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Chapter 6 Electronic Structure of Atoms

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Title: Chapter 6 Electronic Structure of Atoms


1
Chapter 6Electronic Structure of Atoms
2
Electronic Structure
  • Our goal
  • Understand why some substances behave as they do.
  • For example Why are K and Na reactive metals?
    Why do H and Cl combine to make HCl? Why are
    some compounds molecular rather than ionic?
  • Atom interact through their outer parts, their
    electrons.
  • The arrangement of electrons in atoms are
    referred to as their electronic structure.
  • Electron structure relates to
  • Number of electrons an atom possess.
  • Where they are located.
  • What energies they possess.

3
The Wave Nature of Light
  • Study of light emitted or absorbed by substances
    has lead to the understanding of the electronic
    structure of atoms.
  • Characteristics of light
  • All waves have a characteristic wavelength, l,
    and amplitude, A.
  • The frequency, n, of a wave is the number of
    cycles which pass a point in one second.
  • The speed of a wave, v, is given by its frequency
    multiplied by its wavelength
  • For light, speed c.

4
Identifying ? and ?
5
Electromagnetic Radiation
  • Modern atomic theory arose out of studies of the
    interaction of radiation with matter.
  • Electromagnetic radiation moves through a vacuum
    with a speed of 2.99792458 ? 10-8 m/s.
  • Electromagnetic waves have characteristic
    wavelengths and frequencies.
  • Example visible radiation has wavelengths
    between 400 nm (violet) and 750 nm (red).

6
The Electromagnetic Spectrum
7
Class Guided Practice Problem
  • The yellow light given off by a sodium vapor lamp
    used for public lighting has a wavelength of 589
    nm. What is the frequency of this radiation?

Class Practice Problem
  • A laser used to weld detached retinas produces
    radiation with a frequency of 4.69 x 1014 s-1.
    What is the wavelength of this radiation?

8
Quantized Energy and Photons
  • Planck energy can only be absorbed or released
    from atoms in certain amounts chunks called
    quanta.
  • The relationship between energy and frequency is
  • where h is Plancks constant (6.626 ? 10-34 J.s).
  • To understand quantization consider walking up a
    ramp versus walking up stairs
  • For the ramp, there is a continuous change in
    height whereas up stairs there is a quantized
    change in height.

9
The Photoelectric Effect
  • Plancks theory revolutionized experimental
    observations.
  • Einstein
  • Used plancks theory to explain the photoelectric
    effect.
  • Assumed that light traveled in energy packets
    called photons.
  • The energy of one photon

10
Class Guided Practice Problem
  • Calculate the energy of a photon of yellow light
    whose wavelength is 589 nm.

Class Practice Problem
  • (a)Calculate the smallest increment of energy (a
    quantum) that can be emitted or absorbed at a
    wavelength of 803 nm. (b) Calculate the energy
    of a photon of frequency 7.9 x 1014 s-1. (c) What
    frequency of radiation has photons of energy 1.88
    x 10-18 J? Now calculate the wavelength.

11
Line Spectra and the Bohr Model
  • Line Spectra
  • Radiation composed of only one wavelength is
    called monochromatic.
  • Most common radiation sources that produce
    radiation containing many different wavelengths
    components, a spectrum.
  • This rainbow of colors, containing light of all
    wavelengths, is called a continuous spectrum.
  • Note that there are no dark spots on the
    continuous spectrum that would correspond to
    different lines.

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13
Specific Wavelength Line Spectra
When gases are placed under reduced pressure in a
tube and a high voltage is applied, radiation at
different wavelengths (colors) will be emitted.
14
Line Spectra
  • Balmer discovered that the lines in the visible
    line spectrum of hydrogen fit a simple equation.
  • Later Rydberg generalized Balmers equation to
  • where RH is the Rydberg constant (1.096776 ? 107
    m-1), h is Plancks constant (6.626 ? 10-34 Js),
    n1 and n2 are integers (n2 gt n1).

15
Bohr Model
  • Rutherford assumed the electrons orbited the
    nucleus analogous to planets around the sun.
  • However, a charged particle moving in a circular
    path should lose energy.
  • This means that the atom should be unstable
    according to Rutherfords theory.
  • Bohr noted the line spectra of certain elements
    and assumed the electrons were confined to
    specific energy states. These were called orbits.

16
Line Spectra (Colors)
  • Colors from excited gases arise because electrons
    move between energy states in the atom.

17
Line Spectra (Energy)
  • 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).

18
Limitations of the Bohr Model
  • Can only explain the line spectrum of hydrogen
    adequately.
  • Electrons are not completely described as small
    particles.

19
The Wave Behavior of Matter
  • Knowing that light has a particle nature, it
    seems reasonable to ask if matter has a wave
    nature.
  • Using Einsteins and Plancks 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.

20
The Wave Behavior of Matter
  • The Uncertainty Principle
  • Heisenbergs 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

21
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.
  • The square of the wave function, gives the
    probability of finding the electron,
  • that is, gives the electron density for the atom.

