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## PHY 102 – Atoms to Galaxies

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**PHY 102 – Atoms to Galaxies**PHY 102 – Atoms to Galaxies Our early human ancestors most certainly looked at the night sky, and wondered.**Newton’s corpuscular theory of light had a few**difficulties, such as explaining refraction. Light: Particle or Wave?**Newton discovered that white light is composed of the same**system of colors that can be seen in the rainbow (refraction).**From the diffraction experiment with light there is good**evidence that light is a wave. Light: Particle or Wave?**Quantum PhysicsUnlike mechanics (Newton), or**electrodynamics (Maxwell), or relativity (Einstein), quantum mechanics was not developed by one individual. It was rather the result of the work of several scientists in conjunction with a few unexpected experimental measurements.**Quantum PhysicsEven though it was born about a century ago,**there is no general consensus as to what its fundamental principles are. It still is “work in progress.” “If you are you are not confused by quantum physics then you haven’t really understood it.” Niels Bohr “I think I can safely say that nobody understands quantum mechanics.” Richard Feynman**Blackbody Radiation**Blackbody (radiation): Theoretical object that absorbs 100% of the radiation that hits it; perfect emitter too (carbon-graphite: 97%). Ultraviolet catastrophe: the theoretical prediction of early 1900s physics was that an ideal blackbody would emit radiation with infinite power. This was in total contrast with experimental results.**Quantum Physics: December of 1900**Max Planck • proposed that oscillating electrons emitted radiation according to Maxwell’s laws of E & M • proposed that the energy must increase in discrete amounts (quantized) because the frequencies of the oscillating electrons could only take certain values (digital versus analog).**Quantum Physics**Planck’s approach produced a theory with results that matched experimental measurements.**Quantum Physics**Planck’s approach produced a theory with results that matched experimental measurements.**Max Planck, 1918 Physics Nobel Prize**”in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta”**Quantum PhysicsRevisit the double slit experiment with**light.**Quantization of LightRevisit the double slit experiment with**light, this time using extremely dim light.**Quantum PhysicsWhat is coming through the slits? We expect**it to be waves, but then how can we explain the particle-like impacts of light on the screen? We may expect it to be disturbances in the electromagnetic field (light wave), but, as we understand it today, it is a “quantized” magnetic field. For example, take yellow light with a frequency of 5 x 1014 Hz. The EM field allowed to carry this light is allowed to have energies 0 J zero 3.2 x 10-19 J 1 E 6.4 x 10-19 J 2 E 9.6 x 10-19 J 3 E etc.**Quantum PhysicsConsider a typical 100 watt light bulb. About**10% of this energy (10 watt = 10 joule/second) emerges as visible light. Assuming this light to be yellow, in 1 second 10 J / 3.2 x 10-19 J = 3 x 1019 photons are emitted. These are 30 million trillion quanta of energy. So, the amount of energy in 1 photon is really, really, really, really small. We do not notice quantization in our everyday lives.**When carrying radiation of frequency f , an EM field is**allowed to have only the following particular values of total energy: Etotal = 0, hf , 2hf , 3hf , etc., where h = 6.6 x 10-34 J s. Quantum Physics**So, Planck’s equation E = nhf indicates that**electromagnetic waves carry only well defined discrete amounts of energy. When this particle-like waves hit the screen they produce a dot which corresponds to a specific amount of energy. The quantized particle-like waves are called photons. They are energy quanta that act like particles. Quantum Physics**Note that each individual photon “knows” about the**interference pattern regardless of the other photons. The precise impact point of each photon is unpredictable, but the emerging statistical pattern is predictable. Like dice throws, individual outcomes are unpredictable but overall statistics are predictable. Unpredictability, or uncertainty, is characteristic of quantum mechanics.**The most dramatic prediction of Maxwell’s theory of**electromagnetism (1865) was the existence of electromagnetic waves moving at the speed of light. Light itself was just such a wave. Experimentalists then came up with experimental setups to test the theory. Photoelectric Effect**Photoelectric EffectFirst reported in 1839 by Becquerel.