Electrons in Atoms

1
Chapter 5

• Electrons in Atoms

2
Rutherfords Model

• Discovered the nucleus
• Small dense and positive
• Electrons moved around in Electron cloud

3
Bohrs Model

• Why dont the electrons fall into the nucleus?
• Move like planets around the sun.
• In circular orbits at different levels.
• Energy separates one level from another.

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Bohrs Model
Nucleus
Electron
Orbit
Energy Levels
5
Bohrs Model
Nucleus
Electron
Orbit
Energy Levels
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Bohrs Model

• Further away from the nucleus means more energy.
• There is no in between energy
• Energy Levels

Fifth
Fourth
Third
Increasing energy
Second
First
Nucleus
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The Quantum Mechanical Model

• Energy is quantized. It comes in chunks.
• Quanta - the amount of energy needed to move from
  one energy level to another.
• Quantum leap in energy.
• Schrödinger derived an equation that described
  the energy and position of the electrons in an
  atom
• Treated electrons as waves

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The Quantum Mechanical Model

• a mathematical solution
• It is not like anything you can see.

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The Quantum Mechanical Model

• Does have 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 electron is found inside a blurry electron
  cloud
• An area where there is a chance of finding an
  electron.

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Atomic Orbitals and Quantum Numbers

• Principal Quantum Number (n) indicates the main
  energy level occupied by the electron.
• Positive integers 1,2,3,
• Within each energy level the complex math of
  Schrödinger's equation describes several shapes.
• These are called atomic orbitals
• Regions where there is a high probability of
  finding an electron.
• The total number of orbitals that exist in a
  main energy level is equal to n2

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Angular Momentum Quantum Number

• (l) indicates the shape of the orbital.
• Except at E1, orbitals of different shapes
  (sublevels) exist for a given value of n.
• The number of orbital shapes possible is equal to
  n.
• l 0, 1, 2, n-1 (all positive integers)

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Shapes of Orbitals

• n 1 l 0 one orbital s
• n 2 l 0, 1 two orbitals s, p
• n 3 I 0, 1, 2 three orbitals s, p, d

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S orbitals

• One s orbital for every energy level
• Spherical shaped
• Each s orbital can hold 2 electrons
• Called the 1s, 2s, 3s, etc.. orbitals.

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P orbitals

• Start at the second energy level
• 3 different directions
• 3 different shapes (dumbell)
• Each can hold 2 electrons

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P Orbitals
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D orbitals

• Start at the third energy level
• 5 different shapes
• Each can hold 2 electrons

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F orbitals

• Start at the fourth energy level
• Have seven different shapes
• 2 electrons per shape

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F orbitals
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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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Magnetic Quantum Number

• ml
• the orientation of the orbital in 3-D space. (x,
  y, z)
• the values of ml range from l to l
• Ex n1 l0 ml0
• n2 l0, 1 ml -1,0, 1
• n3 l ? ml ?

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Spin Quantum Number

• ms
• electrons are not stationary particles, they
  spin
• they can only spin in two directions, clockwise
  and counterclockwise (designations we have
  assigned them)
• the values of ms are 1/2 or 1/2

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The Address of an Electron

• No two electrons have the same 4 quantum numbers.
• what I know from the quantum numbers of an
  electron
• 1, 0, 0, 1/2
• first principal energy level, s orbital, (x,y,z)
  axis, spinning clockwise
• 3, 1, -1, -1/2
• Third principal energy level, p orbital, x axis,
  spinning counterclockwise

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Aufbau Principle

• German for Building Up
• When the we build an atom with its various
  electrons we start with the lowest energy level
  and build up.

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The easy way to remember filling order
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7s
6s
5s
4s
Increasing energy
3s
2s
1s
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7p
6d
5f
7s
6p
5d
6s
4f
5p
4d
5s
4p
3d
4s
3p
Increasing energy
3s
2p
2s
1s
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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 to electrons go into the 1s orbital
• Notice the opposite spins
• only 13 more

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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

• 118 electrons

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Rewrite when done

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

• Group the energy levels together

• 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2
  5p6 5d105f146s2 6p6 6d10 7s2 7p6

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Exceptions to Electron Configuration
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Orbitals fill in order

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

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Write these electron configurations

• Titanium - 22 electrons
• 1s22s22p63s23p63d24s2
• Vanadium - 23 electrons 1s22s22p63s23p63d34s2
• Chromium - 24 electrons
• 1s22s22p63s23p63d44s2 is expected
• But this is wrong!!

