Chapter 5 : Electrons in Atoms

Problems with Rutherford’s Problems with Rutherford’s Model of the AtomModel of the Atom

Chlorine # 17

Reactive

Potassium # 19

Very reactive

Argon # 18

Not reactive

Does not explain why elements react the way they do!

• It’s because they have It’s because they have different arrangements of different arrangements of electrons!electrons!

Electrons and LightElectrons and Light• An element’s chemical behavior is related to

its arrangement of electrons

• Elements give off different light when burned

• We can analyze light to learn about atoms!

Atomic Emission SpectraAtomic Emission Spectra

The frequencies of the electromagnetic radiation (EMR) emitted by atoms of an element are unique to each element, like fingerprints on people!

The Quest for a Better ModelThe Quest for a Better Model• Electromagnetic radiation (EMR) behaves

like a wave.

Characteristics of a WaveCharacteristics of a Wave

Wavelength = λ

Frequency = f (number of waves that pass a point per second)

1 Hertz (Hz) = 1 wave per second (SI Unit for frequency)

Light as a Light as a

wave…wave…

Types of WavesTypes of Waves

Compressional or Longitudinal Wave (sound or slinky)

Transverse Wave (light, rope) ://www.youtube.com/watch?v=Rbuhdo0AZDU

Light as a WaveLight as a Wave

• We can relate the speed, frequency, and wavelength of EMR with the equation:

v = fv = fv is velocity (m/s)

f is frequency (Hertz – Hz, 1 Hz = 1 wave/sec) is wavelength (m)

The speed of light (c) is a constant!The speed of light (c) is a constant!

c = 3.0 x 10c = 3.0 x 1088 m/s m/s

Velocity and Frequency of LightVelocity and Frequency of Light

v = λf

v (or c for light) = speed of light (3.0 x 108 m/s)

↑ wavelength ↓ frequency

↓ wave length ↑frequency

ProblemsProblemsA helium-neon laser emits a light with a wavelength of 633 nm. What is the frequency of this light?

Use the equation v = λf

3.0 x 108 m/s

First convert nm to m.

633 nmnm

m6.33 x 10-7 mX =

1 x 109

1

= (6.33 x 10-7 m) (f)(6.33 x 10-7 m)(6.33 x 10-7 m)

f4.7 x 1015 1/s or Hz

Then do the math.

=

An FM radio station broadcasts at a frequency of 98.5 MHz. What is the wavelength of the station’s broadcast signal?

Frequency = 98.5 MHzVelocity = 3 x 108 m/sWavelength = X

Use the formula, v = λfRearrange the formula, λ = v/f

Convert 98.5 MHz to Hz

98.5 MHz 1 x 106 Hz = 9.85 x 107 Hz 1MHz

λ = vf so plugging in our values:λ = 3 x 108 m/s / 9.85 x 107 Hz = 3.05 m

Stop.Stop.

Light: Particle or Wave?Light: Particle or Wave?Wave model doesn’t address:

Why heated objects emit only certain frequencies of light at a given temperature?

Why some metals emit electrons when a colored light of a specific frequency shines on them? (photoelectric effect)

http://www.youtube.com/watch?v=WO38qVDGgqw&feature=related

Iron

Dark gray = room tempRed = hot temp

Blue = extremely hot temp

Photoelectric Effect – Photoelectric Effect – The problem with wave theoryThe problem with wave theory

Only certain frequencies of light could emit an electron from a plate of Ag.

Accumulation of low frequencies couldn’t

Einstein and the Dual Nature of EMR (1900)

• Electromagnetic Radiation Electromagnetic Radiation (EMR) acts as a (EMR) acts as a wavewave of of individual individual particlesparticles (photons) (photons)

Wave vs. ParticleWave vs. Particle

Wave Characteristics Particle Characteristics

Light can be reflected. Photons have the ability to knock individual electrons off of a conductor-Photoelectric Effect!

Light shows interference patterns.

Metals glow only specific colors when heated.

WaveWave++

WaveWave

RESULTRESULT

What is the relationship between What is the relationship between energy and frequency? energy and frequency?

Max Planck - 1900Max Planck - 1900Matter gains or loses energy only in small, specific amounts called quantaquanta. This is why we see specific color lines in emission spectra.

A quantumquantum is the minimum amount of energy that can be gained or lost by an atom

EEquantumquantum = = hfhf E is energy

h is Planck’s constant = 6.626 x 10-34 J·s

f is frequency

J is joule, SI Unit for energy

Calculating the energy in a PhotonCalculating the energy in a Photon

Ephoton = hf

E = (6.626 x 10-34 J·s) x (7.23 x 1014 s-1)

E = 4.79 x 10-19 J

Niels Bohr - 1913Niels Bohr - 1913• Worked in Rutherford’s lab• Proposed a quantum model of the atom• Explains why emission spectra were

discontinuous • Predicted frequencies of light in Hydrogen’s

atomic emission spectra

Bohr’s ExplanationBohr’s Explanation• Ground state – lowest energy state of an atom’s electrons• Excited state – when an atom’s electrons gain energy• Electrons move in circular orbits

– Smaller orbit – lower energy state, “energy level”– Larger orbit – higher energy state, “energy level”

An explanation for Emission SpectraAn explanation for Emission Spectra

Ground state

Excited States

Atoms absorb energy and are excited. As the electron returns to the

ground state they give off energy “photon” equal to the difference in energy

levels.

http://www.mhhe.com/physsci/astronomy/applets/Bohr/applet_files/Bohr.html

Bohr’s ModelBohr’s Model

Electrons move around the nucleus in set orbits in specific energy levels. When excited, electrons give off a discrete amount of energy as an emission spectrum.