**Hertz observed it in 1887 but did not explain the phenomenon: An electric current is produced when a metallic surface is exposed to electromagnetic radiation (visible light or x-rays, for example)**In fact, electrons are emitted from the metallic surface due**to absorption of the electromagnetic radiation.**The photoelectric effect was successfully explained by**Albert Einstein who assumed quantization of energy. hf = + K.E.electron hf = e.m. radiation energy = work function K.E.electron = electron kinetic energy Quantum PhysicsPhotoelectric Effect**"for his services to Theoretical Physics, and especially for**his discovery of the law of the photoelectric effect" Albert Einstein, 1921 Physics Nobel Prize**In 1923, Louis de Broglie proposed that matter should**possess wave properties, as much as waves displayed particle characteristics. Even though there was no experimental evidence, he considered energy = m v v = p f = h f = h / p Compute the wavelength associated with a 1 kg ball moving at a speed of 1 m/s: = h / p =6.6 x 10-34 J s / (1 kg 1 m/s) = 6.6 x 10-34 m Waviness of Matter**“for his discovery of the wave nature of electrons”**Louis de Broglie, 1929 Nobel Prize**Use electrons, not light, in the double slit experiment.**What do we get? Compare with the output using light. How do we know that matter has wave properties?**http://video.google.com/videoplay?docid=390849738419231822**The Wave Theory of MatterEvery material particle has wave properties with a wavelength equal to h/mv where m is the particle’s mass and v is its speed.**The Wave Theory of MatterElectrons are not tiny particles**that follow a specific path from the electron source through the slits to the screen. Instead, electrons are quanta, increments of the energy of a spread-out field, just as photons are quanta.**The Wave Theory of MatterRange of visible light: ~ 4 to 7 x**10-7 mSize of the atom: ~ 10-10 m**Nonlocality: This is one of the most exotic behaviors of**microscopic objects such as electrons and photons. A microscopic object knows what happens to another instantaneously, regardless of how far apart they happen to be. In the double-slit experiment with light and with matter, the entire EM field or matter field changed its character instantaneously when an impact appeared on the screen. Nature: Nonlocal and Uncertain**Uncertainty: It is impossible to know exactly both position**and momentum of a particle. The more accuracy applied to the measurement of one of them, the less precision is obtained with the other: x p ≈ h (Heisenberg uncertainty principle) Nature: Nonlocal and Uncertain**"for the creation of quantum mechanics, the application of**which has, inter alia, led to the discovery of the allotropic forms of hydrogen" Werner Heisenberg, 1932 Physics Nobel Prize**He postulated that the electron would follow specific**trajectories around the nucleus of the atom, performing quantum jumps from one trajectory to the other depending on its amount energy. Niels Bohr, in 1913, proposed a partially quantized version of the planetary atom.**"for his services in the investigation of the structure of**the atom and the radiation emanating from them” Niels Bohr, 1922 Physics Nobel Prize**In the 1920s, Bohr along with Max Born, Werner Eisenberg and**others, developed a view of what quantum theory means. Max Born proposed that the wave patterns observed in experiments on microscopic particles were probability patterns.**"for his fundamental research in quantum mechanics,**especially for his statistical interpretation of the wavefunction" Max Born, 1954 Physics Nobel Prize**In 1926, Erwin Schroedinger developed an equation for**studying the motion of matter waves. Schroedinger’s equation is consistent with the energy quantum levels and the probability character of the wave function.**"for the discovery of new productive forms of atomic**theory” Erwin Schrödinger, 1933 Physics Nobel Prize**"for the discovery of new productive forms of atomic**theory” Paul Dirac, 1933 Physics Nobel Prize**Old and famous: find exact solutions to N point masses**moving under their mutual (Newtonian) gravitational forces. N = 2, straightforward solutions, known for a long time. N = 3, chaos breaks loose, literally. Late 1800s: The N-body Problem**1887 Prize for the solution of the three body problem (solar**system stability). Oscar II, King of Sweden and Norway**Mathematical error found in the manuscript.**In fixing the mistake Poincaré discovered sensitive dependence on initial conditions. Henri Poincaré won the competition