Electrons in AtomsElectrons in Atomsandand

The Quantum TheoryThe Quantum Theory

Unit IIIUnit IIICh. 5Ch. 5

Warm Up-02/06/13Warm Up-02/06/13

1.1. Define isotope.Define isotope.

2.2. How do you calculate the number of How do you calculate the number of neutrons in an atom?neutrons in an atom?

3.3. What does an atom’s atomic mass tell What does an atom’s atomic mass tell you?you?

4.4. What can you never change about an What can you never change about an atom?atom?

Warm Up-02/12/13Warm Up-02/12/13

1.1. What does Pauli’s Exclusion Principle tell you What does Pauli’s Exclusion Principle tell you about how electrons enter their orbitals?about how electrons enter their orbitals?

2.2. What does Hund’s Rule tell you about how What does Hund’s Rule tell you about how electrons enter their orbitals?electrons enter their orbitals?

3.3. What does the Aufbau Principle tell you about What does the Aufbau Principle tell you about how electrons enter their orbitals?how electrons enter their orbitals?

Warm UpWarm Up Please complete a K-W-L chart Please complete a K-W-L chart

concerning electron configuration.concerning electron configuration.

1.1.What do I know about electron What do I know about electron configurations?configurations?

2.2.What would I like to know about What would I like to know about electron configurations?electron configurations?

3.3.What did I learn about electron What did I learn about electron configurations (after class)?configurations (after class)?

Warm Up-02/08/13Warm Up-02/08/131.1. How many electrons will fit in the “s” How many electrons will fit in the “s”

sub-orbital?sub-orbital?

2.2. How many electrons will fit in the “p” How many electrons will fit in the “p” sub-orbital? sub-orbital?

3.3. How many electrons will fit in the “d” How many electrons will fit in the “d” sub-orbital?sub-orbital?

4.4. How many electrons will fit in the “f” sub-How many electrons will fit in the “f” sub-orbital?orbital?

5.5. Please draw electron configurations for Please draw electron configurations for the following: He, Na, Mg, Zn and Br.the following: He, Na, Mg, Zn and Br.

Homework: Chapter 3Homework: Chapter 3

Due Date: 02/13/13Due Date: 02/13/13

Page 137: 18-22.Page 137: 18-22.

Page 146: 46-52, omit 51Page 146: 46-52, omit 51

Page 147: 77-80Page 147: 77-80

Warm UpWarm Up1.1. Construct the electron configuration for Construct the electron configuration for

iron.iron.

2.2. Construct the electron configuration for Construct the electron configuration for silicon.silicon.

3.3. Construct the electron configuration for Construct the electron configuration for potassium.potassium.

4.4. Construct the electron configuration for Construct the electron configuration for titanium.titanium.

5.5. Construct the electron configuration for Construct the electron configuration for cobalt.cobalt.

Warm UpWarm Up

1.1. What percent are carbon and oxygen What percent are carbon and oxygen in COin CO22??

2.2. What percent are calcium, sulfur and What percent are calcium, sulfur and oxygen in CaSOoxygen in CaSO44??

3.3. What percent are sodium, nitrogen What percent are sodium, nitrogen and oxygen in NaNOand oxygen in NaNO33??

4.4. What percent are calcium and clorine What percent are calcium and clorine in CaClin CaCl22??

Electromagnetic EnergyElectromagnetic EnergyFrequency (Frequency (); measured in units of hertz (sec); measured in units of hertz (sec -1-1))

Wavelength (Wavelength () - measured units of length: mm, nm) - measured units of length: mm, nm

Amplitude - the height of the waveAmplitude - the height of the wave

Speed (velocity) of electromagnetic energy =Speed (velocity) of electromagnetic energy = 3.00 x 10 3.00 x 1088 m/s m/s

c = c =

Electromagnetic SpectrumElectromagnetic Spectrum

Wavelength (Wavelength () Description Frequency () Description Frequency ())