This discrete amount of energy is a quantum.

http://www.mhhe.com/physsci/astronomy/applets/Bohr/applet_files/Bohr.html

Click the link to make an electron jump!

Bohr used work of others…Bohr used work of others…

• Balmer—made an equation (math) to connect the lines of the hydrogen spectrum to each other.

• Planck—Energy is directly proportional to the frequency of light.

Problem: Bohr’s Model Only Problem: Bohr’s Model Only explains Hydrogenexplains Hydrogen

• Louis de Broglie (1924) – proposed that the energy levels are based on the wave like nature of electrons

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

• It is impossible to know the velocity and position of an electron at any given time

• Bohr gives a specific place for electrons, while Heisenberg says you can’t know where the electrons are at a particular time.

Photon and electron are about the

same mass.

Erwin Schrodinger - 1926Erwin Schrodinger - 1926• Developed the quantum mechanical model

of the atom– Assigns electrons to energy levels like Bohr– Does not predict the path of the electron – It predicts the probability of finding an electron

• An electron’s “atomic orbitalatomic orbital” is the most probable location of the electron at any point in time.

Each dot is a picture of an electron during

a given amount of time.

Where does the electron spend most

of the time?

Boundary represents the location of an

electron 90% of the time.

Stop.Stop.

Each dot is a picture of an electron during

a given amount of time.

Where does the electron spend most

of the time?

Boundary represents the location of an

electron 90% of the time.

Principle Energy LevelsPrinciple Energy Levels

• 7 energy levels

• Lowest energy is 1 – greatest energy 7

• Each level consists of sublevels

The second energy level is larger and the electrons are farther from the nucleus.

s Orbitalss Orbitals

p and d Degenerate Orbitalsp and d Degenerate Orbitals

Degenerate orbitals have exactly the same amount of energy.

f Degenerate Orbitalsf Degenerate Orbitals

Quantum Number

Symbol Possible Values

Definition

Principle n 1,2,3… Major energy Level or shell

Angular Momentum

l 0 to n-1 Sublevel or subshell

Magnetic ml -l to +l Orbital orientation

Spin ms +½ to -½ Spin direction

If Principle

(n) =

Then Angular (l) =

And Magnetic

(ml) =

1 0 (s) 0

2 0 (s)

1 (p)

0

-1, 0, +1

3 0 (s)

1 (p)

2 (d)

0

-1, 0, +1

-2,-1,0,+1,+2

4 0 (s)

1 (p)

2 (d)

3 (f)

0

-1, 0, +1

-2,-1,0,+1,+2

-3,-2,-1,0,1,2,3

0 = s, 1 = p, 2 = d, 3 = f

To Write Ground State Electron To Write Ground State Electron Configurations…Configurations…

1. Lowest energy is the most stable

2. 3 principals or rules to follow—Pauli Exclusion Principle, Aufbau Principle, and Hund’s Rule

For electrons to occupy the same orbital, they must have opposite spin.

• That limits 2 electrons per orbital, written as up or down:

Pauli Exclusion PrinciplePauli Exclusion Principle

Aufbau Principle Aufbau Principle – each electron must occupy the lowest energy state possible.

What that means is:

1.Within a principle energy level, the energy sublevels have different energies.

2.The sublevels increase in energy from s,p,d,f

3.Orbitals in a given energy sublevel have equal energy (they are degenerate).

4.Principal energy levels can overlap.

Hund’s Rule Hund’s Rule In a given sublevel, electrons must occupy

each degenerate orbital before additional electrons can be added.

Pauli Exclusion Principle

Aufbau DiagramAufbau Diagram

Tells you the order orbitals are filled with electrons, in order of increasing energy!

4f 5f 14 e- max 3d 4d 5d 6d 10 e- max 2p 3p 4p 5p 6p 7p 6 e- max1s 2s 3s 4s 5s 6s 7s 8s 2e- max

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, etc.

start at 1s and

follow the arrows…

How can we write this easily?How can we write this easily?

