Chapter 5Chapter 5

“Electrons in Atoms”“Electrons in Atoms”

ChemistryChemistry

Ernest Rutherford’s ModelErnest Rutherford’s Model Discovered dense positive piece at Discovered dense positive piece at

the center of the atom- the center of the atom- “nucleus”“nucleus” Electrons would surround and move Electrons would surround and move

around it, like planets around the around it, like planets around the sunsun

Atom is mostly empty spaceAtom is mostly empty space It did not explain the It did not explain the chemical chemical

propertiesproperties of the elements – a better of the elements – a better description of the description of the electron behaviorelectron behavior was neededwas needed

Rutherford's ModelRutherford's Model

Rutherford's model not completeRutherford's model not complete Did not explain location of electronsDid not explain location of electrons If opposites attract what prevents them from If opposites attract what prevents them from

going into the nucleus?going into the nucleus?

LightLight The study of light led to the development of the The study of light led to the development of the

quantum mechanical model.quantum mechanical model. Light is a kind of electromagnetic radiation.Light is a kind of electromagnetic radiation. Electromagnetic radiation includes many types: Electromagnetic radiation includes many types:

gamma rays, x-rays, radio waves… gamma rays, x-rays, radio waves… Speed of lightSpeed of light = 2.998 x 10 = 2.998 x 1088 m/s, and is m/s, and is

abbreviated “c”abbreviated “c” All electromagnetic radiationAll electromagnetic radiation travels at this same travels at this same

rate when measured in a vacuumrate when measured in a vacuum

Electromagnetic radiation Electromagnetic radiation

Energy and Light Energy and Light

Parts of a waveParts of a wave

Wavelength

AmplitudeOrigin

Crest

Trough

Atoms and EnergyAtoms and Energy

How are the types of light different?How are the types of light different? Energy and Light Energy and Light

– Wavelength, λ

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

Wavelength and FrequencyWavelength and Frequency Are inversely relatedAre inversely related

• As one goes up the other goes down.As one goes up the other goes down. Different frequencies of light are Different frequencies of light are different different

colorscolors of light. of light. There is a wide variety of frequenciesThere is a wide variety of frequencies The whole range is called a The whole range is called a spectrumspectrum

The Math in Chapter 5The Math in Chapter 5

There are 2 There are 2 equations:equations:

1)1) c = c = 2)2) E = hE = h Know these!Know these!

Math in chapter 5Math in chapter 5

E is the energy, in joules, of a quantum of E is the energy, in joules, of a quantum of radiation, radiation,

is the frequency, in s−1, of the radiation is the frequency, in s−1, of the radiation emitted, and h isemitted, and h is

a fundamental physical constant now known asa fundamental physical constant now known as Planck’s constant; h = 6.626 × 10−34 J• sPlanck’s constant; h = 6.626 × 10−34 J• s

ExamplesExamples1)1) What is the wavelength of blue light What is the wavelength of blue light

with a frequency of 8.3 x 10with a frequency of 8.3 x 101515 hz? hz?

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

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

Atomic SpectraAtomic Spectra White lightWhite light is is

made up of all the made up of all the colors of the colors of the visible spectrum.visible spectrum.

Passing it through Passing it through a a prismprism separates separates it.it.

If the light is not whiteIf the light is not white

By heating a gas with By heating a gas with electricity we can get electricity we can get it to give off colors.it to give off colors.

Passing this light Passing this light through a prism does through a prism does something different.something different.

Atomic SpectrumAtomic Spectrum Each element gives off Each element gives off

its own characteristic its own characteristic colors.colors.

Can be used to Can be used to identify the atom.identify the atom.

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

Emission of Energy by AtomsEmission of Energy by Atoms

Atoms can give off light. Atoms can give off light. They first must receive energy and become They first must receive energy and become

excited. excited. The energy is released in the form of a photon. The energy is released in the form of a photon.

The Hydrogen-Atom Line-EmissionThe Hydrogen-Atom Line-EmissionSpectrumSpectrum

The Energy Levels of HydrogenThe Energy Levels of Hydrogen

Only certain types of photons are produced Only certain types of photons are produced when H atoms release energy. Why? when H atoms release energy. Why?

The Energy Levels of HydrogenThe Energy Levels of Hydrogen

Atomic states Atomic states Excited stateExcited state – atom – atom

with excess energy with excess energy Ground stateGround state – atom in – atom in

the lowest possible state the lowest possible state When an H atom When an H atom

absorbs energy from an absorbs energy from an outside source it enters outside source it enters an excited state. an excited state.

The Energy Levels of HydrogenThe Energy Levels of Hydrogen Energy level diagramEnergy level diagram

•Energy in the photon corresponds to the energy used by the atom to get to the excited state.