1-800 m1-800 m Radio wavesRadio waves 101044 - 10 - 1099

1010-1-1 - 10 - 10-2-2 m m RadarRadar 10109 9 - 10- 101010

1010-2-2 - 10 - 10-4-4 m m MicrowavesMicrowaves 10101010 - 10 - 101212

1010-4-4 - 10 - 10-6-6 m m InfraredInfrared 10101212 - 10 - 101414

400-700 nm400-700 nm VisibleVisible 10101414 - 10 - 101515

1010-8-8 - 10 - 10-10-10 m m UltravioletUltraviolet 10101515 - 10 - 101818

1010-10-10 - 10 - 10-13-13 m m X-raysX-rays 10101818 - 10 - 102121

1010-13-13 - 10 - 10-15-15 m m Gamma RaysGamma Rays 10102121 - 10 - 102323

SpectroscopySpectroscopy The method of studying substances The method of studying substances

exposed to some sort of exciting energy.exposed to some sort of exciting energy.

Spectrum Spectrum Observed when white light is dispersed Observed when white light is dispersed

into the colors of the rainbow by a prism or into the colors of the rainbow by a prism or diffraction grating.diffraction grating.

Emission SpectraEmission Spectra

Absorption SpectraAbsorption Spectra

The Photoelectric EffectThe Photoelectric Effect

The emission of electrons from a metal when light The emission of electrons from a metal when light shines upon it. If the light frequency was below a shines upon it. If the light frequency was below a certain level, no electrons were emitted. The wave certain level, no electrons were emitted. The wave theory of light predicted that light of any frequency theory of light predicted that light of any frequency could supply enough energy to eject an electron. could supply enough energy to eject an electron. Scientists could not explain why a certain Scientists could not explain why a certain minimum frequency was required.minimum frequency was required.

RadiationRadiation

Caused by an unstable nucleus which will eject Caused by an unstable nucleus which will eject either a particle or energy until it reaches a either a particle or energy until it reaches a more stable arrangement.more stable arrangement.

EmissionEmission DescriptionDescription

alphaalpha helium nucleus helium nucleus

betabeta high speed electron high speed electron

gammagamma v. high energy X-rays v. high energy X-rays

Planck’s HypothesisPlanck’s Hypothesis

In 1900 Max Planck was studying black body In 1900 Max Planck was studying black body radiation. He suggested that hot objects emit radiation. He suggested that hot objects emit energy in small specific amount called energy in small specific amount called quanta. A quanta. A quantumquantum is the minimum amount of is the minimum amount of energy that can be gained or lost by an atom.energy that can be gained or lost by an atom.

Energy is given off (emitted) in little packets (or Energy is given off (emitted) in little packets (or quanta) called quanta) called photonsphotons..

The amount of energy emitted is proportional to The amount of energy emitted is proportional to the frequency of the light emitted according to the frequency of the light emitted according to the equation:the equation:

E = hE = h

E = energy of a quantum or radiationE = energy of a quantum or radiation

= the frequency of the radiation= the frequency of the radiation

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

Einstein (1905) introduced the concept that Einstein (1905) introduced the concept that electromagnetic radiation has a dual wave-electromagnetic radiation has a dual wave-particle nature.particle nature.

Relationship between electromagnetic Relationship between electromagnetic energy and electronsenergy and electrons

An electromagnetic wave of a certain frequency An electromagnetic wave of a certain frequency has only one possible wavelength: has only one possible wavelength: = c/ = c/

It has only one possible amount of energy:It has only one possible amount of energy:

E = hE = h c and h are constants. If frequency, wavelength c and h are constants. If frequency, wavelength

or energy is known, we can calculate the or energy is known, we can calculate the other two. White light can be thought of as a other two. White light can be thought of as a wave or as a stream of particles, which wave or as a stream of particles, which Einstein called photons. A photon is a particle Einstein called photons. A photon is a particle of radiation having zero rest mass and carries of radiation having zero rest mass and carries a quantum of energy.a quantum of energy.

