Chapter 5“Electrons in Atoms”

Ernest Rutherford’s Model• Discovered dense + piece at

nucleus• Electrons move around it, like

planets around sun• Mostly empty space• Didn’t explain chemical

properties of elements

Niels Bohr’s Model•Why don’t electrons fall into nucleus?•Move like planets around sun.specific circular orbits at different

levels.An amount of fixed energy

separates one level from another.

The Bohr Model of the Atom

Niels Bohr

I pictured the electrons orbiting the nucleus much like planets orbiting the sun.

However, electrons are found in specific circular paths around the nucleus, and can jump from one level to another.

Bohr’s model• Energy level measure of fixed

energy e- can have•Like rungs of ladder

• e- can’t exist between energy levels• can’t stand between rungs on ladder

• Unlike ladder, energy levels not evenly spaced• Higher energy levels closer together

– less energy needed for jump

The Quantum Mechanical Model• Energy is “quantized” - in chunks.• A quantum is exact energy needed to

move e- one energy level to another.• Since energy of atom is never “in

between” quantum leap in energy must exist.

• Erwin Schrodinger (1926) derived equation described energy and position of e- in an atom

SchrodingerSchrodinger

The Quantum Mechanical Model• Very small things behave

differently from big things • quantum mechanical model

is a mathematical solution• not like anything you can

see (like plum pudding!)

The Quantum Mechanical Model

• Has energy levels for e-

• Orbits not circular.

• only tells us probability of finding e- a certain distance from nucleus.

The Quantum Mechanical Model

• e- found inside blurry “electron cloud” (area where there’s chance of finding e-

• Like fan blades or bicycle wheel

Atomic Orbitals

• Principal Quantum Number (n) = the energy level of e- (1, 2, 3, etc.)

• Within each energy level, Schrodinger’s equation describes several shapes.

• called atomic orbitals - regions of space regions of space w/w/ high probability high probability of finding e-

• Sublevels like rooms in a hotel• letters s, p, d, and f

Principal Quantum Number (n)denotes the energy level (shell) e- is located.

Maximum number of e- that can fit in energy level is:

2n2

How many e- in level 2? level 3?

Individual orbitals

sspherical

pdumbell

dclover leaf

fcomplicated

# of orbitals

Maximum electrons

First possible

energy level

1 2 1st

3 6 2nd

5 10 3rd

7 14 4th

By Energy Level• Energy Level 1 (n=1)• Has only s sublevel• 1s (1 orbital)• w/ only 2 e-• 2 total e-

• Energy Level 2 (n=2)• Has s and p

sublevels available• 2s (1 orbital)• w/ 2 e-• 2p (3 orbitals)• w/ 6 e-

• 2s22p6

• 8 total e-

22

6

By Energy Level• Energy level 3 (n=3)• s, p, and d sublevels• 3s (1 orbital)• w/ 2 e-• 3p (3 orbitals)• w/ 6 e-• 3d (5 orbitals)• w/ 10 e-• 3s23p63d10

• 18 total e-

• Energy level 4 (n=4)• s, p, d, and f sublevels• 4s (1 orbital)• w/ 2 e-• 4p (3 orbitals) • w/ 6 e-• 4d (5 orbitals) • w/ 10 e-• 4f (7 orbitals) • w/ 14 e-

• 4s24p64d104f14

• 32 total e-

2

6

10 14

10

6

2

By Energy LevelAny more than

the fourth and not all orbitals fill up.

• You simply run out of e-’s

• orbitals do not fill up in neat order.

• energy levels overlap

• Lowest energy fill first.

s and p orbitals 1:20

d orbitals 3:40

Summary of Principal Energy Levels, Sublevels, and Summary of Principal Energy Levels, Sublevels, and OrbitalsOrbitals

Principal Principal energy energy levellevel

Number Number of of

sublevelssublevels

Type of Type of sublevelsublevel

Max # of Max # of electronselectrons

Electron Electron configurationconfiguration

n = 1n = 1 11 1s (1 orbital)1s (1 orbital) 22 1s1s22

n = 2n = 2 22 2s (1 orbital2s (1 orbital2p (3 orbitals)2p (3 orbitals)

88 2s2s22

2p2p66

n = 3n = 3 33 3s (1 orbital)3s (1 orbital)3p (3 orbitals)3p (3 orbitals)3d (5 orbitals)3d (5 orbitals)

1818 3s3s22

3p3p66

3d3d1010

n = 4n = 4 44 4s (1 orbital)4s (1 orbital)4p (3 orbitals)4p (3 orbitals)4d (5 orbitals) 4d (5 orbitals) 4f (7 orbitals)4f (7 orbitals)

3232 4s4s22

4p4p66

4d4d1010

4f4f1414

EN

ER

GY

Energy Level

3

2

1

1s

2s

2p

3s

3p3d

Electron distribution in an AtomElectron distribution in an Atom

NUCLEUSNUCLEUS

Section 5.2Electron Arrangement in Atoms

• OBJECTIVES:•Describe how to write the electron configuration for an atom.

