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Transcript

Chapter 7 Atomic Structure • Waves wavelength, (peak to peak distance) amplitude, A (peak height) frequency, (number of waves that pass a point per unit time) • speed, v (frequency x wavelength) • • • v • Light speed (constant) = c = 2.99792458 108 m/s Energy--frequency relationship: E h where h = Planck’s constant = 6.626 10-34 J-s Long wavelength --> small frequency--> low energy Short wavelength --> high frequency -->high energy • Planck & Einstein: Energy is quantized. Energy can only be absorbed or released from atoms in certain amounts called quanta. Light is quantized in packets called photons. Light and matter have both wave and particle properties. Wave-Particle Duality • Quantization example: Ramp vs. stairs • Ramp - continuous change in height • Any value is of potential energy is allowed. • Stairs – only certain heights allowed (quantization) • Each stair step represents an allowed potential energy Evidence for Quantization of Energy Photoelectric Effect • Evidence for the particle nature of light • Light shines on a metal surface • If above a threshold frequency---electrons ejected • If below the threshold frequency---no electrons ejected (no matter how intense the light) • Number of electrons ejected depends on light intensity • Recall light comes in photons (particle like nature) Light must have enough energy to knock an electron off of the metal surface. E h Line Spectra • Radiation spanning an array of wavelengths is called continuous (e.g. sunlight). • Prisms separate white light a spectrum of colors. • Spectrum is continuous --- no dark spots (no missing colors) • Elements in gas discharge tubes have line spectra • Not continuous • Only certain colors present • Monochromatic lines = one • Each color has a unique and energy E Bohr correlated lines with electron transitions between energy levels • Bohr model – • Energy of electrons is quantized • Energy states correspond to orbits • Orbits are numbered: principal quantum number (n) • n = 1, is closest to nucleus (lowest energy) • Electrons can only move between orbits by absorbing and emitting energy in quanta (h). • Ground State –electron is in its lowest energy orbit. • Excited State – An outside energy source promotes electron to a higher energy orbit. • Unstable – electrons transition to lower states and give off excess energy as light • Each line (monochromatic color) is from one transition excited state lower state • Energy of light = energy difference between electron states E h 1 1 2.18 10 18 J 2 2 n f ni hc • When ni > nf, energy is emitted. • When nf > ni, energy is absorbed Limitations of the Bohr Model • Only adequately explains hydrogen’s line spectrum. • Electrons are not completely described as small particles. • Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature. • Using Einstein’s and Planck’s equations, de Broglie showed: h mv • The momentum, mv, is a particle property, whereas is a wave property. • de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small. The Uncertainty Principle • Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. • For electrons: we cannot determine their momentum and position simultaneously. • If Δx is the uncertainty in position and Δmv is the uncertainty in momentum, then x·mv h 4 • Schrödinger proposed an equation that contains both wave and particle terms (duality). • Solving the equation leads to wave functions, . • The wave function gives the shape of the electronic orbital. • The square of the wave function, 2, gives the probability of finding the electron, • that is, gives the electron density for the atom. See fig 6.16