Only list the total electrons in each orbital, as a superscript

1. H – 1s1

2. He –1s2

3. Li - 1s2, 2s1

4. Be - 1s2, 2s2

5. B - 1s2, 2s2, 2p1

6. C - 1s2, 2s2, 2p2

7. N - 1s2, 2s2, 2p3

8. O - 1s2, 2s2, 2p4

9. F - 1s2, 2s2, 2p5 10.Ne - 1s2, 2s2, 2p6

Orbital NotationOrbital Notation

• Very similar to electron configuration, only this one takes spin of the electron into account and may include all of the electrons or just the valence (outer energy level) electrons

↑↓Be

2Px 2Py 2Pz2S

Energy Level

Symbol

+ and - spin

↑↓

1S

sublevel

Representing Electron Representing Electron ConfigurationsConfigurations

Electron ConfigurationsElectron Configurations

Sub level diagram – indicates the order that orbitals are filled

What are the orbital diagrams and electron configuration notation for Al and Cl?

Electron Configuration ShorthandElectron Configuration Shorthand

• Substitute noble gases from preceding energy levels in the notation

Li – [He] 2s1

C – [He] 2s2 2p2

Stop.Stop.

Valence ElectronsValence Electrons

• Electrons in the outer most energy levels

S: [Ne] 3s2 3p4

Sulfur has 6 valence electrons (add 2 from s and 4 from p)

How many valence electrons do Ne, Al, and Cl have?

Valence ElectronsValence Electrons

Ne: 1s2, 2s2, 2p6

8 e- on 2nd energy level

Al: 1s2, 2s2, 2p6, 3s2, 3p1

3 e- on 3rd energy level

Cl: 1s2, 2s2, 2p6, 3s2, 3p5

7 e- on 3rd energy level

Lewis Dot ModelsLewis Dot Models

• Only valence electrons – outermost electrons (highest energy level)

• Octet rule – all atoms want to have 8 electrons (H and He want 2) in outer orbit

XSymbol1

6

2

35

4

8

7

Writing Electron Dot StructuresWriting Electron Dot Structures

• Fill the valence electrons 1 at a time in any particular order.

Ca C

O

**

***

*

******

What are the electron dot diagrams for K, Ar and F?

Electron Dot StructuresElectron Dot Structures

Valence electrons are

used in reactions and are

represented by an electron dot

structure.

Ne

H O

N

Periodic Table BlocksPeriodic Table Blocks• Where an element is on the periodic table can

give you clues about its electron configuration.• For the representative elements (A groups), the

A-group number tells you how many valence electrons!

– Alkali earth metals (2AAlkali earth metals (2A*) have 2 valence e-) have 2 valence e-– Halogens (7AHalogens (7A*) have 7 valence e-) have 7 valence e-

*Note: A different method of naming the groups numbers the columns 1-13 starting on the left side of the table and includes the transition metals. In this system group 2A = group 2, group 3A = group 13

END OF CHEM 1 UNIT 5!!!

(the rest is for Pre-AP)

Modern Atomic Theory

• Any electron in an atom can be described by 4 quantum numbers

• Principal Quantum Number

• Azimuthal (Angular Momentum) Quantum Number

• Magnetic Quantum Number

• Spin Quantum Number

Principal Quantum Number (n)

Related to the size and energy of principal energy level.

The farther away from the nucleus the more energy the electron has

1 < 2 < 3 < 4 < 5 < 6 etc….

Azimuthal Quantum Number (Angular Momentum) = l

• Refers to the subshells in each principal energy level (n)

• S = 0• P = 1• D = 2• F = 3

n l

1 0

2 0

1

3 0

1

2

4 0

1

2

3

Magnetic Quantum Number (ml)

• Specifies the orbital within a energy level where an electron is likely to be found

n l Orbital designation

ml

1 0 1s 0

2 0 2s 0

1 2p -1,0,+1

3 0 3s 0

1 3p -1,0,+1

2 3d -2,-1,0-,1,2

4 0 4s 0

1 4p -1,0,+1

2 4d -2,-1,0-,1,2

3 4f -3,-2,-1,0,1,2,3

Spin Quantum Number (ms)

• + ½ or – ½

• Electrons in the same orbitals must have opposite spins (Pauli Exclusion Principle)

n l Orbital designation

ml ms

1 0 1s 0 + ½, - ½

2 0 2s 0 + ½, - ½

1 2p -1,0,+1 + ½, - ½

3 0 3s 0 + ½, - ½

1 3p -1,0,+1 + ½, - ½

2 3d -2,-1,0-,1,2 + ½, - ½

4 0 4s 0 + ½, - ½

1 4p -1,0,+1 + ½, - ½

2 4d -2,-1,0-,1,2 + ½, - ½

3 4f -3,-2,-1,0,1,2,3 + ½, - ½

n l ml ms

2 1 -1 + ½ or

What are the quantum numbers for A? B?

A B

2,1,0,-½ 3,0,0,+½

So to summarize

There are four quantum numbers that describe every electron– Principal Quantum # - Energy Level (1-7)– Angular Momentum or Azimuthal Quantum # -

Type of Orbital (s,p,d,f)– Magnetic Quantum # - Orientation of the

orbital (x, y, z, xy, xz, yz, etc.)– Spin Quantum # - Spin (+ or -)