Section 5.2Electron Arrangement in Atoms

• OBJECTIVES:•Explain why the actual electron configurations for some elements differ from those predicted by the aufbau principle.

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

aufbau diagram - page 133

Aufbau is German for “building up”

Electron Configurations…• …the way electrons arranged in various

orbitals around nuclei of atoms. Three rules tell us how:

1) Aufbau principle - electrons enter the lowest energy first.

• causes difficulties b/c overlap of orbitals of different energies – follow diagram!follow diagram!

2) Pauli Exclusion Principle - 2 electrons max per orbital (hotel room) - different spins

Pauli Exclusion PrincipleNo two electrons in an atom can have the same four quantum numbers.

Wolfgang Pauli

To show the different direction of spin, a pair in the same orbital is written as:

Quantum Numbers

Each electron in an atom has a unique set of 4 quantum numbers which describe it.

1) Principal quantum number2) Angular momentum quantum number3) Magnetic quantum number4) Spin quantum number

Electron Configurations3) Hund’s Rule- When electrons occupy

orbitals of equal energy, they don’t pair up until they have to.

• write e- configuration for Phosphorus

We need to account for all 15 e-’s in phosphorus

• The first two electrons go into the 1s orbital

Notice the opposite direction of the spins

• only 13 more to go...

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2s orbital

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2p orbital

• only 5 more...Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 3s orbital

• only 3 more...Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The last three electrons go into the 3p orbitals.

They each go into separate shapes (Hund’s)

• 3 unpaired electrons

= 1s22s22p63s23p3 Orbital notation

Stairstep pattern

• An internet program about electron configurations is:

Electron Configurations

(Just click on the above link)

I electron config 3:24

Orbitals fill in an order •Lowest energy higher energy.•Adding e-’s changes energy of orbital. Full orbitals are best situation.

•half filled orbitals lower energy, next best•more stable.•Changes filling order

Write the electron configurations for these elements:• Titanium - 22 electrons

1s22s22p63s23p64s23d2

• Vanadium - 23 electrons

1s22s22p63s23p64s23d3

• Chromium - 24 electrons

1s22s22p63s23p64s23d4 (expected)But this is not what happens!!

Chromium is actually:•1s22s22p63s23p64s13d5

•Why?•This gives us two half filled orbitals

(the others are all still full)

•Half full is slightly lower in energy.•The same principal applies to copper.

Copper’s electron configuration

• Copper has 29 electrons so we expect: 1s22s22p63s23p63d94s2

• But the actual configuration is:• 1s22s22p63s23p63d104s1

• This change gives one more filled orbital and one that is half filled.

• Remember these exceptions: d4, d9

Irregular configurations of Cr and Cu

Chromium steals a 4s electron to make its 3d sublevel HALF FULL

Copper steals a 4s electron to FILL its 3d sublevel

Section 5.3Physics and the Quantum Mechanical Model• OBJECTIVES:

•Describe the relationship between the wavelength and frequency of light.

Section 5.3Physics and the Quantum Mechanical Model• OBJECTIVES:

•Identify the source of atomic emission spectra.

Section 5.3Physics and the Quantum Mechanical Model• OBJECTIVES:

•Explain how the frequencies of emitted light are related to changes in electron energies.

Section 5.3Physics and the Quantum Mechanical Model• OBJECTIVES:

•Distinguish between quantum mechanics and classical mechanics.

Light• Study of light led to development of quantum

mechanical model.• Light is electromagnetic radiation.• EM radiation: gamma rays, x-rays, radio

waves, microwaves• Speed of light = 2.998 x 108 m/s

• abbreviated “c”• “celeritas“ Latin for speed

• All EM radiation travels same in vacuum

- Page 139

“R O Y G B I V”

Frequency Increases

Wavelength Longer

Parts of a wave

Wavelength

Amplitude

Origin

Crest

Trough

Equation:

c =

c = speed of light, a constant (2.998 x 108 m/s)

(nu) = frequency, in units of hertz (hz or sec-1) (lambda) = wavelength, in meters

Electromagnetic radiation propagates through space as a wave moving at the speed of light.

