Chapter 13 Electrons in Atoms

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Chapter 13Electrons in Atoms

• Charles Page High School
• Dr. Stephen L. Cotton

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Section 13.1Models of the Atom

• OBJECTIVES
• Summarize the development of atomic theory.

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Section 13.1Models of the Atom

• OBJECTIVES
• Explain the significance of quantized energies of
  electrons as they relate to the quantum
  mechanical model of the atom.

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Greek Idea

• Democritus and Leucippus
• Matter is made up of solid indivisible particles
• John Dalton - one type of atom for each element

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J. J. Thomsons Model

• Discovered electrons
• Atoms were made of positive stuff
• Negative electron floating around
• Plum-Pudding model

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Ernest Rutherfords Model

• Discovered dense positive piece at the center of
  the atom- nucleus
• Electrons would surround it
• Mostly empty space
• Nuclear model

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Niels Bohrs Model

• He had a question Why dont the electrons fall
  into the nucleus?
• Move like planets around the sun.
• In circular orbits at different levels.
• Amounts of energy separate one level from
  another.
• Planetary model

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Bohrs planetary model

• Energy level of an electron
• analogous to the rungs of a ladder
• electron cannot exist between energy levels, just
  like you cant stand between rungs on ladder
• Quantum of energy required to move to the next
  highest level

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The Quantum Mechanical Model

• Energy is quantized. It comes in chunks.
• A quanta is the amount of energy needed to move
  from one energy level to another.
• Since the energy of an atom is never in between
  there must be a quantum leap in energy.
• Erwin Schrodinger derived an equation that
  described the energy and position of the
  electrons in an atom

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The Quantum Mechanical Model

• Things that are very small behave differently
  from things big enough to see.
• The quantum mechanical model is a mathematical
  solution
• It is not like anything you can see.

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The Quantum Mechanical Model

• Has energy levels for electrons.
• Orbits are not circular.
• It can only tell us the probability of finding
  an electron a certain distance from the
  nucleus.

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The Quantum Mechanical Model

• The atom is found inside a blurry electron
  cloud
• A area where there is a chance of finding an
  electron.
• Draw a line at 90
• Think of fan blades

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Atomic Orbitals

• Principal Quantum Number (n) the energy level
  of the electron.
• Within each energy level, the complex math of
  Schrodingers equation describes several shapes.
• These are called atomic orbitals - regions where
  there is a high probability of finding an
  electron.
• Sublevels- like theater seats arranged in sections

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Summary
of shapes
Max electrons
Starts at energy level
s
1
2
1
p
3
6
2
5
10
3
d
7
14
4
f
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By Energy Level

• First Energy Level
• only s orbital
• only 2 electrons
• 1s2

• Second Energy Level
• s and p orbitals are available
• 2 in s, 6 in p
• 2s22p6
• 8 total electrons

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By Energy Level

• Third energy level
• s, p, and d orbitals
• 2 in s, 6 in p, and 10 in d
• 3s23p63d10
• 18 total electrons

• Fourth energy level
• s,p,d, and f orbitals
• 2 in s, 6 in p, 10 in d, ahd 14 in f
• 4s24p64d104f14
• 32 total electrons

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By Energy Level

• Any more than the fourth and not all the orbitals
  will fill up.
• You simply run out of electrons

• The orbitals do not fill up in a neat order.
• The energy levels overlap
• Lowest energy fill first.

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Section 13.2Electron Arrangement in Atoms

• OBJECTIVES
• Apply the aufbau principle, the Pauli exclusion
  principle, and Hunds rule in writing the
  electron configurations of elements.

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Section 13.2Electron Arrangement in Atoms

• OBJECTIVES
• Explain why the electron configurations for some
  elements differ from those assigned using the
  aufbau principle.

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Aufbau diagram - page 367
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Electron Configurations

• The way electrons are arranged in atoms.
• Aufbau principle- electrons enter the lowest
  energy first.
• This causes difficulties because of the overlap
  of orbitals of different energies.
• Pauli Exclusion Principle- at most 2 electrons
  per orbital - different spins

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Electron Configuration

• Hunds Rule- When electrons occupy orbitals of
  equal energy they dont pair up until they have
  to.
• Lets determine the electron configuration for
  Phosphorus
• Need to account for 15 electrons

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• The first two electrons go into the 1s orbital
• Notice the opposite spins
• only 13 more to go...

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• The next electrons go into the 2s orbital
• only 11 more...

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• The next electrons go into the 2p orbital
• only 5 more...

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• The next electrons go into the 3s orbital
• only 3 more...

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• The last three electrons go into the 3p orbitals.
• They each go into separate shapes
• 3 unpaired electrons
• 1s22s22p63s23p3

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The easy way to remember

• 1s2

• 2 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2

• 4 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2

• 12 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2

• 20 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2

• 38 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2

• 56 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
  4f14 5d10 6p6 7s2

• 88 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
  4f14 5d10 6p6 7s2 5f14 6d10 7p6

• 108 electrons

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Exceptional Electron Configurations
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Orbitals fill in order

• Lowest energy to higher energy.
• Adding electrons can change the energy of the
  orbital.
• Half filled orbitals have a lower energy.
• Makes them more stable.
• Changes the filling order

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Write these electron configurations

• Titanium - 22 electrons
• 1s22s22p63s23p64s23d2
• Vanadium - 23 electrons
• 1s22s22p63s23p64s23d3
• Chromium - 24 electrons
• 1s22s22p63s23p64s23d4 expected
• But this is wrong!!