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Chromium is actually

• 1s22s22p63s23p63d54s1
• Why?
• This gives us two half filled orbitals.

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Chromium is actually

• 1s22s22p63s23p63d54s1
• Why?
• This gives us two half filled orbitals.

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Chromium is actually

• 1s22s22p63s23p63d54s1
• Why?
• This gives us two half filled orbitals.

• Slightly lower in energy.
• The same principle applies to copper.

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Coppers electron configuration

• Copper has 29 electrons so we expect
• 1s22s22p63s23p63d94s2
• But the actual configuration is
• 1s22s22p63s23p63d104s1
• This gives one filled orbital and one half filled
  orbital.
• Remember these exceptions
• d4s2 ? d5 s1
• d9s2 ? d10s1

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In each energy level

• The number of electrons that can fit in each
  energy level is calculated with
• Max e- 2n2 where n is energy level
• 1st
• 2nd
• 3rd

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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

• 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 l -Greek letter
  lambda.

55
Frequency

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

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Frequency and wavelength

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

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Spectrum
Radiowaves
Microwaves
Infrared .
Ultra-violet
X-Rays
GammaRays
Long Wavelength
Short Wavelength
Visible Light
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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.
• Energy and frequency are directly related.

59
Energy and frequency

• E h x n
• E is the energy of the photon
• n is the frequency
• h is Plancks constant
• h 6.626 x 10 -34 Joules sec.

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The Math in Chapter 5

• Only 2 equations
• c ln
• E hn
• c is always 3.00 x 108 m/s
• h is always 6.626 x 10-34 J s

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Examples

• What is the frequency of red light with a
  wavelength of 4.2 x 10-5 cm?
• What is the wavelength of KFI, which broadcasts
  at with a frequency of 640 kHz?
• What is the energy of a photon of each of the
  above?

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Atomic Spectrum

• How color tells us about atoms

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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 or 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 line spectra
• unique to each element.
• These are emission spectra
• Mirror images are absorption spectra
• Light with black missing

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An explanation of Atomic Spectra
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Where the electron starts

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

70
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

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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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The Bohr Ring Atom
n 4
n 3
n 2
n 1
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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 wave length
  and it behaves as a wave
• If we combine Emc2 , cln, E 1/2 mv2 and E
  hn
• We can get l h/mv (de Broglies equation)
• The wavelength of a particle.

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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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Diffraction

• When light passes through, or reflects off, a
  series of thinly spaced lines, it creates a
  rainbow effect
• because the waves interfere with each other.

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A wave moves toward a slit.
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A wave moves toward a slit.
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A wave moves toward a slit.
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A wave moves toward a slit.
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A wave moves toward a slit.
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Comes out as a curve
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Comes out as a curve
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Comes out as a curve
90
with two holes
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with two holes
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with two holes
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with two holes
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with two holes
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Two Curves
with two holes
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Two Curves
with two holes
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Two Curves
with two holes
Interfere with each other
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Two Curves
with two holes
Interfere with each other
crests add up
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
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Several waves
Several Curves
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Several waves
Several Curves
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Several waves
Several Curves
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Several waves
Several Curves
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Several waves
Several waves
Several Curves
Interference Pattern
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Diffraction

• Light shows interference patterns
• Light is a wave
• What will an electron do when going through two
  slits?
• Go through one slit or the other and make two
  spots
• Go through both and make a interference pattern

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Electron as Particle
Electron gun
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Electron as wave
Electron gun
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Which did it do?

• It made the diffraction pattern
• The electron is a wave
• Led to Schrödingers equation

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The physics of the very small

• Quantum mechanics explains how the very small
  behaves.
• Quantum mechanics is based on probability because

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Heisenberg Uncertainty Principle

• It is impossible to know exactly the speed and
  position of a particle.
• The better we know one, the less we know the
  other.
• The act of measuring changes the properties.

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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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After
Before
Photon changes wavelength
Photon
Electronchanges velocity
Moving Electron