Chapter 6: Electronic Structure and the Periodic Table

1
Chapter 6 Electronic Structure and the Periodic
Table

• Chapter Outline
• 6.1 Light, Photon 6.5 Orbital Diagrams of
  
• Energies, and Atomic Atoms
• Spectra 6.6 Electron Arrangements
• 6.2 The Hydrogen Atom in Monoatomic
  Ions
• 6.3 Quantum Numbers, 6.7 Periodic Trends in
  the
• Energy Level, and in the
  Properties of
• 6.4 Electron Configurations in Atoms

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Introduction

• Review of Structure of Atom
• (i) Atom has positively charged nucleus
  which contains protons and neutrons.
• (ii) The number of protons in the nucleus is
  characteristic of the atoms of a particular
  element.
• (iii) The nucleus is surrounded by negatively
  charged electrons.

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Introduction (Contd)

• In this chapter we will focus on electron
  arrangements in atoms, paying close attention to
  the relative energies of different electrons
  (energy levels) and their spatial locations
  (orbitals, orbital diagram).
• The electron configuration and the orbital
  diagram of an atom of an element can be decduced
  from its position in the periodic table.
• Using the periodic table, we can predict atomic
  and ionic radii as well as ionization energy and
  electronegavtivity.

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Light, Photon Energies, and Atomic Spectra

• Light travels through space as a wave, which is
  made of crests and troughs. There are two
  characteristics of waves we will look at
• a) Wavelength (?) The distance between two
  consecutive crests or troughs, most often
  measured in meters or nanometers (1nm 10-9m)

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Waves (Contd)

• b) Frequency (?) the number of wave cycles
  (successive crests or troughs) that pass a given
  point in unit time. Reported in hertz (Hz),
  which is cycles/second.

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Speed of Waves

• The speed of a wave can be calculated from the
  following equation
• c ??
• Where c is the speed of light, 2.998 x 108 m/s.

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The Particle Nature of Light

• Max Planck and Albert Einstein shoed that light
  was both a wave and a particle. The particles
  that make up light are called photons.
• The energy of a photon can be calculated as
  follows
• E h? hc/?

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Units of Energy

• The SI unit of energy is the joule (J). A joule
  is a small quantity one joule of electrical
  energy would keep a 10-W light bulb burning for
  only 1/10 of a second.
• Energy is often expressed in kilojoules (kJ).
• 1 kJ 103J
• The h in Plancks equation is called Plancks
  constant.
• h 6.626 x 10-34 J s

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Atomic Spectra

• Newton, in the 17th century, discovered that
  visible (white) light from the sun can be
  separated into its various colors using a prism.
  The spectrum that is obtained is continuous it
  contains all wavelengths from 400-700nm.

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Spectra of Elements in the Gas Phase

• If the light from a gas discharge tube containing
  a particular element is passed through a prism,
  only narrow colored lines are observed. This
  pattern of lines emitted by elements is called
  its line spectrum.
• The line spectrum of an element is characteristic
  of that element and can be used to identify it.
  Not all the lines in a line spectrum are in the
  visible region.

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Line Spectrum (Contd)

• The lines in a line spectrum indicate the
  wavelength of the photon that was given off by
  the element. Since these photons appears to have
  discrete wavelengths, they must also have
  discrete energies since
• E h? hc/?

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Line Spectrum (Contd)

• The lines in the spectrum are produced when a
  photon of energy is released.
• This release of a photon coincides with the
  movement of an electron from one energy level to
  another.
• It is from this observation, that it was
  discovered that the electronic energy levels in
  an atom are quantized.

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Energy Levels (Contd)

• In theory, it is possible to unravel all the
  energy levels of an atom using its line spectrum.

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Line Spectrum of Hydrogen
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Energy Levels of Hydrogen

• UV(Lyman) Visible (Balmer) IR (Paschen)
• 121.53 656.28 1875.90
• 102.54 486.13 1281.80
• 97.23 434.05 1093.80
• 93.75 410.18 1004.93
• 93.05 397.01

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The Hydrogen Atom

• Niels Bohr was the first to deduce the electronic
  structure of the hydrogen atom. He was awarded
  the Nobel Prize in physics in 1922.
• In his theory, Bohr assumed that a hydrogen atom
  consisted of a central proton about which an
  electron moves in a circular orbit.

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The Bohr Model

• He related the electrostatic force (attraction)
  between the proton and the electron to the
  centrifugal force due to the circular motion of
  the atom.
• Bohr was able to express the energy of the
  electron in terms of the radius of the electrons
  orbit.
• Classical Argument Coulombs Law of
  Electrostatic attraction and Newtons Laws of
  Motion.

