Chapter 13

“Electrons in Atoms”

Credits: Stephen L. CottonCharles Page High School

Mr. DanielOlympic High School

Section 13.3Physics and the Quantum Mechanical Model

OBJECTIVES:• Describe the relationship between the

wavelength and frequency • Distinguish between quantum mechanics

and classical mechanics. of light.Identify the source of atomic emission spectra.•Explain how the frequencies of emitted light are related to changes in electron energies.

Light Visible light is a type of electromagnetic

radiation. Electromagnetic radiation is a form of energy

and includes many types: gamma rays, x-rays, radio waves, visible light…

Speed of light (c) = 3.00 x 108 m/s All electromagnetic radiation travels at this

same rate when measured in a vacuum

Parts of a Wave

Wavelength

AmplitudeNode

Crest

Trough

- Page 373

“R O Y G B I V”

Frequency Increases

Wavelength Shorter

Long Wavelength

Low Frequency

Low ENERGY

Short Wavelength

High Frequency

High ENERGY

Wavelength Table

Wavelength and Frequency: Are inversely related

• As one increases the other decreases. Different frequencies of visible light are different

colors. There is a wide variety of frequencies Spectrum: A whole range of electromagnetic

wavelengths. (e.g. the visible light spectrum)

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Low Frequency

High Frequency

Long Wavelength

Short Wavelength

Visible Light

Low Energy

High Energy

The Electromagnetic Spectrum

So what is Energy? All energy is quantized A quantum is a “packet” of energy.

Not all quanta (plural) are the same size.

(eggs are not all the same size either, but all are eggs)

So what is Light Energy? Light is a form of energy. Therefore, light must be quantized A quantum of light energy is called a photon.

Einstein determined that light is not only a wave, but is also a particle!

He demonstrated it in an experiment that showed the photoelectric effect

Photoelectric Effect

Photoelectric EffectPhotoelectric EffectExperiment demonstrates the particle nature of light.Experiment demonstrates the particle nature of light.

So what is Light Energy? (con’t)

Therefore, light has what is called wave-particle duality. It has characteristics of both waves and particles.

Wave-Particle Duality (again)J.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

Section 13.1Models of the Atom

OBJECTIVES:

• Identify the inadequacies in the Rutherford atomic model.

• Identify the new proposal in the Bohr model of the atom.

• Describe the energies and positions of electrons according to the quantum mechanical model.•Describe how the shapes of orbitals related to different sublevels differ.

Ernest Rutherford’s Model Discovered dense positive

piece at the center of the atom- “nucleus”

Electrons would surround and move around the nucleus

Atom is mostly empty space It did not explain the chemical

properties of the elements – a better description of the electron behavior was needed

Niels Bohr’s Model Why don’t the electrons fall into the nucleus?

He agreed with Rutherford that electrons move around the nucleus, But:

• In specific circular paths, or orbits (like planets around the sun), at specific energy levels.

• An amount of fixed energy separates one electron energy 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 energy levels around the nucleus, and can jump from one level to another.

Bohr’s Model Electrons occupy specific energy levels

• analogous to the rungs of a ladder The electron cannot exist between energy

levels, just like you can’t stand between rungs on a ladder

A quantum of energy is the amount of energy required to move an electron from one energy level to another (plural: quanta)

Since the energy of an atom is never “in between” there must be a quantum leap in energy.

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 the

electron up to different energy levels. The electron is now said to be in an “excited state”

Changing the energy The electron is unstable at the higher energy

level and as it falls back to the ground state, it gives the energy back in the form of light

They fall down in specific steps Each step has a different energy (quantum)

and results in a different color of light.

Changing the energy

Origin of Line SpectraOrigin of Line Spectra

Balmer seriesBalmer series

The further electrons fall, the more energy is released and the higher the frequency of light emitted.

This is a simplified explanation! Remember, the orbitals also have different

sublevels within the principle energy levels

Ultraviolet Visible Infrared

Atomic Spectra

White light is made up of all the colors of the visible spectrum.

Passing it through a prism separates it.

But not all light is 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 of light.

The colors can be used to identify the atom.

This is how we know what elements stars are made of.

• This is called a bright line spectrum

• Unique to each element, like fingerprints!

• Very useful for identifying elements

Explanation of Atomic Spectra

ground state - the lowest energy level of the electron.

In summary. When an electron at ground state receives a quantum of energy it jumps directly to a higher energy level. The electron is unstable and immediately drops to a lower energy level. As it drops it gives off the same amount of

The Quantum Mechanical Model

Problems with Bohr’s theory :Problems with Bohr’s theory :

It was only successful for H- no other It was only successful for H- no other elements followed his predictions.elements followed his predictions.

