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Quantum Physics When we consider the motion of objects on the atomic level, we find that our classical approach does not work very well. For example, quantum physics describes how electrons surround the nucleus of the atom and other subatomic actions. Therefore, for understanding motion on the microscopic scale we must use Quantum Mechanics. "I think I can safely say that nobody understands quantum mechanics." - Richard P. Feynman "I don't like it, and I'm sorry I ever had anything to do with it" - Erwin Schrödinger "Anyone who is not shocked by the quantum theory has not understood it." - Niels Bohr We know some small particles like electrons, protons, and neutrons. Quantum physics even describes the particles which make these particles! (The model of an atom that you were taught in high-school is a approximation). The electrons don't orbit like planets; they form blurred clouds of probabilities around the nucleus. Protons and neutrons? They're each made of three quarks, each with its own 'flavor' and one of three 'colors'. Lets not forget the gluons, the even smaller particles that hold this mess together when they collect and form glueballs. The quantum model of the atom is much more complex than the traditional model. The world of subatomic particles is a very bizarre one, filled with quantum probabilities and organized chaos. For example, the exact position and velocity of an electron is very hard to find because attempts to "see" it involve bouncing other particles off of it. By doing this, you've just changed the electron's velocity, so your data is useless. What quantum physics does is give us the statistical probability of the electron's location at any one moment. Blackbody Radiation One of the earliest indications that classical physics was incomplete came from attempts to describe blackbody radiation. A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black. Blackbody radiation is the emission of electromagnetic waves from the surface of an object. The distribution of blackbody radiation depends only the temperature of the object and is independent of the material. The Blackbody Distribution The intensity spectrum emitted from a blackbody has a characteristic shape. The maximum of the intensity is found to occur at a wavelength given by Wien’s Displacement Law: fpeak = (5.88 × 1010 s-1·K-1)T T = temperature of blackbody (K) Notice the plot is versus frequency on these plots, but since it is related to wavelength via, f λ = c λmaxT = 2.90 × 10 m K −3 Example: The solar radiation curve approximates closely a blackbody at 5900K. What region of the spectrum is the sun most intense? 2.90 × 10−3 m K −7 λmax = 5900 K = 4.915 × 10 m = 491.5nm Consequences: What part of the spectrum is this? 2.90 × 10−3 m K T=300K = 9.667 × 10−6 m λmax = 300 K = 9.667 microns What portion of the spectrum is this? 2.90 × 10−3 m K T=3 million K = 9.667 × 10−10 m λmax = 6 3. × 10 K =9.667Å = 0.97nm What portion of the spectrum is this? 2.90 × 10−3 m K T=3K = 9.667 × 10−3 m λmax = 3K =9.667mm What portion of the spectrum is this? The Ultraviolet Catastrophe Classical physics can describe the shape of the blackbody spectrum only at long wavelengths. At short wavelengths there is complete disagreement. This disagreement between observations and the classical theory is known as the ultraviolet catastrophe. Planck’s Solution In 1900, the German physicist Max Planck was able to explain the observed blackbody spectrum by assuming that it originated from oscillators on the surface of the object and that the energies associated with the oscillators were discrete or quantized: En = nhf n = 0, 1, 2, 3… n is an integer called the quantum number h is Planck’s constant: 6.62 × 10-34 J·s f is the frequency Planck’s idea of quanta was the beginning of quantum physics. The smallest packet of energy a electron can give or absorb. (Like you can’t take an elevator to the 32nd ½ floor). With electrons any energy is a whole number of quantas. The correct mathematical work to Planck’s work was later done by Erwin Schroedinger, an Austrian scientist. Quantization of Light Einstein proposed that light itself comes in chunks of energy, called photons. Light is a wave, but also a particle. The energy of one photon is E = hf where f is the frequency of the light and h is Planck’s constant. Useful energy unit: 1 eV = 1.6 × 1019 J Quantum Mechanics The essence of quantum mechanics is that certain physical properties of a system (like the energy) are not allowed to be just any value, but instead must be only certain discrete values. Example (a) Find the energy of 1 (red) 650 nm photon. (b) Find the energy of 2 (red) 650 nm photons. The PhotoElectric Effect When light is incident on a surface (usually a metal), electrons can be ejected. This is known as the photoelectric effect. Around the turn of the century, observations of the photoelectric effect were in disagreement with the predictions of classical wave theory. Observations of the Photoelectric Effect • No electrons