our knowledge of physical phenomena on the atomic scale • discovery of the wave nature of electrons • postulated the wave nature of electrons, one of the basis of the quantum physics. • subatomic entities have properties of both waves and particles at the same time.

Max Planck The Nobel Prize in Physics 1918
• was able to deduce the relationship between the energy and the frequency of radiation • considered to be the founder of quantum theory • initially rejected the discovery of the photoelectric effect • energy of waves could be described as consisting of small packets or quanta

Albert Einstein 1921 Nobel Prize in Physics
• best known for his theory of relativity and specifically mass-energy equivalence, E = mc2 • Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.“ • an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency

Niels Bohr Nobel Prize in physics in 1922
• studied under Ernest Rutherford • conducted experiments under J. J. Thomson. • published his model of atomic structure in 1913, introducing the theory of electrons traveling in orbits around the atom's nucleus • introduced the idea that an electron could drop from a higher-energy orbit to a lower one, emitting a photon (light quantum) of discrete energy. • This became a basis for quantum theory. • In 1922, Bohr was awarded the Nobel Prize in physics "for his services in the investigation of the structure of atoms and of the radiation emanating from them".

Bohr's theory
• represented electrons as orbiting the nucleus of an atom • when an electron changed orbits it did not move in a continuous trajectory from one orbit around the nucleus to another • instead, it suddenly disappeared from its original orbit and reappeared in another orbit • Each distance at which an electron can orbit is a function of a quantized amount of energy. • The closer to the nucleus an electron orbits, the less energy it takes to remain in that orbital.

Bohr's theory
• Electrons that absorb a photon gain a quantum of energy, so they jump to an orbit that is farther from the nucleus, while electrons that emit a photon lose a quantum of energy and so jump to an inner orbital. • Electrons cannot gain or lose a fractional quantum of energy, and so they cannot have a position that is at a fractional distance between allowed orbitals. • Allowed orbitals were designated as whole numbers using the letter n with the innermost orbital being designated n = 1, the next out being n = 2, and so on. Any orbital with the same value of n is called an electron shell.

• A standing wave can only be formed when the wave's length fits the available vibrating entity • no partial fragments of wave crests or troughs are allowed • wave must be a continuous formation of crests and troughs all around the circle • Each electron must be its own standing wave in its own discrete orbital.

electrons can only appear under conditions that permit a standing wave

Erwin Schrödinger The Nobel Prize in Physics 1933
• disliked the generally accepted dual description in terms of waves and particles, with a statistical interpretation for the waves • tried to set up a theory in terms of waves only • This led him into controversy with other leading physicists. • won Nobel prize “for the discovery of new productive forms of atomic theory"

Erwin Schrödinger
• wavefunction is described in Schrödinger's equation by three properties (later Wolfgang Pauli added a fourth) • The three properties were (1) an "orbital" designation, indicating whether the particle wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy, (2) the shape of the orbital, i.e., an indication that orbitals were not just spherical but other shapes, and (3) the magnetic moment of the orbital, which is a manifestation of force exerted by the charge of the electron as it rotates around the nucleus.

Werner Heisenberg
• one of the founders of quantum mechanics • acknowledged to be one of the most important physicists of the twentieth century • student of Niels Bohr • was head of the German atomic bomb project • received the Nobel Prize in physics in 1932 "for the creation of quantum mechanics, the application of which has led to the discovery of the allotropic forms of hydrogen" .

Werner Heisenberg
• developed the full quantum mechanical theory in 1925 at the young age of 23 • mentor was Niels Bohr • created a mathematical description of quantum mechanics built on what could be observed - the light emitted from atoms in their characteristic atomic spectra • studied the electron orbital on the model of a charged ball on a spring

Quantum mechanics
• the study of the relationship between energy quanta (radiation) and matter • between valence shell electrons and photons • The word “quantum” (Latin, “how much”) in quantum mechanics refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest