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Bohrs Model (Contd)

• In order to move beyond this point, Bohr assumed
  that the electron in the hydrogen can only have
  certain definite energies.
• Bohr developed the following equation
• En -RH/n2
• RH (Rydberg constant) 2.180 x 10-18 J
• n principal quantum number (n positive integral
  value)

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3 Assumptions

• 1. Bohr designated zero energy as the point at
  which the proton and electron are completely
  separated. Energy has to be absorbed to reach
  that point. In practical terms, the electron, in
  all its allowed energy states, must have an
  energy below zero (negative number).

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Assumptions (Contd)

• 2. Ordinarily, the hydrogen atom is in its
  lowest-energy state, referred to as the ground
  state, for which n 1. When an electron absorbs
  sufficient energy, it moves to a higher excited
  state. In hydrogen, the first excited state is n
  2.
• 3. When an excited state given off energy as a
  photon of light, it drops back to a lower energy
  level. The electron can return to the ground
  state or to a lower excited state.

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Assumptions (Contd)

• The energy of the photon evolved is equal to the
  difference in energy between the two states
• ?E hv Ehi Elo
• In hydrogen, the Balmer series involves from
  transitions to level n 2 from higher levels.
  The lyman series involves transitions to n 1.

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Quantum Mechanical Model

• When Bohrs work was extended to a two electron
  system (helium), the errors associated with the
  calculated energies rises to 5 vs 0.1 for
  hydrogen.
• This led to the abandonment of the idea that the
  electron moved around the nucleus in a
  well-defined orbit at a fixed distance.

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Quantum Mechanics (Contd)

• De Broglie suggested that if light could show the
  properties of particles as well as waves, then
  perhaps an electron could also act as a wave.

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Differences Between Quantum and Classical
Mechanics

• Quantum mechanics differs from Bohrs Model in
  the following ways
• 1. The kinetic energy of an electron is inversely
  related to the volume of the region to which it
  is confined. As the electron moves closer and
  closer to the nucleus, the electrostatic energy
  decreases (becomes more negative). If this were
  the only factor, the electron should radiate
  energy and fall into the nucleus. However, the
  kinetic energy is increasing at the same time,
  b/c the electron is with in a smaller and smaller
  volume.

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Differences (Contd)

• 2. It is impossible to specify the precise
  position of an electron in an atom at a given
  instant. We can neither describe in detail the
  path an electron takes about the nucleus. All we
  can do is estimate the probability of finding an
  electron in a certain region.

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Schrödingers Equation

• Schrödingers equation takes the form of a
  differential equation to express the wave
  properties of electrons.
• This equation can be used to solve for the
  amplitude (height), ?, of the electron wave at
  various points in space.
• ? is known as the wave function

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Wavefunction (Contd)

• The square of the wave function, ?2, is directly
  proportional to the probability of finding the
  electron at a particular point.
• e.g. If ?2 is twice as large at point A then
  point B, then the probability of finding the
  electron at point A is twice as great then
  finding it at point B

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Wavefunction (Contd)

• An electron cloud diagram illustrates how ?2
  varies moving out from the nucleus.
• The color fades moving out from the nucleus in
  any direction (value of ?2 drops
  proportionately).
• The electron distribution can also be shown by
  drawing the orbital within which there is a 90
  chance of finding the electron.
• In the case of hydrogen, the orbital is
  spherical (probability is independent of
  direction).

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Quantum Numbers, Energy Levels, and Orbitals

• There are many solution for ?, each associated
  with a set of numbers called quantum numbers.
  There are 3 quantum numbers, given the symbols n,
  l, and ml. A fourth quantum number, ms, is
  needed to completely describe an orbital.
• A wave function corresponding to a particular set
  of three quantum numbers is referred to as an
  atomic orbital.
• Orbitals differ from each other in shape, energy,
  and spatial orientation of their electron cloud.

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First Quantum Number, n

• n represents the principal energy level. The
  energy of the electron increases as n increases
  (and the electron is found urther out from the
  nucleus).
• n 1, 2, 3, 4.

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Second Quantum Number, l Sublevels (s, p, d, f)

• Every principal quantum level has 1 or more
  sublevels, denoted by l. The quantum numbers n
  and l are related l can take on any value from 0
  to a maximum of n 1.
• l 0, 1, 2, ., (n 1)
• e.g. n 1, l 0
• n 2, l 0, 1
• In general, in the nth principal quantum level,
  there are n different sublevels.