are emitted if the frequency of the incident photons is below some cutoff value, independent of intensity. • The maximum kinetic energy of the emitted electrons does not depend on the light intensity. • The maximum kinetic energy of the emitted electrons does depend on the photon frequency. • Electrons are emitted almost instantaneously from the surface. The Photoelectric Effect Explained (Einstein 1905, Nobel Prize 1921) The photoelectric effect can be understood as follows: • Electrons are emitted by absorbing a single photon. • A certain amount of energy , called the work function, W0, is required to remove the electron from the material. • The maximum observed kinetic energy is the difference between the photon energy and the work function. Kmax = E – W0 E = photon energy "just shows emission" E = W0 means Kmax is zero Cutoff Frequency f0 = W0 /h The work function is a property of the individual metal Element Aluminum 4.3 Carbon Work Functio n Element Nickel 5.1 5.0 Silicon 4.8 Copper 4.7 Silver 4.3 Gold 5.1 Sodium 2.7 (eV) Work Functio n (eV) Application: Photocells, Solar Cells If the energy of a photon is high enough it can break bonds in molecules/materials Walker Problem 25, pg. 1008 Zinc and cadmium have photoelectric work functions given by WZn = 4.33 eV and WCd = 4.22 eV, respectively. (a) If both metals are illuminated by UV radiation of the same wavelength, which one gives off photoelectrons with the greater maximum kinetic energy? Explain. (b) Calculate the maximum kinetic energy of photoelectrons from each surface if λ = 275 nm. The Mass and Momentum of a Photon Photons have momentum, but no mass. We cannot use the formula p = mv to find the momentum of the photon. Instead: hf h p= = c λ The Wave Nature of Particles We have seen that light is described sometimes as a wave and sometimes as a particle. In 1924, Louis deBroglie proposed that particles also display this dual nature and can be described by waves too! The deBroglie wavelength of a particle is related to its momentum: λ= h/p (Use p = γm0v if the velocity is large.) That is why you can make an atom laser! Example If an electron has a speed of 1.00 × 106 m/s, what is its wavelength? Example The maximum momentum of electrons at the Jefferson Lab accelerator in Newport News is 6 GeV/c. (a) What is the wavelength of those electrons? (b) Why is the wavelength well suited to the study of nuclear physics? We can investigate wave properties of particles through interference/diffraction - X-rays - Electrons - Neutrons - Atoms like hydrogen or helium Bragg equation 2d sin θ = mλ m = 1,2,3... Heisenberg Uncertainty Principle To describe a particle a physicist would refer four properties, the position of the electron, its momentum, its energy, and the time. Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties (let´s built two pairs: momentum-position or energy-time) are measured at the same time. "The more precisely the POSITION is determined, the less precisely the MOMENTUM is known" WERNER HEISENBERG (1901 - 1976) Determinism of Classical Mechanics • Suppose the positions and speeds of all particles in the universe are measured to sufficient accuracy at a particular instant in time • It is possible to predict the motions of every particle at any time in the future (or in the past for that matter) “An intelligent being knowing, at a given instant of time, all forces acting in nature, as well as the momentary positions of all things of which the universe consists, would be able to comprehend the motions of the largest bodies of the world and those of the smallest atoms in one single formula, provided it were sufficiently powerful to subject all the data to analysis; to it, nothing would be uncertain, both future and past would be present before its eyes.” Pierre Simon Laplace Measuring the position of an electron • Shine light on electron and detect reflected light using a microscope • Minimum uncertainty in position is given by the wavelength of the light • So to determine the position accurately, it is necessary to use light with a short wavelength Measuring the momentum of an electron • By Planck’s law E = hc/λ, a photon with a short wavelength has a large energy • Thus, it would impart a large ‘kick’ to the electron • But to determine its momentum accurately, electron must only be given a small kick • This means using light of long wavelength! Fundamental Trade Off … • Use light with short wavelength: accurate measurement of position but not momentum • Use light with long wavelength: accurate measurement of momentum but not position h ΔxΔp ≥ =h 2π The more accurately you know the position (i.e., the smaller Δx is) , the less accurately you know the momentum (i.e., the larger Δp is); and vice versa Heisenberg’s Uncertainty Principle involving energy and time h ΔEΔt ≥ =h 2π • The more accurately we know the energy of a body, the less accurately we know how long it possessed that energy • The energy can be known with perfect precision (ΔE = 0), only if the measurement is made over an infinite period of time (Δt = ∞)