Electronic Structure of Atoms

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Electronic Structure of Atoms
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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.

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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.

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Identifying ? and ?
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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 ? 108 m/s.
• Electromagnetic waves have characteristic
  wavelengths and frequencies.
• Example visible radiation has wavelengths
  between 400 nm (violet) and 750 nm (red).

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The Electromagnetic Spectrum
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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?

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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.

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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

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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.

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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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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.
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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).

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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.

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Line Spectra (Colors)

• Colors from excited gases arise because electrons
  move between energy states in the atom.

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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).

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Limitations of the Bohr Model

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

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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.

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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

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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.

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Electron Density Distribution
Probability of finding an electron in a hydrogen
atom in its ground state.
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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)

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Orbitals and Quantum Numbers
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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?

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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).

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The s-Orbitals
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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.

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The p-Orbitals
Electron-distribution of a 2p orbital.
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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.

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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.

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Orbitals and Their Energies
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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.

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Electron Spin and the Pauli Exclusion Principle
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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.

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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).

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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.

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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

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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.

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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.

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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.