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Chromium is actually

• 1s22s22p63s23p64s13d5
• Why?
• This gives us two half filled orbitals.
• Slightly lower in energy.
• The same principal applies to copper.

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Coppers electron configuration

• Copper has 29 electrons so we expect
  1s22s22p63s23p64s23d9
• But the actual configuration is
• 1s22s22p63s23p64s13d10
• This gives one filled orbital and one half filled
  orbital.
• Remember these exceptions d4, d9

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Section 13.3Physics and the Quantum Mechanical
Model

• OBJECTIVES
• Calculate the wavelength, frequency, or energy of
  light, given two of these values.

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Section 13.3Physics and the Quantum Mechanical
Model

• OBJECTIVES
• Explain the origin of the atomic emission
  spectrum of an element.

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Light

• The study of light led to the development of the
  quantum mechanical model.
• Light is a kind of electromagnetic radiation.
• Electromagnetic radiation includes many kinds of
  waves
• All move at 3.00 x 108 m/s c

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Parts of a wave
Origin
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Parts of Wave - p.372

• Origin - the base line of the energy.
• Crest - high point on a wave
• Trough - Low point on a wave
• Amplitude - distance from origin to crest
• Wavelength - distance from crest to crest
• Wavelength is abbreviated by the Greek letter
  lambda l

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Frequency

• The number of waves that pass a given point per
  second.
• Units cycles/sec or hertz (hz or sec-1)
• Abbreviated by Greek letter nu n
• c ln

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Frequency and wavelength

• Are inversely related
• As one goes up the other goes down.
• Different frequencies of light are different
  colors of light.
• There is a wide variety of frequencies
• The whole range is called a spectrum, Fig. 13.10,
  page 373

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Radiowaves
Microwaves
Infrared .
Ultra-violet
X-Rays
GammaRays
Long Wavelength
Short Wavelength
Visible Light
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Prism

• White light is made up of all the colors of the
  visible spectrum.
• Passing it through a prism separates it.

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If the light is not white

• By heating a gas with electricity we can get it
  to give off colors.
• Passing this light through a prism does something
  different.

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Atomic Spectrum

• Each element gives off its own characteristic
  colors.
• Can be used to identify the atom.
• How we know what stars are made of.

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• These are called discontinuous spectra, or line
  spectra
• unique to each element.
• These are emission spectra
• The light is emitted given off
• Sample 13-2 p.375

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Light is a Particle

• Energy is quantized.
• Light is energy
• Light must be quantized
• These smallest pieces of light are called
  photons.
• Photoelectric effect?
• Energy frequency directly related.

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Energy and frequency

• E h x ?
• E is the energy of the photon
• ? is the frequency
• h is Plancks constant
• h 6.6262 x 10 -34 Joules x sec.
• joule is the metric unit of Energy

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The Math in Chapter 11

• 2 equations so far
• c ??
• E h?
• Know these!

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Examples

• What is the wavelength of blue light with a
  frequency of 8.3 x 1015 hz?
• What is the frequency of red light with a
  wavelength of 4.2 x 10-5 m?
• What is the energy of a photon of each of the
  above?

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Explanation of atomic spectra

• When we write electron configurations, we are
  writing the lowest energy.
• The energy level, and where the electron starts
  from, is called its ground state- the lowest
  energy level.

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Changing the energy

• Lets look at a hydrogen atom

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Changing the energy

• Heat or electricity or light can move the
  electron up energy levels (excited)

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Changing the energy

• As the electron falls back to ground state, it
  gives the energy back as light

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Changing the energy

• May fall down in steps
• Each with a different energy

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Ultraviolet
Visible
Infrared

• Further they fall, more energy, higher frequency.
• This is simplified
• the orbitals also have different energies inside
  energy levels
• All the electrons can move around.

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What is light?

• Light is a particle - it comes in chunks.
• Light is a wave- we can measure its wavelength
  and it behaves as a wave
• If we combine Emc2 , c??, E 1/2 mv2 and E
  h?
• We can get ? h/mv
• called de Broglies equation
• Calculates the wavelength of a particle.

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Sample problem

• What is the approximate mass of a particle having
  a wavelength of 10-7 meters, and a speed of 1
  m/s?
• Use ? h/mv
• 6.6 x 10-27
• (Note 1 J N x m 1 N 1 kg x m/s2

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Matter is a Wave

• Does not apply to large objects
• Things bigger than an atom
• A baseball has a wavelength of about 10-32 m
  when moving 30 m/s
• An electron at the same speed has a wavelength of
  10-3 cm
• Big enough to measure.

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The physics of the very small

• Quantum mechanics explains how the very small
  behaves.
• Classic physics is what you get when you add up
  the effects of millions of packages.
• Quantum mechanics is based on probability

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Heisenberg Uncertainty Principle

• -It is impossible to know exactly the location
  and velocity of a particle.
• The better we know one, the less we know the
  other.
• Measuring changes the properties.
• Instead, analyze interactions with other particles

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More obvious with the very small

• To measure where a electron is, we use light.
• But the light moves the electron
• And hitting the electron changes the frequency of
  the light.

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Before
After
Photon changes wavelength
Photon
Electron Changes velocity
Moving Electron
Fig. 13.19, p. 382