I. Waves & Particles (p ) Ch. 5 - Electrons in Atoms

A. Waves zWavelength ( ) - length of one complete wave from crest to crest zFrequency ( ) - # of waves that pass a point during a certain time period yhertz (Hz) = 1 cycle/s zAmplitude (A) - distance from the origin to the trough or crest

A. Waves A greater amplitude (intensity) greater frequency (color) crest origin trough A

B. EM Spectrum LOWENERGYLOWENERGY HIGHENERGYHIGHENERGY

LOWENERGYLOWENERGY HIGHENERGYHIGHENERGY ROYG.BIV redorangeyellowgreenblueindigoviolet

B. EM Spectrum zFrequency & wavelength are inversely proportional c = · c:speed of light (3.00  10 8 m/s) :(greek lamba) wavelength (m, nm, etc.) :(greek nu) frequency (Hz, cycles/sec or s -1 ) = c/ Hey, what’s nu?

B. EM Spectrum GIVEN: = ? = 434 nm = 4.34  m c = 3.00  10 8 m/s WORK : = c = 3.00  10 8 m/s 4.34  m = 6.91  Hz zEX: Find the frequency of a photon with a wavelength of 434 nm.

C. Quantum Theory zPlanck (1900) yObserved - emission of light from hot objects…white hot is hotter than red hot yLead to conclusion that - energy is emitted in small, specific amounts (quanta) yQuantum - minimum amount of energy change… minimum “jump” in energy

C. Quantum Theory zPlanck (1900) vs. Classical TheoryQuantum Theory

C. Quantum Theory zEinstein (1905) yObserved - photoelectric effect in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation waves due to specific quanta of energyelectrons

C. Quantum Theory zEinstein (1905) explained the quantum theory of light yConcluded - light has properties of both waves (diffuse location) and particles (finite location) “wave-particle duality” yPhoton - particle of light that carries a quantum of energy

Einsteins Miracle Year zHistorians still call the year 1905 the annus mirabilis, the miracle year because in that year Einstein published four remarkable scientific papers ranging from the smallest scale to the largest, through fundamental problems about the nature of energy, matter, motion, time and space. zIn March 1905, Einstein created the quantum theory of light, the idea that light exists as tiny packets, or particles, which he called photons. Alongside Max Planck's work on quanta of heat Einstein proposed one of the most shocking idea in twentieth century physics: we live in a quantum universe, one built out of tiny, discrete chunks of energy and matter. zHe also “proved” existence of atoms and developed General Theory and Special Theory of Relativity zGo to _theory.html for more _theory.html

C. Quantum Theory E:energy (J, joules) h:Planck’s constant (  J·s) :frequency (Hz or s -1 ) E = h zThe energy of a photon is directly proportional to its frequency.

Energy is related to the color seen zThe energy of a photon is inversely proportional to the wavelength, thus different energies are seen as different colors (wavelengths) zHigher energy photons have higher frequencies (proportional) and shorter wavelengths (inversely proportional).

The EMS is the full range of energies possible for photons

C. Quantum Theory GIVEN: E = ? = 4.57  Hz h =  J·s WORK : E = h E = (  J·s ) ( 4.57  Hz ) E = 3.03  J zEX: Find the energy of a red photon with a frequency of 4.57  Hz.

More Einstein Discoveries zAnd then, in June, Einstein completed special relativity - which added a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves. Such a contradiction took a supremely confident mind to propose. Einstein, age 26, saw light as wave and particle, picking the attribute he needed to confront each problem in turn. zEinstein wasn't finished yet. Later in 1905 came an extension of special relativity in which Einstein proved that energy and matter are linked in the most famous relationship in physics: E=mc2. (The energy content of a body is equal to the mass of the body times the speed of light squared). This equation predicted an evolution of energy roughly a million times more efficient than that obtained by ordinary physiochemical means. At first, even Einstein did not grasp the full implications of his formula, but even then he suggested that the heat produced by radium could mark the conversion of tiny amounts of the mass of the radium salts into energy. zAnd after 1905, Einstein achieved what no one since has equaled: a twenty year run at the cutting edge of physics. For all the miracles of his miracle year, his best work was still to come: zIn 1907, he confronted the problem of gravitation. Einstein began his work with one crucial insight: gravity and acceleration are equivalent, two facets of the same phenomenon.

