Electronic Structure of Atoms

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Electronic Structure of Atoms

• Chapter 6

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Introduction

• Almost all chemistry is driven by electronic
  structure, the arrangement of electrons in atoms
• What are electrons like?
• Our understanding of electrons has developed
  greatly from quantum mechanics

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6.1 Wave Nature of Light

• If we excite an atom, light can be emitted.
• This nature of this light is defined by the
  electron structure of the atom in question
• light given off by H is different from that by He
  or Li, etc.
• Each element is unique

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6.1 Wave Nature of Light

• The light that we can see (visible light) is only
  a small portion of the electromagnetic spectrum
• Visible light is a type of electromagnetic
  radiation (it contains both electric and
  magnetic components)
• Other types include radio waves, x-rays, UV rays,
  etc. (fig. 6.4)

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The Wave Nature of Light
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The Wave Nature 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.
• c nl

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c vs. l vs. n

• The longer the wavelength, the fewer cycles are
  seen
• c l x n
• radio station KDKB-FM broadcasts at a frequency
  of 93.3 MHz. What is the wavelength of the radio
  waves?

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Quantized Energy and Photons

• Classical physics says that changes occur
  continuously
• While this works on a large, classical theories
  fail at extremely small scales, where it is found
  that changes occur in discrete quantities, called
  quanta
• This is where quantum mechanics comes into play

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Quanta

• We know that matter is quantized.
• At a large scale, pouring water into a glass
  appears to proceed continuously. However, we
  know that we can only add water in increments of
  one molecule
• Energy is also quantized
• There exists a smallest amount of energy that can
  be transferred as electromagnetic energy

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Quantization of light

• A physicist named Max Planck proposed that
  electromagnetic energy is quantized, and that the
  smallest amount of electromagnetic energy that
  can be transferred is related to its frequency

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Quantization of light

• E hn
• h 6.63 x 10-34 J.s (Planck's constant)
• Electromagnetic energy can be transferred in
  inter multiples of hn. (2hn, 3hn, ...)
• To understand quantization consider the notes
  produced by a violin (continuous) and a piano
  (quantized)
• a violin can produce any note by placing the
  fingers at an appropriate spot on the bridge.
• A piano can only produce notes corresponding to
  the keys on the keyboard.

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Photoelectric effect

• If EM radiation is shined upon a clean metal
  surface, electrons can be emitted
• For any metal, there is a minimum frequency below
  which no electrons are emitted
• Above this minimum, electrons are emitted with
  some kinetic energy
• Einstein explained this by proposing the
  existence of photons (packets of light energy)
• The Energy of one photon, E h?.

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Quantized Energy and Photons
The Photoelectric Effect
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Sample

• Calculate the energy of one photon of yellow
  light whose wavelength is 589 nm

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Sample Problems

• A violet photon has a frequency of 7.100 x 1014
  Hz.
• What is the wavelength (in nm) of the photon?
• What is the wavelength in Å?
• What is the energy of the photon?
• What is the energy of 1 mole of these violet
  photons?

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Free Response Type Question

• Chlorophyll a, a photosynthetic pigment found in
  plants, absorbs light with a wavelength of 660
  nm.
• Determine the frequency in Hz
• Calculate the energy of a photon of light with
  this wavelength

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Bohrs Model of the Hydrogen Atom

• 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.
• If we pass white light through a prism, we can
  see the continuous spectrum of visible light
  (ROYGBIV)
• Some materials, when energized, produce only a
  few distinct frequencies of light
• neon lamps produce a reddish-orange light
• sodium lamps produce a yellow-orange light
• These spectra are called line spectra

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Bohrs Model of the Hydrogen Atom
Line Spectra
Shows that visible light contains many wavelengths
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Bohrs Model of the Hydrogen Atom
Bohrs Model Colors from excited gases arise
because electrons move between energy states in
the atom.
Only a few wavelengths emitted from elements
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Bohrs Model of the Hydrogen Atom
Bohrs 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 E
(-2.18 x 10-18 J)(1/n2) Where n is the
principal quantum number (i.e., n 1, 2, 3, .
and nothing else) ground state most stable
(n 1) excited state less stable (n gt
1) When n 8, En 0
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Bohr Model

• To explain line spectrum of hydrogen, Bohr
  proposed that electrons could jump from energy
  level to energy level
• When energy is applied, electron jumps to a
  higher energy level
• When electron jumps back down, energy is given
  off in the form of light
• Since each energy level is at a precise energy,
  only certain amounts of energy (DE Ef Ei)
  could be emitted
• I.e.

