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Second Lecture: Modern Atoms and the Electromagnetic Interaction

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Second Lecture: Modern Atoms and the Electromagnetic Interaction HC 209H: Discovery of Fundamental Particles and Interactions Second Lecture: Modern Atoms and the Electromagnetic Interaction Chris Potter University of Oregon HC 209H: Second Lecture – p.1/10 Electrostatic Force and the Planetary Atom Isaac Newton (1642-1727), an English mathematician and physicist, formulated the classical laws of motion and gravity. He also invented (with Leibniz) Calculus. Newton’s law of gravity: the attractive gravitational force between masses m1 and m2, separated by a distance r, is (G is a constant) = × m1×m2 Fg G r2 Charles-Augustin de Coulomb (1736-1806), a French physicist, formulated the law of electrostatic attraction. Coulomb’s electrostatic law: the attractive or repulsive electrostatic force between electric charges q1 and q2, separated by a distance r, is (k is a constant) = × q1×q2 Fe k r2 Planets in our solar system are held in orbit around the sun by gravity. In the planetary atom, negatively Charles-Augustin de Coulomb by charged electrons are held in orbit around a positively Louis Hierle (Credit: Wikipedia) charged nucleus by electrostatic attraction. HC 209H: Second Lecture – p.2/10 Light as an Electromagnetic Wave James Clerk Maxwell (1831-1879), a Scottish physicist, formulated the unified laws of electric fields E~ and magnetic fields B~ . ∇· E~ = 0 ∇· B~ = 0 ∇× ~ − ∂B~ E = ∂t ∇× ~ 1 ∂E~ B = c2 ∂t James Clerk Maxwell, Engraving (Credit: Wikipedia) Changing magnetic fields B~ induce electric fields E~ , and changing electric fields E~ induce magnetic fields B~ : this is light. The wavelength λ and time frequency ν are related to Credits: Wikimedia Commons (top), the speed of light by c = λν. Encyclopedia Brittanica (bottom) HC 209H: Second Lecture – p.3/10 Light as a Particle, the Photon γ Max Planck (1858-1947), a German physicist, first modeled blackbody radiation in 1900 by assuming light exists discrete energy packets, E = hν = hc/λ. Blackbody spectrum (Credit: Encyclopedia Brittanica) Albert Einstein (1879-1955), a German-American physicist, explained in 1910 the photoelectric effect with photons, in which light shining on matter yields electron emission if the frequency ν > E/h. So which is it, is light a wave or a particle? Answer: Albert Einstein ca 1922 (Credit: both. This is the quantum wave/particle duality. Wikipedia) HC 209H: Second Lecture – p.4/10 Subatomic Particles: Electron, Proton, Neutron The modern atom cannot by the atom of the Early Greek philosophers, which was indivisible. What we call an atom is made of protons, neutrons and electrons and is therefore divisible. The Atomic Number Z and Atomic Weight A from Mendeleev’s Peridic Table of the Elements tell us how many protons are in the nucleus: Z protons and A − Z neutrons. Cavendish Laboratory Staff, 1933 All three particles were discovered by physicists at the Cavendish Lab, Cambridge University. The electron (e−) was discovered in 1898 by J.J. Thompson, an English physicist in the cathode ray tube. The nucleus was discovered in 1911 by Ernest Rutherford (with Geiger and Marsden at Manchester), a physicist from New Zealand. The neutron (n) was discovered in 1932 by James Chadwick, an English physicist. HC 209H: Second Lecture – p.5/10 The Bohr Atom, or Quantum Mechanics Problem: the hydrogen planetary atom is unstable. Solution: quantum mechanics. Niels Bohr (1885-1962), a Danish physicist, successfully modelled the light emission spectra of hydrogen assuming that the electron angular momentum is quantized. Bohr assumed (1913) angular momentum L = rmv is quantized, L = n × h/2π (n = 1, 2, 3, 4,...), and set the centripetal force equal to the Coulomb force, e×e = m×v2 k r2 r Solving, he obtains quantized energies and orbits: 2 En = E1/n 2 rn = n × r1 λ = hc/∆E n=1,2,3,. Niels Bohr (Credit: Wikipedia) HC 209H: Second Lecture – p.6/10 The Neutrino: A Desperate Remedy In beta decay of an atom, studied in the early 20th century, the atomic number increases by 1, Z → Z + 1 but the atomic weight stays (almost) the same A → A (mp ≈ mn). One energetic electron e− is emitted from the nucleus. The energy spectrum of the electron is distributed from zero up to Emax and looks like this: (Credit: Wikimedia Commons) Physicists interpreted beta decay as neutron decay n → p + e−, but in that case the electron energy should be sharply peaked near Emax due to energy conservation: En = Ep + Ee− . In 1930 Wolfgang Pauli, a German physicist, postulated the existence of a third particle in beta decay: the neutrino ν, n → p + e− + ν. He doubted it would ever be directly observed. HC 209H: Second Lecture – p.7/10 Atomic Scales: Distance, Mass, Energy −11 Distance. A person is a couple of m tall. The Bohr radius r1 = 5 × 10 m. −27 Mass. A person mass is a few tens of kg. The proton mass is mp = 2 × 10 kg. −18 Energy. A 60 Watt lightbulb emits 60 J/s. The Bohr energy is E1 = −2 × 10 J. Powers of Ten (graphic is clickable) HC 209H: Second Lecture – p.8/10 Fundamental Particles ca 1935 The following table supersedes the Periodic Table of the elements - all With quantum mechanics, a mathematical ordinary matter is made of these. theory, the detailed chemical properties of elements could be explained based on how Light Heavy Interaction electrons arranged themselves around e− p γ nuclei. However, problems remained... ν n The electrostatic force of repulsion should keep protons in the nucleus apart. What Picture of complex atoms: (stronger) force keeps them bound in the nucleus? What interaction accounts for nuclear beta decay, n → pe−ν? Is the neutrino a real particle or does it just save energy conservation? The proton p and neutron n are very heavy compared to the electron. Are they fundamental particles (in the sense of Democritus) or composite? (Credit: Encyclopedia Brittanica) HC 209H: Second Lecture – p.9/10 Worksheet 2 Preparation A very common unit of energy in particle physics is the electron volt (eV=1.6 × 10−19 J). The eV is the energy gained by an electron passing through a voltage difference of one volt. 103 eV=keV (kilo electron volt) 106 eV=MeV (mega electron volt) 109 eV=GeV (giga electron volt) From E = mc2, a very common unit of mass is the eV/c2, MeV/c2, GeV/c2 etc. 3 Kinetic energy of ideal gas molecule: Ek = 2 kT Depicted here is an electron transitioning from n = 3 to n = 2 2 2 The radii at these n are r3 = 3 r1 = 9r1 and r2 = 2 r1 = 4r1, and the change in energy is 2 2 ∆E = E1/3 − E1/2 = E1(1/9 − 1/4). The energy ∆E lost by the electron appears as a photon γ with wavelength λ = hc/∆E. HC 209H: Second Lecture – p.10/10.
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