Wavelength and Frequency• inversely related

•one gets bigger, other smaller• Different frequencies of light different

colors • wide variety of frequencies (spectrum)

- Page 140

Use Equation: c =

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Low Frequency

High Frequency

Long Wavelength

Short WavelengthVisible Light

Low Energy

High Energy

Long Wavelength

=Low Frequency

=Low ENERGY

Short Wavelength

=High Frequency

=High ENERGY

Atomic Spectra• White light all

colors of visible spectrum.

• prismprism separates it.

If the light is not white• heating gas with

electricity will emit colors.

• Passing this light through prism different.

Atomic Spectrum• Each element gives

off own characteristic colors.

• This is how we know composition of stars

• atomic emission spectrum

• Unique to each element, like fingerprints!

• ID’s elements

Light is a Particle?• Energy is quantized.• Light is energy…..• light must be quantized• photons photons smallest pieces of light• Photoelectric effect –

• Matter emits e- when it absorbs energy• Albert Einstein Nobel Prize in chem

• Energy & frequency: directly related.

Planck-Einstein Equation: E = hEE = Energy, in units of Joules (kg·m = Energy, in units of Joules (kg·m22/s/s22)) (Joule is metric unit of energy)(Joule is metric unit of energy)

hh = Planck’s constant (6.626 x 10 = Planck’s constant (6.626 x 10-34-34 J·s) J·s)(reflecting sizes of energy (reflecting sizes of energy quanta))

= frequency, in units of hertz (hz, sec= frequency, in units of hertz (hz, sec-1-1))

energy (E ) of electromagnetic radiation is directly proportional to frequency () of radiation.

The Math in Chapter 5• There are 2 equations:

1) c = 2) E = h Put these on your 3 x 5 notecard!

Examples1) What is the wavelength of blue

light with a frequency of 8.3 x 1015 hz?

2) What is the frequency of red light with a wavelength of 4.2 x 10-5 m?

3) What is the energy of a photon of each of the above?

Explanation of atomic spectra

• electron configurations written in lowest energy.

• energy level, and where electron starts from, called it’s ground stateground state - lowest energy level.

Changing the energy• Let’s look at a hydrogen atom, with only

one electron, and in the first energy level.

Changing the energy• Heat, electricity, or light can move electron

up to different energy levels. The electron is now said to be ““excitedexcited””

Changing the energy• As electron falls back to ground state, it

gives energy back as lightlight

Experiment #6, page 49-

• may fall down in specific steps• Each step has different energy

Changing the energy

{{{

Lyman series (UV) Balmer series

(visible)

Paschen series

(infrared)

• further they fall, more energy released = higher frequency

• orbitals also have different energies inside energy levels

• All 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 wavelength

and it behaves as a wave• combine E=mc2 , c=, E = 1/2 mv2 and E =

hthen we can get:

= h/mv (from Louis de Broglie)Calculates wavelength of a particle.

• called de Broglie’s equation • He said particles exhibit properties of waves

Wave-Particle DualityJ.J. Thomson won the Nobel prize for describing the electron as a particle.

His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron.

The electron is a particle!

The electron is an energy

wave!

Confused? You’ve Got Company!

“No familiar conceptions can be woven around the electron;

something unknown is doing we don’t know what.”

Physicist Sir Arthur Eddington

The Nature of the Physical World

1934

The physics of the very small•Quantum mechanics explains how very small particles behave•Quantum mechanics is an explanation for subatomic particles and atoms as waves

•Classical mechanics describes the motions of bodies much larger than atoms

Heisenberg Uncertainty Principle• impossible to know exact location and

velocity of particle• better we know one, less we know

other• Measuring changes properties.• True in quantum mechanics, but not

classical mechanics

Heisenberg Uncertainty Principle

You can find out where the electron is, but not where it is going.

OR…

You can find out where the electron is going, but not where it is!

“One cannot simultaneously determine both the position and momentum of an electron.”

Werner Heisenberg

It is more obvious with the very small objects•To measure where e-, we use light

•But light energy (photon) moves e- due to small mass

•And hitting e- changes frequency of light

Moving Electron

Photon

Before

Electron velocity changes

Photon wavelengthchanges

After

Fig. 5.16, p. 145