22
Electron Density Distribution
Probability of finding an electron in a hydrogen
atom in its ground state.
23
The Three Quantum Numbers
  • Schrödingers equation requires 3 quantum
    numbers
  • Principal Quantum Number, n. This is the same as
    Bohrs n. As n becomes larger, the atom becomes
    larger and the electron is further from the
    nucleus. (n 1, 2, 3)
  • Azimuthal Quantum Number, l. This quantum number
    depends on the value of n. The values of l begin
    at 0 and increase to (n - 1). We usually use
    letters for l (s, p, d and f for l 0, 1, 2, and
    3). Usually we refer to the s, p, d and
    f-orbitals. (l 0, 1, 2n-1). Defines the shape
    of the orbitals.
  • Magnetic Quantum Number, ml. This quantum number
    depends on l. The magnetic quantum number has
    integral values between -l and l. Magnetic
    quantum numbers give the 3D orientation of each
    orbital in space. (m -l01)

24
Orbitals and Quantum Numbers
25
Class Guided Practice Problem
  • (a) For n 4, what are the possible values of l?
    (b) For l 2. What are the possible values of
    ml? What are the representative orbital for the
    value of l in (a)?

Class Practice Problem
  • (c) How many possible values for l and ml are
    there when (d) n 3 (b) n 5?

26
Representations of Orbitals The s-Orbitals
  • All s-orbitals are spherical.
  • As n increases, the s-orbitals get larger.
  • As n increases, the number of nodes increase.
  • A node is a region in space where the probability
    of finding an electron is zero.
  • At a node, ?2 0
  • For an s-orbital, the number of nodes is (n - 1).

27
The s-Orbitals
28
The p-Orbitals
  • There are three p-orbitals px, py, and pz.
  • The three p-orbitals lie along the x-, y- and z-
    axes of a Cartesian system.
  • The letters correspond to allowed values of ml of
    -1, 0, and 1.
  • The orbitals are dumbbell shaped.
  • As n increases, the p-orbitals get larger.
  • All p-orbitals have a node at the nucleus.

29
The p-Orbitals
Electron-distribution of a 2p orbital.
30
The d and f-Orbitals
  • There are five d and seven f-orbitals.
  • Three of the d-orbitals lie in a plane bisecting
    the x-, y- and z-axes.
  • Two of the d-orbitals lie in a plane aligned
    along the x-, y- and z-axes.
  • Four of the d-orbitals have four lobes each.
  • One d-orbital has two lobes and a collar.

31
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32
Orbitals and Quantum Numbers
  • Orbitals can be ranked in terms of energy to
    yield an Aufbau diagram.
  • As n increases, note that the spacing between
    energy levels becomes smaller.
  • Orbitals of the same energy are said to be
    degenerate.

33
Orbitals and Their Energies
34
Electron Spin and the Pauli Exclusion Principle
  • Line spectra of many electron atoms show each
    line as a closely spaced pair of lines.
  • Stern and Gerlach designed an experiment to
    determine why.
  • A beam of atoms was passed through a slit and
    into a magnetic field and the atoms were then
    detected.
  • Two spots were found one with the electrons
    spinning in one direction and one with the
    electrons spinning in the opposite direction.

35
Electron Spin and the Pauli Exclusion Principle
36
Electron Spin and the Pauli Exclusion Principle
  • Since electron spin is quantized, we define ms
    spin quantum number ? ½.
  • Paulis 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.

37
Electron Configurations Hunds Rule
  • Electron configurations tells us in which
    orbitals the electrons for an element are
    located.
  • Three rules
  • electrons fill orbitals starting with lowest n
    and moving upwards
  • no two electrons can fill one orbital with the
    same spin (Pauli)
  • for degenerate orbitals, electrons fill each
    orbital singly before any orbital gets a second
    electron (Hunds rule).

38
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40
Electron Configurations and the Periodic Table
  • The periodic table can be used as a guide for
    electron configurations.
  • The period number is the value of n.
  • Groups 1A and 2A (1 2) have the s-orbital
    filled.
  • Groups 3A - 8A (13 - 18) have the p-orbital
    filled.
  • Groups 3B - 2B (3 - 12) have the d-orbital
    filled.
  • The lanthanides and actinides have the f-orbital
    filled.

41
Class Guided Practice Problem
  • Write the electron configurations for the
    following atoms (a) Cs and (b) Ni

Class Practice Problem
  • Write the electron configurations for the
    following atoms (a) Se and (b) Pb

42
Condensed Electron Configurations
  • Neon completes the 2p subshell.
  • Sodium marks the beginning of a new row.
  • So, we write the condensed electron configuration
    for sodium as
  • Na Ne 3s1
  • Ne represents the electron configuration of
    neon.
  • Core electrons electrons in Noble Gas.
  • Valence electrons electrons outside of Noble
    Gas.

43
Transition Metals
  • After Ar the d orbitals begin to fill.
  • After the 3d orbitals are full, the 4p orbitals
    begins to fill.
  • Transition metals elements in which the d
    electrons are the valence electrons.

44
Lanthanides and Actinides
  • From Cs onwards the 4f orbitals begin to fill.
  • Note La Xe6s25d14f0
  • Elements Ce - Lu have the 4f orbitals filled and
    are called lanthanides or rare earth elements.
  • Elements Th - Lr have the 5f orbitals filled and
    are called actinides.
  • Most actinides are not found in nature.
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