Wolfgang Pauli
• noted for his work on the theory of spin, and in particular the discovery of the exclusion principle • in 1945, he received the Nobel Prize in Physics for his "decisive contribution through his discovery in 1925 of a new law of Nature, the exclusion principle or Pauli principle." He had been nominated for the prize by Einstein. • stated that no two electrons could exist in the same quantum state

Uncertainty principle
• when a moving particle is viewed as a wave it is less certain where the particle is • the more certain the position of a particle is known, the less certain the momentum is known • the electron had to be described by every point where the electron could possibly inhabit • an electron in a certain n-sphere had to be within a certain range from the nucleus depending upon its energy

Uncertainty principle
• the number of places that an electron can be in its orbital becomes finite • An electron's location in an atom is defined to be in its orbital, but stops at the nucleus and before the next n-sphere orbital begins. • no more than two electrons can inhabit the same orbital

Enrico Fermi Nobel Prize in Physics in 1938
• noted for his work on the development of the first nuclear reactor • contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics. • Fermi was awarded the Nobel Prize in Physics in 1938 for his work on induced radioactivity. • suggested that some of his experiments could have produced lighter elements • theory of beta decay, and the discovery of slow neutrons, which was to prove pivotal for the working of nuclear reactors • Worked on “Manhattan Project”

Quantum mechanics
• initially developed to explain the atom, especially the spectra of light emitted by different atomic species. • quantum theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by Maxwell's laws of classical electromagnetism • described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons • This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments.

Quantum mechanics
• a physical science dealing with the behavior of matter and energy on the scale of atoms and subatomic particles / waves • forms the basis for the contemporary understanding of how very large objects such as stars and galaxies, and cosmological events such as the Big Bang, can be analyzed and explained • is the foundation of several related disciplines including nanotechnology, condensed matter physics, quantum chemistry, structural biology, particle physics, and electronics.

Quantum mechanics
• founded by Werner Heisenberg and Erwin Schrödinger • term was first coined by Max Born in 1924 • acceptance by the general physics community of quantum mechanics is due to its accurate prediction of the physical behavior of systems, including systems where Newtonian mechanics fails • general relativity is limited—in ways quantum mechanics is not—for describing systems at the atomic scale or smaller, at very low or very high energies, or at the lowest temperatures • Through a century of experimentation and applied science, quantum mechanical theory has proven to be very successful and practical.

Quantum Numbers
• each electron has a set of four numbers, called quantum numbers • no two electrons in the same atom can have the same four quantum numbers • the "primary quantum number" is given the symbol n • n designates the energy level and distance from the nucleus

Quantum Numbers
• The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. • Schroedinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found.

The three coordinates that come from Schroedinger's wave equations are • the principal (n), • angular (l), • and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.

• describes the size of the orbital Orbitals for which n = 2 are larger than those for which n = 1, for example. • Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. • Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2). • The principal quantum number therefore indirectly describes the energy of an orbital.

principal quantum number (n)

angular quantum number (ℓ)
• describes the shape of the orbital • Orbitals have shapes that are best described as spherical (ℓ = 0), polar (ℓ = 1), or cloverleaf (ℓ = 2). • They can even take on more complex shapes as the value of the angular quantum number becomes larger.

magnetic quantum number (m)
• There is only one way in which a sphere (ℓ = 0) can be oriented in space. Orbitals that have polar (ℓ = 1) or cloverleaf (ℓ = 2) shapes, however, can point in different directions. • We therefore need a third quantum number, known as the magnetic quantum number (m), to describe the orientation in space of a particular orbital. • (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)

Spin Quantum Number, (s)
• spin is a property of electrons that is not related to a sphere spinning • it was first thought to be this way, hence the name spin, but it was soon realized that electrons cannot spin on their axis like the Earth does on its axis. • If the electron did this, its surface would be moving at about ten times the speed of light • the electron's surface would have to move faster than the speed of light and this isn't possible. • In 1925, Wolfgang Pauli demonstrated the need for a fourth quantum number.

the valid quantum states
1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g 6s 6p 6d 6f 6g 7h 7s 7p 7d 7f 7g 7h 8i

Atomic and Molecular Orbitals

d-orbitals

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