Atomic Structure

All waves have a characteristic wavelength,, and amplitude, A. Frequency,, 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 = 3.00x10 8 m s -1. A Brief History of Time The Wave Nature of Light

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 (  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: Quantized Energy and Photons

Nature of Waves: Quantized Energy and Photons

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) 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 n i > n f, energy is emitted. When n f > n i, energy is absorbed Line Spectra and the Bohr Model

Bohr Model Line Spectra and the Bohr Model CyberChem (Fireworks) video Mathcad (Balmer Series)

Line Spectra and the Bohr Model: Balmer Series Calculations

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. Line Spectra and the Bohr Model

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  x is the uncertainty in position and  mv is the uncertainty in momentum, then The Wave Behavior of Matter

Energy and Matter Size of MatterParticle PropertyWave Property Large – macroscopic MainlyUnobservable Intermediate – electron Some Small – photonFewMainly E = m c 2

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 ). Quantum Mechanics and Atomic Orbitals

Solving Schrodinger’s Equation gives rise to ‘Orbitals.’ These orbitals provide the electron density distributed about the nucleus.electron density Orbitals are described by quantum numbers.

Orbitals and Quantum Numbers Schrödinger’s equation requires 3 quantum numbers: 1.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, …. ) 2.Azimuthal 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. 3.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

Quantum Numbers of Wavefuntions Quantum #SymbolValuesDescription Principle n1,2,3,4,…Size & Energy of orbital Azimuthal  0,1,2,…(n-1) for each n Shape of orbital Magneticmm -  …,0,…+  for each  Relative orientation of orbitals within same  Spinmsms +1/2 or –1/2Spin up or Spin down Azimuthal Quantum #  Name of Orbital 0 s (sharp) 1 p (principal) 2 d (diffuse) 3 f (fundamental) 4 g

Quantum Mechanics and Atomic Orbitals nℓ Orbital Name m ℓ (“sub-orbitals) Comment

Orbitals and Quantum Numbers Quantum Mechanics and Atomic Orbitals

The s-Orbitals Representations of Orbitals

The p-Orbitals Representations of Orbitals

d-orbitals

Many-Electron Atoms Orbitals and Their Energies Orbitals CD

Electron Spin and the Pauli Exclusion Principle Many-Electron Atoms

Electron Spin and the Pauli Exclusion Principle Since electron spin is quantized, we define m s = 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. Many-Electron Atoms

Figure 6.27 Orbitals CD

Figure 6.28 Orbitals CD

Many-Electron Atoms Orbitals and Their Energies Orbitals CD

Electron Configurations SpeciesElectron ConfigurationBox OrbitalComment

Metals, Nonmetals, and Metalloids Metals Figure 7.14

Two Major Factors: principal quantum number, n, and the effective nuclear charge, Z eff. Periodic Trends

Figure 7.5: Radius video Clip

Figure 7.6

Figure 7.10 IE clip

Figure 7.9

Electron Affinities Electron affinity is the opposite of ionization energy. Electron affinity: the energy change when a gaseous atom gains an electron to form a gaseous ion: Cl(g) + e -  Cl - (g) Electron affinity can either be exothermic (as the above example) or endothermic: Ar(g) + e -  Ar - (g)

Figure 7.11: Electron Affinities

Group Trends for the Active Metals Group 1A: The Alkali Metals

Group Trends for the Active Metals Group 2A: The Alkaline Earth Metals

Group Trends for Selected Nonmetals Group 6A: The Oxygen Group

Group Trends for Selected Nonmetals Group 7A: The Halogens

Group Trends for the Active Metals Group 1A: The Alkali Metals Alkali metals are all soft. Chemistry dominated by the loss of their single s electron: M  M + + e - Reactivity increases as we move down the group. Alkali metals react with water to form MOH and hydrogen gas: 2M(s) + 2H 2 O(l)  2MOH(aq) + H 2 (g)

Group Trends for the Active Metals Group 2A: The Alkaline Earth Metals Alkaline earth metals are harder and more dense than the alkali metals. The chemistry is dominated by the loss of two s electrons: M  M e -. Mg(s) + Cl 2 (g)  MgCl 2 (s) 2Mg(s) + O 2 (g)  2MgO(s) Be does not react with water. Mg will only react with steam. Ca onwards: Ca(s) + 2H 2 O(l)  Ca(OH) 2 (aq) + H 2 (g)

Atomic Structure