Chapter 5

Electrons in Atoms

Greek Idea Democritus and

Leucippus Matter is made up

of indivisible particles

Dalton - one type of atom for each element

1 Summarize the development of the atomic theory in terms of the following:

Thompson - atom was a positive ball with electrons in it

Rutherford - atom had nucleus with electrons around it

Thomson’s Model

Discovered electrons Atoms were made of

positive stuff Negative electron

floating around “Plum-Pudding” model

Rutherford’s Model Discovered dense

positive piece at the center of the atom• Nucleus• Electrons

moved around• Mostly empty

space

Bohr’s Model Why don’t 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.

Quantum mechanical model - atom has no definite shape

#1. Summarize the development of the atomic theory in terms of the following:

Bohr - atom had electrons in orbits around nucleus

Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Bohr’s ModelIn

crea

sing

ene

rgy

Nucleus

First

Second

Third

Fourth

Fifth

} Further away

from the nucleus means more energy.

There is no “in between” energy

Energy Levels

#2. Define energy level and relate the energy level to the rungs of a ladder. Define quantum of energy.

There are energy levels around the nucleus. Think of a ladder

nucleus

1st

2nd

3rd

4th

These are the regions where an electron is likely to be found.

Electrons in levels farther from the nucleus contain more energy

Quantum of energy - the amount of energy that moves an electron up one level

Etc.

Waves vs. particles

Are electrons energy waves or particles? Both. They show properties of each and must be described as such: as particles - they have mass (1/1840 of a

proton) as energy waves - they can be emitted

from an atom as a measurable wave.

#3. Explain what is meant by the phrase “the energies of electrons are said to be quantized”.

Quantized energies means that each electron contains a specific amount of energy and that these amounts are not continuous, but units of energy. The electrons can’t “slide” from one energy level to another - they immediately appear in the next level..

#4. Explain the significance of quantized energies and the quantum mechanical model of the atom.

It is significant because it changes the way we look at energy. Instead of thinking that there are an infinite number of temperatures between 50ºC and 51ºC, we are forced to admit that there are a finite number of temperatures between these two degrees. And as something heats up, its temperature goes up by jumps rather than flowing smoothly.

#5. Explain why it is difficult to build a model of a quantum mechanical model of an atom

To build a model, you must know the where things are and their shape.

The electrons can’t be pinpointed and we only know where they are most likely to be found.

Sometimes electrons are even a long ways from the nucleus.

You can’t model anything this vague. Electrons also behave as waves and not

particles

The Bohr Model of the Atom

Neils Bohr

I pictured electrons orbiting the nucleus much like planets orbiting the sun.But I was wrong! They’re more like bees around a hive.

WRONG!!!

Quantum MechanicalModel of the Atom

Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found.These laws are beyond the scope of this class. . . . .

But why? Hmmm lets see an example

Schrodinger Wave Equation

22

2 2

8dh EV

m dx

Equation for probabilityprobability of a single electron being found along a single axis (x-axis)

Erwin Schrodinger

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

The Quantum Mechanical Model – Some Points

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.

Schrodinger derived an equation that described the energy and position of the electrons in an atom.

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.

The Quantum Mechanical Model – Some Points cont.

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.

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 %

The Quantum Mechanical Model

#6. Distinguish among principal energy level, energy sublevel, and atomic orbital.

Principal energy level• Any of the major energy levels that contain

electrons - the rungs on the ladder• designated as 1, 2, 3, 4, etc.

Energy sublevel• Locations within the principal energy level

where specific electrons are found. Atomic orbital

• An orbital describes the shape of the energy sublevel and designated as s, p, d, & f orbitals

Old

Electron Energy Level (Shell)Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. Number of electrons that can fit in a shell:

2n2

Orbital shapes are defined as the surface that

contains 90% of the total electron probability.

An orbital is a region within an energy level where there is a probability of finding an electron. This is a probability diagram for the s orbital in the first energy level…

1 energy sublevel: s orbital

2 energy sublevels:s & p orbitals

3 energy sublevels:s, p & d orbitals

4 energy sublevels:s, p, d & f orbitals

#7. State how the principal energy levels are designated and identify the number of sublevels within each principal energy level.

Old

nucleus

Atomic Orbitals Principal Quantum Number (n) = the energy level

of the electron.

Within each energy level the complex math of Schrodinger’s equation describes several shapes.

These are called atomic orbitals

Regions where there is a high probability of finding an electron.

1 s orbital for every energy level

Spherical shaped

Each s orbital can hold 2 electrons Called the 1s, 2s, 3s, etc.. orbitals.

S orbitals

Orbitals of the same shape (s, for instance) grow

larger as n increases…

Nodes are regions of low probability within an

orbital.

Sizes of s orbitals

P orbitals Start at the second energy level 3 different directions 3 different shapes Each can hold 2 electrons (opposite spins)

- three dumbbell-shaped p orbitals in

each energy level above n = 1,

- each assigned to its own axis (x, y and z) in space.

P orbital shape

P Orbitals - all together

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

Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of

“double dumbells”…and a “dumbell

with a donut”!

F orbitals Start at the fourth fourth energy level

Have seven different shapes

2 electrons per shape

Yes - There are no atoms big enough to require orbitals beyond F.

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

#7. State how the principal energy levels are designated and identify the number of sublevels within each principal energy level.

The principal energy levels are designated as n = 1, n = 2, n = 3, n = 4, n = 5, etc.