Therefore,Therefore, EEphotonphoton = h = h

The Hydrogen Atom Line-Emission SpectrumThe Hydrogen Atom Line-Emission Spectrum

See p. 127 for an explanation of ground state and See p. 127 for an explanation of ground state and excited state for an atom.excited state for an atom.

Ground state - The smallest orbit an electron can Ground state - The smallest orbit an electron can occupy.occupy.

The energy of the photon, EThe energy of the photon, Ephoton photon , corresponds to the , corresponds to the

energy difference between the different energy energy difference between the different energy levels in an atom [ Elevels in an atom [ E11 and E and E22 , for example]. , for example].

Rutherford-Bohr AtomRutherford-Bohr Atom

This is referred to as the Planetary Atomic This is referred to as the Planetary Atomic Model because they proposed that the Model because they proposed that the negatively-charged electrons stay "in orbit" negatively-charged electrons stay "in orbit" around the positively-charged nucleus in the around the positively-charged nucleus in the same way that the planets stay in orbit same way that the planets stay in orbit around the sun.around the sun.

The Quantum Theory and the The Quantum Theory and the Hydrogen AtomHydrogen Atom

Energy is given off in quanta. Bohr Energy is given off in quanta. Bohr pointed out that the absorption of light pointed out that the absorption of light by hydrogen at definite wavelengths by hydrogen at definite wavelengths corresponds to definite changes in the corresponds to definite changes in the energy of the electron.energy of the electron.

He concluded that the orbits must have He concluded that the orbits must have orbits of definite diameter.orbits of definite diameter.

MechanicsMechanics

Newtonian MechanicsNewtonian Mechanics - describes visible - describes visible objects at ordinary velocities.objects at ordinary velocities.

Quantum MechanicsQuantum Mechanics - describes extremely - describes extremely small particles at velocities near that of lightsmall particles at velocities near that of light

Modern Atomic StructureModern Atomic Structure

E = mcE = mc22

E = hE = h mc mc22 = h = hmvmv22 = h = h mvmv22 = hv/ = hv/

= hv/mv = hv/mv22 = h/mv = h/mvmomentum = mv = pmomentum = mv = p

= h/p = h/p

Heisenberg (1927)Heisenberg (1927)

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

It is not possible to know precisely the It is not possible to know precisely the position of an electron and its momentum position of an electron and its momentum (velocity) at the same instant.(velocity) at the same instant.

SchrödingerSchrödinger

Developed a mathematical equation to Developed a mathematical equation to describe the wave-like behavior of the describe the wave-like behavior of the electron.electron.

The equation is very complicated (using The equation is very complicated (using second partial derivatives)second partial derivatives)

is the wave function. The equation is the wave function. The equation related the amplitude of the wave related the amplitude of the wave function (function () to any point in space ) to any point in space around the nucleus.around the nucleus.

Max Born showed that Max Born showed that ||||22 gives the gives the probability of finding the electronprobability of finding the electron at at the point in space for which the the point in space for which the equation was solved.equation was solved.

EinsteinEinsteinProposed that electromagnetic radiation Proposed that electromagnetic radiation

can be viewed as a steam of “particles” can be viewed as a steam of “particles” called photons.called photons.

The energy of each photon is given by:The energy of each photon is given by:E = hE = h = h(c/ = h(c/))

E = mcE = mc22 “Energy has mass” “Energy has mass”m=E/cm=E/c22 = (hc/ = (hc/)/c)/c22 = h/ = h/ccm=mass of a photon of light with a m=mass of a photon of light with a

wavelength wavelength

ConclusionsConclusions

Energy is quantizedEnergy is quantized

Electromagnetic radiation shows some Electromagnetic radiation shows some characteristics of mattercharacteristics of matter

Light as a wave: (sine wave)Light as a wave: (sine wave)

Light as a stream of photons:Light as a stream of photons:

Wave Mechanical Model of the AtomWave Mechanical Model of the Atom

Bohr’s model was based on classical physics Bohr’s model was based on classical physics and was shown to be inadequate.and was shown to be inadequate.