The Bohr Model of the AtomThe Bohr Model of the Atom

Bohr’s model of the atom Quantized energy levels Electron moves in a circular orbit Electron jumps between levels by absorbing or

emitting photon of a particular wavelength

The Bohr Model of the AtomThe 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 modelBohr’s model Energy levelEnergy level of an electron of an electron

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

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

AA quantumquantum of energy is the amount of of energy is the amount of energy required to move an electron from energy required to move an electron from one energy level to anotherone energy level to another

Problems with the Bohr ModelProblems with the Bohr Model

It makes poor predictions regarding the It makes poor predictions regarding the spectra of larger atoms. spectra of larger atoms.

It does not predict the relative intensities It does not predict the relative intensities of spectral lines. of spectral lines.

The Bohr Model does not explain fine The Bohr Model does not explain fine structure and hyperfine structure in structure and hyperfine structure in spectral lines. spectral lines.

The Quantum Mechanical The Quantum Mechanical ModelModel

Energy is “quantized” - It comes in chunks.Energy is “quantized” - It comes in chunks. A A quantumquantum is the amount of energy needed to is the amount of energy needed to

move from one energy level to another.move from one energy level to another. Since the energy of an atom is never “in between” Since the energy of an atom is never “in between”

there must be a quantum leap in energy.there must be a quantum leap in energy. In 1926, In 1926, Erwin SchrodingerErwin Schrodinger derived an derived an

equationequation that described the energy and position of that described the energy and position of the electrons in an atomthe electrons in an atom

Schrodinger’s Wave EquationSchrodinger’s Wave Equation22

2 2

8dh EV

m dx

Equation for the probabilityprobability of a single electron being found along a single axis (x-axis)Erwin SchrodingerErwin Schrodinger

The Schrödinger Wave EquationThe Schrödinger Wave Equation Electrons do not travel around the Electrons do not travel around the

nucleus in neat orbits,, as Bohr had nucleus in neat orbits,, as Bohr had postulated..postulated..

Instead,, they exist in certain regions Instead,, they exist in certain regions called orbitals..called orbitals..

An orbital is a three-dimensional region An orbital is a three-dimensional region around the nucleus that indicates the around the nucleus that indicates the probable location off an electron..probable location off an electron..

Things that are very small Things that are very small behave differentlybehave differently from things from things big enough to see.big enough to see.

The The quantum mechanical quantum mechanical modelmodel is a is a mathematical mathematical solutionsolution

It is not like anything you can It is not like anything you can see see (like plum pudding!)(like plum pudding!)

The Quantum Mechanical The Quantum Mechanical ModelModel

Has energy levels for electrons.Has energy levels for electrons. Orbits are not circular.Orbits are not circular. It can only tell us the It can only tell us the probabilityprobability of of

finding an electron a certain distance finding an electron a certain distance from the nucleus.from the nucleus.

The Quantum Mechanical The Quantum Mechanical ModelModel

The atom is found The atom is found inside a blurry inside a blurry “electron cloud”“electron cloud”

An area where there is An area where there is a a chance chance of finding an of finding an electron.electron.

Think of fan bladesThink of fan blades

The Quantum Mechanical The Quantum Mechanical ModelModel

Atomic OrbitalsAtomic Orbitals Principal Quantum NumberPrincipal Quantum Number (n) = the (n) = the

energy level of the electron: 1, 2, 3, etc.energy level of the electron: 1, 2, 3, etc. Within each energy level, the complex math Within each energy level, the complex math

of Schrodinger’s equation describes several of Schrodinger’s equation describes several shapes.shapes.

These are called These are called atomic orbitalsatomic orbitals (coined by (coined by scientists in 1932) - regions where there is a scientists in 1932) - regions where there is a high probability of finding an electron.high probability of finding an electron.

Sublevels- like theater seats arranged in Sublevels- like theater seats arranged in sections: letters s, p, d, and fsections: letters s, p, d, and f

Shape of 1s OrbitalShape of 1s Orbital

Shape of 2p OrbitalShape of 2p Orbital

Shape of 3d OrbitalsShape of 3d Orbitals

Principal Quantum NumberPrincipal Quantum NumberGenerally symbolized by “n”, it denotes the shell (energy level) in which the electron is located.

Maximum number of electrons that can fit in an energy level is:

2n2

How many e- in level 2? 3?

SummarySummary

s

p

d

f

# of shapes (orbitals)

Maximum electrons

Starts at energy level

1 2 1

3 6 2

5 10 3

7 14 4

By Energy LevelBy Energy Level

First Energy LevelFirst Energy Level Has only s orbitalHas only s orbital only 2 electronsonly 2 electrons 1s1s22

Second Energy Second Energy LevelLevel

Has s and p orbitals Has s and p orbitals availableavailable

2 in s, 6 in p2 in s, 6 in p 2s2s222p2p66

8 total electrons8 total electrons

By Energy LevelBy Energy Level

Third energy levelThird energy level Has s, p, and d Has s, p, and d

orbitalsorbitals 2 in s, 6 in p, and 10 2 in s, 6 in p, and 10

in din d 3s3s223p3p663d3d1010

18 total electrons18 total electrons

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

orbitalsorbitals 2 in s, 6 in p, 10 in d, 2 in s, 6 in p, 10 in d,

and 14 in fand 14 in f 4s4s224p4p664d4d10104f4f1414

32 total electrons32 total electrons

By Energy LevelBy Energy Level

Any more than the Any more than the fourth and not all the fourth and not all the orbitals will fill up.orbitals will fill up.