There may be as many as four sublevels (orbitals) in each principal energy level

1 has one sublevel

called “1s” with 1 orbital

2 has two sublevels

2s, 2p 2p has 3

orbitals

3 has three sublevels

3s, 3p, 3d 3d has 5

orbitals

4 has four sublevels

4s, 4p, 4d, 4f

1s

2s, 2p

3s, 3p, 3d

4s, 4p, 4d, 4f

The number of the principal energy level tells you how many sub energy levels (orbitals) are in that level.

The letters “ss”, “pp”, “dd” and “ff” tell you the shape of the orbital

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

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

Orbital filling table

5.2

Electron Configurations

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

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

Writing electron configuration H = 1s1

He = 1s2

Li = 1s2 2s1

B = 1s2 2s2 2p1

Writing electron configuration C = 1s2 2s2 2p2

1s 2s 2p’s

N = 1s2 2s2 2p3

Write an electron configuration for fluorine

1s2 2s2 2p5

Write an electron configuration for boron

1s2 2s2 2p1

The first to electrons go into the 1s orbital

Notice the opposite spins

only 13 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 2s orbital

only 11 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 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 seperate shapes

• 3 upaired electrons

• 1s22s22p63s23p3

The easy way to remember

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2

• 2 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2

• 4 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

• 12 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2

• 20 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2

• 38 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

• 56 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 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

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

4f14 5d10 6p6 7s2

5f14 6d10 7p6 • 108 electrons

The periodic table is arranged to show which orbital is being filled

s orbital p orbitald orbitalf orbital

State the maximum number of electrons that can go into each of the following sublevels:

2s

2 3p

6 4s

2 3d

10

4p

6 5s

2 4f

14 5p

6

State the number of electrons in the highest occupied energy level of these atoms.

Barium • 2p1 one

Sodium• 3s1 one

Aluminum• 3p1 one

Write electron configurations for atoms of these elements:

selenium• 1s2 2s2 2p6 3s2 3p6

4s2 3d10 4p4

• [Ar] 4s2 3d10 4p4

vanadium• 1s2 2s2 2p6 3s2 3p6

4s2 3d3

• [Ar] 4s2 3d3

nickel• 1s2 2s2 2p6 3s2 3p6

3s3 3p6 • [Ar] 4s2 3d8

calcium• 1s2 2s2 2p6 3s2 3p6

4s2

• [Ar] 4s2

oxygen• 1s2 2s2 2p4

• [He] 2s2 2p4

s orbital is being filleds orbital is

being filled

p orbital isbeing filled

d orbital is being filled

Exceptions to Electron Configuration

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

Write these electron configurations

Titanium - 22 electrons

1s22s22p63s23p64s23d2

Vanadium - 23 electrons 1s22s22p63s23p64s23d3

Chromium - 24 electrons

1s22s22p63s23p64s23d4 is expected But this is wrong!!

Chromium is actually 1s22s22p63s23p64s13d5

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

Copper’s electron configuration Copper has 29 electrons so we

expect1s22s22p63s23p64s23d9

But the actual configuration is1s22s22p63s23p64s13d10

This gives one filled orbital and one half filled orbital.

Remember these exceptions

Light/ WavesA Quick Review

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

Wavelength

AmplitudeOrgin

Crest

Trough

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• is abbreviated Greek letter lambda.

Frequency The number of waves that pass a

given point per second. Units are cycles/sec or hertz (hz) Abbreviated the Greek letter nu

c =

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

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Low energy

High energy

Low Frequency

High Frequency

Long Wavelength

Short WavelengthVisible Light

Atomic SpectrumSec 5.3

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.

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.

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.

Atoms can emit or absorb only specific frequencies of light

• These are called discontinuous spectra

• Or line spectra

• unique to each element.

• These are emission spectra

• The light is emitted given off.

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 E is the energy of the photon is the frequency h is Planck’s constant

• h = 6.6262 x 10 -34 Joules sec. joule is the metric unit of Energy

The Math in Chapter 5 Only 2 equations

c = E = h

Plug and chug.

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?

An explanation of Atomic Spectra

So Where Does It Come From Anyway?

Where the electron starts When we write electron

configurations we are writing the lowest energy.

The energy level and electron starts from is called its ground state.

So……… Do the electrons ever change

orbitals?

YES!

For Electrons to Change Orbitals they

Must absorb energy to move up to a higher orbital (energy level)

Must release energy to move down to a lower orbital (energy level)

Energy in the Atom is Quantified

Max Plank theorized that electrons can absorb or emit only specific amounts of energy.

Quantum amounts – no more no less, must be exact.

Many Things are Quantified

Some are not

The Energy Involved is Light A photon

is a quantum of light energy.

Lets Watch What Happens http://spiff.rit.edu/classes/phys301/lec

tures/spec_lines/Atoms_Nav.swf

Changing the energy Let’s look at a hydrogen atom

Changing the energy 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

May fall down in steps Each with a different energy

Changing the energy

{{{

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.

Ultraviolet Visible Infrared

Emission Spectra of an Atom Acts like a fingerprint

Can Identify the type of atom from its spectral lines.

How helium was first discovered, by observing the Sun’s light spectra

Part of the Sun’s SpectrumDo you think the sun is made of more than one thing?

Why?

ALL the Light You SEE Was at one point emitted by an excited

atom.

So 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=, E = 1/2

mv2 and E = h We can get = h/mv The wavelength of a particle.

Matter is a Wave Does not apply to large objects Things bigger that 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.

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 because

Heisenberg Uncertainty Principle

It is impossible to know exactly the speed and velocity 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

ElectronChanges velocity

Photon changes wavelength

After