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Second Quantum Number (Contd)

• Sublevels are commonly designated by letters
  rather than numbers. The letters used are s, p,
  d, and f.
• Quantum number, l 0 1 2 3
• Type of sublevel s p d f
• In designating a sublevel, a number is included
  to indicate the the principle level as well.
• e.g. 1s (n 1, l 0)
• 2p (n 2, l 1)

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Second Energy Level (Contd)

• For hydrogen, the energy of the electron is
  independent of the value of l. For multielectron
  systems, the energy is dependent on both l and n.
• ns

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Third Quantum Number, ml

• Each sublevel contains one or more orbital, which
  differ from each other by the value of the third
  quantum number, ml.
• ml determines the direction in space of the
  electron cloud surrounding the nucleus.
• For a given value of l, ml can have any integral
  value including 0 between l and l
• e.g. ml l, , 1, 0, -1, , -l

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Third Quantum Number (Contd)

• E.g. The electron in the hydrogen atom occupies
  the 1s orbital in the ground state.
• All s orbitals are spherical, they differ only
  in size. As n increases, so does the radius of
  the orbital
• For a p sublevel (l 1), ml -1, 0, 1 that is
  within a given p sublevel, there are 3 different
  orbitals, often referred to as px, py, and pz.
• In general, for a sublevel of quantum level l,
  there are a total of 2l 1 orbitals.

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Fourth Quantum Number, ms

• The quantum number ms is assigned to electron
  spin. An electron has magnetic properties that
  correspond to those of a charged particle
  spinning on its axis. Two spins are possible
  clockwise or counterclockwise
• ms can have one of two possible values ½ or
  ½ .

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Fourth Quantum Number (Contd)

• Electrons which have the same spin (ms) are said
  to have parallel spins. Those that have
  different values are said to have opposed spins.

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Pauli Exclusion Principle

• No two electrons may have the same set of four
  quantum numbers. Suggested by Wolfgang Pauli in
  1925.
• What is the practical implication of this theory
  in regards to the distribution of electrons
  around the nucleus?

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Example

• Consider 2s orbital
• n 2 l 0 ml 0
• To satisfy the Pauli exclusion principle, the two
  electrons must have different spins (values of ms)

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Capacities of Principal Levels, Sublevels and
Orbitals

• Summary of Quantum Number Rules
• I. Each principle level of quantum number n
  contains a total of n sublevels.
• II. Each sublevel of quantum number l contains a
  total of 2l 1 orbitals
• s sublevel (l 0) 1 orbital
• p sublevel (l 1) 3 orbitals
• d sublevel (l 2) 5 orbitals
• f sublevel (l 3) 7 orbitals
• III. Each orbital can hold two electrons, which
  must have opposed spins.

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Allowed Sets of Quantum Numbers

• Table 6.3 The number of electrons in a sublevel
  is found by adding up all the electrons in the
  orbitals within that sublevel

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Electron Configuration in Atoms

• Electron configuration indicates the number of
  electrons (using a superscript) in each sublevel
  (orbital).
• e.g. 1s22s22p5
• Note electron configurations assume gaseous
  atoms in the ground state.

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Filling of Sublevels and the Periodic Table

• Figure 6.8 shows the periodic table and the
  trends in electron configuration.
• The atoms of elements in a group of the periodic
  table have the same distribution of electrons in
  the outermost energy level

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Trends In the Periodic Table

• I. Elements in group 1 and 2 are filling s
  sublevels.
• II. Elements in groups 13-18 fill p sublevels
• III. The transition metals fill d sublevels
• IV. The lanthanides and actinides fill f
  sublevels.

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Orbital Diagrams of Atoms

• Electron configurations show the number of
  electrons in each sublevel.
• Orbital diagrams show how electrons are
  distributed in orbitals.
• Orbitals are represented by ( ), and electron
  are represented by up and down arrows.

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Hunds Rule

• When several orbitals of equal energy are
  available, as in a given sublevel, electrons
  enter singly with parallel spins.
• In all filled orbitals, the two electrons have
  opposed spins.
• In accordance with Hunds Rule, within a given
  sublevel there are as many half-filled orbitals
  as possible.

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Experimental Basis for Hunds Rule

• Hunds Rule was verified by doing experiments
  with a variety of solids in a magnetic field.
• Solids with unpaired electrons are attracted
  into the field (paramagnetic)
• Solids that are not attracted into the field
  (slightly repelled)have no unpaired electrons
  (diamagnetic)

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Electron Arrangements in Monoatomic Ions

• In general, when electrons are added or removed,
  they are done so from sublevels in the highest
  energy level (typically s orbitals first).
• Metals typically form cations that have a noble
  gas configuration.

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Transition Metal Cations

• The transition metals to the right of Sc do not
  form ions with a noble gas configuration.
• Why?
• When transition metals form cations, the outer
  most s electrons are lost first.

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Trends in the Periodic Table

• Atomic Radius decreases across from left to
  right increase from top to bottom.
• Ionic Radius Positive ions are smaller than the
  atoms they are derived from.
• Negative ions are larger than the atoms they are
  derived from.

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Ionization Energy

• Ionization Energy is a measure of how difficult
  it is to remove an electron from a gaseous atom.
• Increases across the periodic table from left to
  right.
• Decreases down the periodic table.