Chapter 5

Electrons in Atoms

Rutherford’s Model

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

Bohr’s Model

• Why don’t the electrons fall into the nucleus?
• Move like planets around the sun.
• In circular orbits at different levels.
• Energy separates one level from another.

Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Bohr’s Model

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

Increasing energy

Nucleus

First

Second

Third

Fourth

Fifth

}

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

The Quantum Mechanical Model

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

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.

The Quantum Mechanical Model

• The electron is found inside a blurry “electron cloud”
• An area where there is a chance of finding an electron.
• Draw a line at 90 %

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)

Parts of a wave

Origin

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 λ −Greek letter lambda.

Frequency

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

c = λν

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

Spectrum

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Long Wavelength

Short Wavelength

Visible Light

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.

Energy and frequency

• E = h x n
• E is the energy of the photon
• n is the frequency
• h is Planck’s constant
• h = 6.626 x 10 ^-34 Joules sec.

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

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?

Atomic Spectrum

How color tells us about atoms

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.

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.

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

An explanation of Atomic Spectra

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.

Changing the energy

• Let’s look at a hydrogen atom

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

Changing the energy

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

Changing the energy

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

Changing the energy

The Bohr Ring Atom

n = 3

n = 4

n = 2

n = 1

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{

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• 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.

Ultraviolet

Visible

Infrared

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 E=mc² , c=ln, E = 1/2 mv² and E = hn
• We can get l = h/mv
• The wavelength of a particle.

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.

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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Electron Configurations

We know the 2,8,8,18,18, 32, 32 arrangement, but there is much more detail to this. Electron configurations give us the exact location of all the electrons WITHIN the energy levels themselves.

Atomic Orbitals

• Principal Quantum Number (n) = the energy level of the electron.
• 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.

S orbitals

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

P orbitals

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

P Orbitals

D orbitals

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

F orbitals

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

F orbitals

Images

J mol

Summary

s

p

d

f

# of shapes

Max electrons

Starts at energy level

1

2

1

3

6

2

5

10

3

7

14

4

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

Filling order

• Lowest energy fill first.
• The energy levels overlap
• The orbitals do not fill up order of energy level.
• Counting system
• Each box is an orbital shape
• Room for two electrons

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

Electron Configuration

• Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .
• Let’s determine the electron configuration for Phosphorus
• Need to account for 15 electrons

Increasing energy

1s

2s

3s

4s

5s

6s

7s

Increasing energy

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p

6d

4f

5f

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

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

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

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

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

The easy way to remember

• 1s²

• 2 electrons

Fill from the bottom up following the arrows

• 1s² 2s²

• 4 electrons

Fill from the bottom up following the arrows

• 1s² 2s² 2p⁶ 3s²

• 12 electrons

Fill from the bottom up following the arrows

• 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

• 20 electrons

Fill from the bottom up following the arrows

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

• 38 electrons

Fill from the bottom up following the arrows

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

• 56 electrons

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

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

Rewrite when done

• Group the energy levels together

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

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

Exceptions to Electron Configuration

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

Write these electron configurations

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

Chromium is actually

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

Chromium is actually

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

Chromium is actually

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

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

Copper’s 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
• d⁴s^{2 →} d⁵ s¹
• d⁹s^{2 →} d¹⁰s¹

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
• 1^st�
• 2^nd

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• 3^rd

A wave moves toward a slit.

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A wave moves toward a slit.

77

A wave moves toward a slit.

78

A wave moves toward a slit.

79

A wave moves toward a slit.

80

81

82

Comes out as a curve

83

Comes out as a curve

84

Comes out as a curve

85

with two holes

86

with two holes

87

with two holes

88

with two holes

89

with two holes

90

with two holes

Two Curves

91

with two holes

Two Curves

92

Two Curves

with two holes

Interfere with each other

93

Two Curves

with two holes

Interfere with each other

crests add up

94

Several waves

95

Several waves

96

Several waves

97

Several waves

98

Several waves

99

Several waves

100

Several waves

101

Several waves

102

Several waves

103

Several waves

104

Several waves

Several Curves

105

Several waves

Several Curves

106

Several waves

Several Curves

107

Several waves

Several Curves

108

Several waves

Several waves

Interference Pattern

Several Curves

109

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

Electron “gun”

Electron as Particle

Electron “gun”

Electron as wave

Which did it do?

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

The physics of the very small

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

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.

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.

Moving Electron

Photon

Before

Electron�changes velocity

Photon changes wavelength

After

Electron Configuration Practice

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Tell the electron configurations of each of the following, giving full, short-cut and orbital diagrams.

1. Sn
2. Co
3. Cl-
4. Kr

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Light Waves

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5. Calculate the Energy of a Photon with a wavelength of 6.57 x 10^-5 cm.