Download Quantum Theory: Wave Properties, Plank's Equation, and Electron's Dual Nature and more Exams Chemistry in PDF only on Docsity! Chapter 7: Quantum Theory and the Electronic Structure of Atoms "Compromising your future to the city council of Bethesda, Maryland." Wave Prooerties and Plank's EQuation u = \»). Relates the speed, frequency, and wavelength of a wave. With electromagnetic radiation. u is c, the speed of light. Make sure wavelength is in meters -use nm by mistake instead and you'll be off by nine or so powers of ten. E=b1) 6 r:. = h'\l" ~E = E..f -E J Relates the energy of a quantum to its wavelength. "h" is a constant, 6.63 * 10-34 J*s. Often before you use this one you'll have to figure out the frequency -just use the first equation first. The Dual Nature of the Electron ) = \'\ IV'\. v Matter can behave like a wave if its in motion -this equation quantifies it. "m" is mass in kg; "v" is velocity in m/s; "A" is wavelength in meters; "h" is Plank's constant. Do not confuse this equation with u = uA; they aren't the same thing. A= (h)/(mv) is for PARTICLES IN MOTION (hummingbirds, jets, tennis balls) while u = uA is for W A YES (light, radio, microwaves). Bobr's Model Bohr ran with Plank's ideas (that energy is emitted in discrete packets) to model the electron cloud of a hydrogen atom. Said the electron orbited the nucleus in a circular orbit at a specific distance (n; 1,2,3,4...) around the nucleus. Proved himself correct by predicting wavelengths of light produced by the emission spectrum. Problems With Bohr's Model Bohr's model only worked with hydrogen -anything more complicated than that and it fell apart. Also had problems with the implications of the De Broglie equation -if an electron had wave particles, how could it be "located" in a specific orbit? Fixinl! Bobr's Model- Modern Ouantum Pb~sics Bohr's model was rectified by incorporating the wave properties of an electron. Being a wave, it was impossible to identify the exact position of an electron while at the same time knowing its momentum (the Heisenberg uncertainty principle). Austrian physicist named SchrMinger then models the hydrogen atom with obscenely complicated math. The obscenely complicated math becomes known as the SchrMinger equation. The solution, the wave function, contains three variables, and solving for the variables produces the first three quantum numbers (n, I, ml). The wave function squared, <p2, is a measure of probability of finding the electron in a given piece of space at a given instant. The pieces of real estate are called atomic orbital to differentiate them from Bohr's earlier model. ~ Wbat Reallv CbaoS!ed. as Faras- \,:e ~Il ~are..: Replace the word "definitely" (as in Bohr's nice predictable electrons in circular planetary orbits) with the "words probably somewhere around here, most of the time." This equation ties the energy of the photon emitted during an emission to the states, n, involved. "ni" is the intial state (1,2,3,4...) and "nf'is the final state (also 1,2,3,4...).