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Bohrs Model of the Hydrogen Atom
Bohrs Model We can show that ?E (-2.18 x
10-18 J)(1/nf2 - 1/ni2 ) When ni gt nf, energy
is emitted. When nf gt ni, energy is absorbed.
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Sample calculation (Free Response Type Question)

• In the Balmer series of hydrogen, one spectral
  line is associate with the transition of an
  electron from the fourth energy level (n4) to
  the second energy level n2.
• Indicate whether energy is absorbed or emitted as
  the electron moves from n4 to n2. Explain
  (there are no calculations involved)
• Determine the wavelength of the spectral line.
• Indicate whether the wavelength calculated in the
  previous part is longer or shorter than the
  wavelength assoicated with an electron moving
  from n5 to n2. Explain (there are no
  calculations involved)

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Wave Behavior of Matter

• EM radiation can behave like waves or particles
• Why can't matter do the same?
• Louis de Broglie made this very proposal
• Using Einsteins and Plancks equations, de
  Broglie supposed

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What does this mean?

• In one equation de Broglie summarized the
  concepts of waves and particles as they apply to
  low mass, high speed objects
• As a consequence we now have
• X-Ray diffraction
• Electron microscopy

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Sample Exercise

• Calculate the wavelength of an electron traveling
  at a speed of 1.24 x 107 m/s. The mass of an
  electron is 9.11 x 10-28 g.

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The Uncertainty Principle
Heisenbergs Uncertainty Principle on the mass
scale of atomic particles, we cannot determine
the exactly the position, direction of motion,
and speed simultaneously. For electrons we
cannot determine their momentum and position
simultaneously.
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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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Quantum Mechanics and Atomic Orbitals
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Quantum Mechanics and Atomic Orbitals
If we solve the Schrödinger equation, we get
wave functions and energies for the wave
functions. We call wave functions
orbitals. 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.
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Orbitals and Quantum Numbers Azimuthal Quantum
Number, l. Shape 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. Magnetic Quantum Number, ml direction
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.
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Orbitals and Quantum Numbers
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Sample Exercise

• Which element (s) has an outermost electron that
  could be described by the following quantum
  numbers (3, 1, -1, ½ )?

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You Try

• Which element (s) has an outermost electron that
  could be described by the following quantum
  numbers (4, 0, 0, ½)

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Quantum Mechanics and Atomic Orbitals
Orbitals can be ranked in terms of energy to
yield an Aufbau diagram. Note that the following
Aufbau diagram is for a single electron
system. As n increases, note that the spacing
between energy levels becomes smaller.
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Representation 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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Representation of Orbitals
The s Orbitals
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Representation of Orbitals
The p Orbitals There are three p-orbitals px,
py, and pz. (The three p-orbitals lie along the
x-, y- and z- axes. 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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Representation of Orbitals
The p Orbitals
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Representation of Orbitals
The d and f Orbitals There are 5 d- and 7
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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Representation of Orbitals
The d Orbitals
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Orbitals in Many Electron Atoms
Orbitals of the same energy are said to be
degenerate. All orbitals of a given subshell
have the same energy (are degenerate) For
example the three 4p orbitals are degenerate
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Orbitals in Many Electron Atoms
Energies of Orbitals
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Orbitals in Many Electron Atoms

• 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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Orbitals in Many Electron Atoms
Electron Spin and the Pauli Exclusion Principle
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Orbitals in Many Electron Atoms
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

• 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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Details

• Valence electrons- the electrons in the outermost
  energy levels (not d).
• Core electrons- the inner electrons.
• C 1s2 2s2 2p2

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Fill from the bottom up following the arrows

• 1s2

2s2
2p6
3s2
3p6
4s2
3d10
4p6
5s2
4d10
5p6
6s2

• 12

• 56

• electrons

• 4

• 20

• 38

• 2

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Electron Configurations and the Periodic Table
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Electron Configurations and the Periodic Table
There is a shorthand way of writing electron
configurations Write the core electrons
corresponding to the filled Noble gas in square
brackets. Write the valence electrons
explicitly. Example, P 1s22s22p63s23p3 but Ne
is 1s22s22p6 Therefore, P Ne3s23p3.
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Exceptions

• Ti Ar 4s2 3d2
• V Ar 4s2 3d3
• Cr Ar 4s1 3d5
• Mn Ar 4s2 3d5
• Half filled orbitals.
• Scientists arent sure of why it happens
• same for Cu Ar 4s1 3d10

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More exceptions

• Lanthanum La Xe 6s2 5d1
• Cerium Ce Xe 6s2 4f1 5d1
• Promethium Pr Xe 6s2 4f3 5d0
• Gadolinium Gd Xe 6s2 4f7 5d1
• Lutetium Pr Xe 6s2 4f14 5d1

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Diamagnetism and Paramagnetism

• Diamagnetism
• Repelled by magnets
• Occurs in elements where all electrons are paired
• Usually group IIA or noble gases

• Paramagnetism
• Attracted to magnets
• Occurs in elements with one or more unpaired
  electrons
• Most elements are paramagnetic