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Chapter 7: Electronic Structure of Atoms

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  1. Quantum Theory Electrons in atoms can have only certain discrete energies, referred to as energy states or energy levels. Normally, the electron is in the state of lowest energy called the ground state (n=1). By absorbing a certain definite amount of energy, the electron can move to a higher level, called an excited state (n=2,3...). When electrons return to lower energy levels, energy may be given off as light. The difference in energy between the levels can be deduced from the wavelength or frequency of the light.

    Postulates of the Quantum Theory

    1. Atoms and molecules can only exist in certain states, characterized by definite amounts of energy. When an atom or molecule changes its state, it absorbs or emits an amount of energy just sufficient to bring it to another state.

    2. When atoms or molecules absorb or emit light in moving from one energy state to another, the wavelengths (lambda) of the light is related to the energies of the two states by the equation.

      Ehi - Elo = hc / lambda (absorbed photon, higher energy state)

      (delta E = Efinal - Einitial = Ehi - Elo)

      Elo - Ehi = - hc / lambda (emitted photon, lower energy state)

      hc = 1.196x105 (kJ * nm) / mol

    3. The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.

  2. Bohr Model
    Bohr postulated that an electron moves about the nucleus in circular orbits of fixed radius. By absorbing energy, it moves to a higher orbit of larger radius; energy is given off as light (photons) when the electron returns.
    diagram
    The fixed radii was based on spectroscopy; Lyman Series (ultraviolet), Balmar Series (visible light), Paschen Series (infrared)

    Basic Equation development:
    mvr = n h / (2 pi)     (1)
    mvr = angular momentum, m = mass, v = velocity, r = radius of electrons orbit.
    From experiment the electron's energy was restricted in the following way:
    E = -B / n2     (2)
    n is an integer from spectroscopy,
    B = -1312 kJ /mol (Ionization energy)
    Equation (2) allowed Bohr to find the energy of the photon, then plugging the energy into Einstein's equation deltaE = hc / lambda and solving for wavelength lambda = hc / delta E

    Note 1: Bohr is now capable of finding the wavelength of light theoretically, his calculations match experimental work with spectroscopy (for hydrogen).
    Note 2: Using Bohr's equations, the ionization energy could also be found. (Ionization energy is the energy required to remove an electron from a gaseous atom)

  3. Wave Mechanical Model (Quantum mechanical atom)

    By the mid-1920's it had become apparent that the Bohr model could not be made to work for atoms other than hydrogen. A new approach was formed by three physicists; Werner Heisenberg, Louis de Broglie, and Erwin Schrodinger.

    1. Louis de Broglie
      lambda = h / mv he stated that the electron orbiting the nucleus must fit into the circumference of the circle an integral number of times, 2 pi r = n lambda, combining the two equations gives 2 pi r = nh / mv, rearranging this equation gives m v r = n h / 2 pi Bohr's equation, but based on different premises that are physically true.
      F.Y.I. h / 2 pi = hbar

    2. Werner Heisenberg
      Heisenberg uncertainty principle: "There is a fundamental limitation to just how precisely we can know both the position and the momentum of a particle at a given time." We can't determine the position and velocity of an electron at the same time. Therefore Bohr's equation dealing with knowing the electrons' position can't be used.
      m v 2x = nh / 2 pi
      (deltap)(deltax) = nh / 4 pi (p is momentum, x is position)

    3. Erwin Schrodinger
      Developed an equation based on the probability of an electron's given position in space at any given time. This study of the electron's probable location has come to be called quantum mechanics.
  4. Scrodinger's equation is based on the four quantum numbers: n, l, ml, ms
    n = period, principle energy level
    l = s, p, d, f orbital type, sublevel
    ml = orientation of orbitals (angular momentum)
    ms = spin

    1. Principle Energy Level
      n = 1, 2, 3, etc. Value of n is the main factor (but not the only one) that determines the energy of an electron and its distance from the nucleus.
      Maximum capacity for energy level = 2n2

    2. Sublevels
      l = 0, 1, 2, ... (n-1)
      n = 1 l = 0 (One sublevel)
      n = 2 l = 0, 1 (Two sublevels)
      n = 3 l = 0, 1, 2 (Three sublevels)
      n = 4 l = 0, 1, 2, 3 (Four sublevels)

      electrons for which
      l = 0 are called s (Stands for sharp) spherical
      l = 1 are called p (Stands for principle) perpendicular
      l = 2 are called d (Stands for diffuse)
      l = 3 are called f (Stands for fundamental)

      The letters come from the atomic spectrum series from the 20th century.

    3. Orbitals
      Each sublevel contains one or more orbitals. ml describes the orientation of the electron cloud. For any value of l, ml may have any integral values between -l and l.

      i.e. l = 2 ml = -2, -1, 0, 1, 2 (5 oribtals)

      For any l there are 2l + 1 orbitals in that sublevel.

    4. Spin
      ms = spin an electron. Can have one of 2 spins + 1 / 2, and - 1 / 2.
      Electrons that have the same value of ms are said to have parallel spins. Electrons that have different ms values are said to have opposed spins. For 2 electrons to exist in thee same orbital, they must have opposed spins.

    Pauli Exclusion Principle: No two electrons in the same atom can have the same set of quantum numbers.

    Procedure for placing electrons in an atom:
    Aufbau Principle: Electrons are added to sublevels in the order of increasing energy. Generally fills each sublevel before beginning the next.

    Hund's Rule: When filling orbitals of equal energy (degenerate orbitals) order is such that as many electrons as possible remain unpaired.


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