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Atomic Structure. Wave-Particle Duality. The Wave Nature of Light. All waves have a characteristic wavelength, l , and amplitude, A . Frequency, n , of a wave is the number of cycles which pass a point in one second.
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The Wave Nature of Light • All waves have a characteristic wavelength, l, and amplitude, A. • Frequency, n, of a wave is the number of cycles which pass a point in one second. • Speed of a wave, c, is given by its frequency multiplied by its wavelength: • For light, speed = c = 3.00x108 m s-1. • The speed of light is constant! • Higher Quality video (2:30 into video).
Quantized Energy and Photons • Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. • The relationship between energy and frequency is where h is Planck’s constant ( 6.626 10-34 J s ) .
Quantized Energy and Photons The Photoelectric Effect and Photons • Einstein assumed that light traveled in energy packets called photons. • The energy of one photon is:
Line Spectra and the Bohr Model Line Spectra • Radiation composed of only one wavelength is called monochromatic. • Radiation that spans a whole array of different wavelengths is called continuous. • White light can be separated into a continuous spectrum of colors. • Note that there are no dark spots on the continuous spectrum that would correspond to different lines.
Line Spectra and the Bohr Model Bohr Model • Colors from excited gases arise because electrons move between energy states in the atom. (Electronic Transition) Bohr Video
Line Spectra and the Bohr Model Bohr Model • Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. • After lots of math, Bohr showed that where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).
Line Spectra and the Bohr Model Bohr Model • We can show that • When ni > nf, energy is emitted. • When nf > ni, energy is absorbed
Line Spectra and the Bohr Model Bohr Model Mathcad (Balmer Series) CyberChem (Fireworks) video
Line Spectra and the Bohr Model: Balmer Series Calculations Fall 2012
Line Spectra and the Bohr Model Limitations of the Bohr Model • Can only explain the line spectrum of hydrogen adequately. • Can only work for (at least) one electron atoms. • Cannot explain multi-lines with each color. • Electrons are not completely described as small particles. • Electrons can have both wave and particle properties.
The Wave Behavior of Matter • 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: • 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 Wave Behavior of Matter 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 Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then
Energy and Matter E = m c2
Quantum Mechanics and Atomic Orbitals • Schrödinger proposed an equation that contains both wave and particle terms. • Solving the equation leads to wave functions. • The wave function gives the shape of the electronic orbital. [“Shape” really refers to density of electronic charges.] • The square of the wave function, gives the probability of finding the electron ( electron density ). TBBT: QM-joke
Quantum Mechanics and Atomic Orbitals Solving Schrodinger’s Equation gives rise to ‘Orbitals.’ These orbitals provide the electron density distributed about the nucleus. Orbitals are described by quantum numbers. Sledge-O-Matic- Analogy
Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers • Schrödinger’s equation requires 3 quantum numbers: • Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. ( n = 1 , 2 , 3 , 4 , …. ) • Angular Momentum Quantum Number, . This quantum number depends on the value of n. The values of begin at 0 and increase to (n - 1). We usually use letters for (s, p, d and f for = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals. • Magnetic Quantum Number, m. This quantum number depends on . The magnetic quantum number has integral values between - and + . Magnetic quantum numbers give the 3D orientation of each orbital.
Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers
Representations of Orbitals The s-Orbitals
Representations of Orbitals The p-Orbitals
Orbitals and Their Energies Orbitals CD Many-Electron Atoms
Many-Electron Atoms Electron Spin and the Pauli Exclusion Principle
Many-Electron Atoms • Electron Spin and the Pauli Exclusion Principle • Since electron spin is quantized, we define ms = spin quantum number = ½. • Pauli’s Exclusions Principle: no two electrons can have the same set of 4 quantum numbers. • Therefore, two electrons in the same orbital must have opposite spins.
Figure 6.27 Orbitals CD Figure 6.27
Orbitals CD Figure 6.28
Orbitals and Their Energies Orbitals CD Many-Electron Atoms
Metals, Nonmetals, and Metalloids Metals Figure 7.14
Periodic Trends Two Major Factors: • principal quantum number, n, and • the effective nuclear charge, Zeff.