It introduced the quantum idea artificially.It introduced the quantum idea artificially.

Heisenberg Uncertainty Principle

You can find out where the electron is, but not its energy

OR…

You can know how much energy it has, but not where it is!

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

Werner Heisenberg

Heisenberg Uncertainty Principle

It is impossible to know exactly the location and velocity of a particle simultaneously.

The better we know one, the less we know the other.

Measuring one property, changes the other.

Moving Electron

Photon

Before

Electron velocity changes

Photon wavelengthchanges

After

In 1926, Erwin Schrodinger derived an equation that described the energy and probable position of the electrons in an atom

Schrodinger’s Wave Equation22

2 2

8dh EV

m dx

His equation determined the probabilityprobability of finding a single electron along a single axis (x-axis)

Erwin SchrodingerErwin Schrodinger

Particles which are very small and travel very quickly (like electrons) behave very differently from objects big enough to observe.

The quantum mechanical model is a mathematical solution describing how those particles act.

The Quantum Mechanical Model

Describes energy levels for electrons. Electrons move in an unpredictable manner We can only determine the probability of

finding an electron a certain distance from the nucleus.

The Quantum Mechanical Model

The electrons are probably located inside a blurry “electron cloud”

The area where there is the greatest chance of finding an electron.

The Quantum Mechanical Model

Atomic Orbitals Principal Quantum Number (n) = the energy

level of the electron: 1, 2, 3, etc. Within each energy level, there are sub-

levels (like theater seats arranged in sections): letters s, p, d, and f

The complex math of Schrodinger’s equation describes several shapes

These are the atomic orbitals - regions where there is a 90% probability of finding an electron.

Principal Quantum NumberThe Principle Quantum Number (n) denotes the shell (energy level) in which the electron is located.

The maximum number of electrons that fit into an energy level can be calculated:

2n2

Summary

s

p

d

f

# of orbitals

Max. electrons

Starts at energy level

1 2 1

3 6 2

5 10 3

7 14 4

Types of OrbitalsTypes of Orbitals

s orbitals orbital p orbitalp orbital d orbitald orbital

Types of

Atomic Orbitals

By Energy Level First Energy Level Has only an s

sublevel only 2 electrons 1s2

Second Energy Level

Has s and p sublevels

2 e- in s, 6 e- in p 2s22p6

8 total electrons

By Energy Level Third energy level Has s, p, and d

sublevels 2 e- in s, 6 e- in p,

and 10 e- in d 3s23p63d10

18 total electrons

Fourth energy level Has s, p, d, and f

sublevels 2 e- in s, 6 e- in p, 10

e- in d, and 14 e- in f 4s24p64d104f14

32 total electrons

By Energy Level Beyond the fourth

energy level, not all sublevels fill up.

You simply run out of electrons

So only the s, p, d and f sublevels are used

Because the energy levels overlap the orbitals do not fill up in a consistent pattern

However, the lowest energy orbitals fill first.

Section 13.2Electron Arrangement in Atoms

OBJECTIVES:• Describe how to write the electron

configuration for an atom.• Explain why the actual electron configurations for some elements differ from those predicted by the aufbau principle.

Incr

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nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

aufbau diagram

Electron Configurations… …are the way electrons are arranged in

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

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

• This becomes complex because of the overlap of orbitals of different energies – follow the diagram!

2) Pauli Exclusion Principle – there are at most 2 electrons per orbital - with opposite spins

Pauli Exclusion Principle

No 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:

Electron Configurations3) Hund’s Rule- When electrons occupy

orbitals of equal energy, they don’t pair up until each orbital has one electron.

Let’s write the electron configuration for Phosphorus

We need to account for all 15 electrons in phosphorus

The first two electrons go into the 1s orbital

Notice the opposite direction of the spins

only 13 more to go...Incr

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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

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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 sublevel.

They each go into separate orbitals (Hund’s)

• 3 unpaired electrons

• = 1s22s22p63s23p3

Orbitals fill in an order: Lowest energy to higher energy.

Adding electrons can change the energy of the orbital. Full sublevels are the most stable arrangement.

Half filled sublevels have a lower energy than partially filled sublevels, and are next most stable.

Write the electron configurations for these elements:

Zirconium - 40 electrons [Kr] 5s2 4d2

Tantalum - 73 electrons [Xe] 6s2 4f14 5d3

Chromium - 24 electrons [Ar] 4s2 3d4 (expected)But this is not what happens with Chromium

Chromium is actually: [Ar]4s13d5

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: [Ar] 4s2 3d9

But the actual configuration is: [Ar]4s13d10

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

Remember these exceptions: Groups ending in d4 and 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