You simply run out You simply run out of electronsof electrons

The orbitals do The orbitals do notnot fill up in a neat fill up in a neat order.order.

The energy levels The energy levels overlapoverlap

Lowest energy fill Lowest energy fill first.first.

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 133Aufbau is German for “building up”

Electron Configurations…Electron Configurations… ……are the way electrons are arranged in are the way electrons are arranged in

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

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

• This causes difficulties because of the overlap This causes difficulties because of the overlap of orbitals of different energies – follow the of orbitals of different energies – follow the diagram!diagram!

2)2) Pauli Exclusion PrinciplePauli Exclusion Principle - at most 2 - at most 2 electrons per orbital - different spinselectrons per orbital - different spins

Pauli Exclusion PrinciplePauli 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:

Quantum NumbersQuantum 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 ConfigurationsElectron Configurations

3)3) Hund’s RuleHund’s Rule-- When electrons occupy When electrons occupy orbitals of equal energy, they don’t pair orbitals of equal energy, they don’t pair up until they have to.up until they have to.

Let’s write the electron configuration Let’s write the electron configuration for Phosphorus for Phosphorus

We need to account for all 15 electrons in We need to account for all 15 electrons in phosphorusphosphorus

The first two electrons go The first two electrons go into the 1s orbitalinto the 1s orbital

Notice the opposite Notice the opposite direction of the spinsdirection of the spins

only 13 more to go...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

Orbitals fill in an order Orbitals fill in an order Lowest energy to higher energy.Lowest energy to higher energy. Adding electrons can change the Adding electrons can change the

energy of the orbital. energy of the orbital. Full orbitalsFull orbitals are are the absolute best situation.the absolute best situation.

However,However, half filledhalf filled orbitals have a orbitals have a lower energy, and are next bestlower energy, and are next best• Makes them more stable.Makes them more stable.• Changes the filling orderChanges the filling order

Write the electron configurations Write the electron configurations for these elements:for these elements:

Titanium - 22 electronsTitanium - 22 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d22

Vanadium - 23 electronsVanadium - 23 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d33

Chromium - 24 electronsChromium - 24 electrons 1s1s222s2s222p2p663s3s223p3p664s4s223d3d4 4 (expected)(expected) But this is not what happens!!But this is not what happens!!

Chromium is actually:Chromium is actually: 1s1s222s2s222p2p663s3s223p3p664s4s113d3d55

Why?Why? This gives us two This gives us two half filled orbitalshalf filled orbitals

(the others are all still full)(the others are all still full) Half full is slightly lower in energy.Half full is slightly lower in energy. The same principal applies to copper.The same principal applies to copper.

Copper’s electron Copper’s electron configurationconfiguration

Copper has 29 electrons so we expect: Copper has 29 electrons so we expect: 1s1s222s2s222p2p663s3s223p3p664s4s223d3d99

But the But the actual configurationactual configuration is: is: 1s1s222s2s222p2p663s3s223p3p664s4s113d3d1010

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

Remember these exceptions: Remember these exceptions: dd44, , dd99

Irregular configurations of Cr and CuIrregular 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

Noble-Gas NotationNoble-Gas Notation

Example::Example:: Sodium’s electron-configuration notation Sodium’s electron-configuration notation

would be: 1swould be: 1s22 2s 2s22 2p 2p66 3s 3s11

We can simplify it using the noble gas that We can simplify it using the noble gas that comes before sodium,, which is neon..comes before sodium,, which is neon..

Neon's configuration is 1sNeon's configuration is 1s22 2s 2s22 2p 2p66

We simplify sodium's configuration by placing We simplify sodium's configuration by placing the symbol for neon in brackets and then we the symbol for neon in brackets and then we just add on..[Ne] 3sjust add on..[Ne] 3s11

The physics of the very smallThe physics of the very small Quantum mechanicsQuantum mechanics explains how explains how

very smallvery small particles behave particles behave• Quantum mechanics is an explanation Quantum mechanics is an explanation

for subatomic particles and atoms as for subatomic particles and atoms as waveswaves

Classical mechanicsClassical mechanics describes the describes the motions of bodies much larger than motions of bodies much larger than atomsatoms

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

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

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

Measuring changes the properties.Measuring changes the properties. True in quantum mechanics, but not True in quantum mechanics, but not

classical mechanicsclassical mechanics

Heisenberg Uncertainty PrincipleHeisenberg 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