More Einstein Discoveries zEven the minor works resonated. For example, in 1910, Einstein answered a basic question: 'Why is the sky blue?' His paper on the phenomenon called critical opalescence solved the problem by examining the cumulative effect of the scattering of light by individual molecules in the atmosphere. zThen in 1915, Einstein completed the General Theory of Relativity - the product of eight years of work on the problem of gravity. In general relativity Einstein shows that matter and energy actually mold the shape of space and the flow of time. What we feel as the 'force' of gravity is simply the sensation of following the shortest path we can through curved, four-dimensional space-time. It is a radical vision: space is no longer the box the universe comes in; instead, space and time, matter and energy are, as Einstein proves, locked together in the most intimate embrace. ( Look at a scenario designed by HHO to explain of why time varies according to general relativity theory - see Time variations )Time variations zIn 1917, Einstein published a paper which uses general relativity to model the behavior of an entire universe. Einstein's paper was the first in the modern field of cosmology - the study of the behavior of the universe as a whole. Returning to the quantum, by 1919, six years before the invention of quantum mechanics and the uncertainty principle Einstein recognized that there might be a problem with the classical notion of cause and effect. Given the peculiar, dual nature of quanta as both waves and particles, it might be impossible, he warned, to definitively tie effects to their causes. zIn 1924 and 1925 Einstein still made significant contributions to the development of quantum theory. His last work on the theory built on ideas developed by Satyendra Nath Bose, and predicted a new state of matter (to add to the list of solid, liquid, and gas) called a Bose-Einstein condensate. The condensate was finally created at exceptionally low temperatures only last year.

More Einstein Discoveries zEinstein always had a distaste for modern quantum theory - largely because its probabilistic nature forbids a complete description of cause and effect. But still, he recognized many of the fundamental implications of the idea of the quantum long before the rest of the physics community did. (In 'Albert Einstein: Creator and Rebel' by Hoffmann, the author describes that Max Planck himself was sceptical of his own quantum hypothesis which was highly distasteful to him and introduced merely as 'an act of desperation'. Between 1900 and 1905 the quantum concept remained in limbo. In all the world there seems to have been in those years only one man to dare take it seriously. That man was Einstein who immediately sensed the importance of Planck's work and used the idea in his own paper about the theory of light). After the quantum mechanical revolution of 1925 through 1927, Einstein spent the bulk of his remaining scientific career searching for a deeper theory to subsume quantum mechanics and eliminate its probabilities and uncertainties. He generated pages of equations, geometrical descriptions of fields extending through many dimensions that could unify all the known forces of nature. None of the theories worked out. It was a waste of time... and yet : zContemporary theoretical physics is dominated by what are known as 'String theories.' They are multi-dimensional. (Some versions include as many as 26 dimensions, with fifteen or sixteen curled up in a tiny ball.) They are geometrical - the interactions of one multi-dimensional shape with another produces the effects we call forces, just as the 'force' of gravity in general relativity is what we feel as we move through the curves of four-dimensional space-time. And they unify, no doubt about it: in the math, at least, all of nature from quantum mechanics to gravity emerges from the equations of string theory. As it stands, string theories are unproved, and perhaps unprovable, as they involve interactions at energy levels far beyond any we can handle. But they are beautiful, to those versed enough in the language of mathematics to follow them. And in their beauty (and perhaps in their impenetrability) they are the heirs to Einstein's primitive, first attempts to produce a unified field theory. zBetween 1905 to 1925, Einstein transformed humankind's understanding of nature on every scale, from the smallest to that of the cosmos as a whole. Now, nearly a century after he began to make his mark, we are still exploring Einstein's universe.