Mid-1920’s: a new approach was taken by de Mid-1920’s: a new approach was taken by de Bröglie, Heisenberg and Schrödinger.Bröglie, Heisenberg and Schrödinger.

De Bröglie proposed that the electron, which De Bröglie proposed that the electron, which had been considered a particle only, also had been considered a particle only, also showed wave properties.showed wave properties.

Schrödinger attacked the problem by putting Schrödinger attacked the problem by putting emphasis on the wave properties.emphasis on the wave properties.

Atomic Orbitals & Quantum NumbersAtomic Orbitals & Quantum Numbers

The quantum theory describes the behavior of The quantum theory describes the behavior of electrons. There are four quantum numbers electrons. There are four quantum numbers which are needed to describe the electron in an which are needed to describe the electron in an atom (n, atom (n, ll, m, s). Remember, no two electrons in , m, s). Remember, no two electrons in an atom can have the same four quantum an atom can have the same four quantum numbers.numbers.

nn, The Principal Quantum Number represents the , The Principal Quantum Number represents the main energy level, its "main energy level, its "sizesize". ".

Can have values of 1, 2, 3, 4, …Can have values of 1, 2, 3, 4, …

ll, Angular Momentum Quantum Number, , Angular Momentum Quantum Number, describes the "describes the "shapeshape" of the orbital. These " of the orbital. These are multiple energy states that are grouped are multiple energy states that are grouped very close together. Can have values from 0 very close together. Can have values from 0 to n-1. The number of sublevels for energy to n-1. The number of sublevels for energy level "n" = nlevel "n" = n

n = 1 » 1 subleveln = 1 » 1 sublevel

n = 2 » 2 sublevelsn = 2 » 2 sublevels

n = 3 » 3 sublevelsn = 3 » 3 sublevels

n = 4 » 4 sublevelsn = 4 » 4 sublevels

mm, Magnetic Quantum Number, describes , Magnetic Quantum Number, describes the the orientationorientation (direction) of the orbital (direction) of the orbital in space; that is, the direction in which it in space; that is, the direction in which it points. Can have values from -points. Can have values from -ll to + to +ll

Degenerate orbitals are those orbitals Degenerate orbitals are those orbitals with the same size (n) and shape (l) with the same size (n) and shape (l) which have the same energy. which have the same energy.

the three 2p orbitalsthe three 2p orbitals

the five 3d orbitalsthe five 3d orbitals

ss, Electron Spin Quantum Number. Electrons can , Electron Spin Quantum Number. Electrons can spinspin either clockwise or counterclockwise. either clockwise or counterclockwise.

s can have one of two values depending on the s can have one of two values depending on the direction of the rotation: +1/2 or -1/2direction of the rotation: +1/2 or -1/2

Quantum Number OverviewQuantum Number Overview

n - principal quantum number - size of energy n - principal quantum number - size of energy levellevel values: 1, 2, 3, 4,…values: 1, 2, 3, 4,…

ll - energy sublevel - shape of the orbital - energy sublevel - shape of the orbital values: 0 to n-1values: 0 to n-1

m - orbital Q.N. - orientation in space (direction)m - orbital Q.N. - orientation in space (direction) values: - values: - ll to + to + ll

s - spin Q.N.s - spin Q.N. values: +1/2, -1/2values: +1/2, -1/2

Rules for Filling OrbitalsRules for Filling Orbitals

Aufbau PrincipleAufbau Principle - Build up the electrons from - Build up the electrons from the bottomthe bottom

Pauli Exclusion PrinciplePauli Exclusion Principle - No two electrons can - No two electrons can have the same set of four (4) quantum have the same set of four (4) quantum numbers.numbers.

Hund's RuleHund's Rule - Add one electron to each orbital - Add one electron to each orbital of degenerate orbitals until all orbitals have at of degenerate orbitals until all orbitals have at least one electron. Then start pairing up the least one electron. Then start pairing up the remaining electrons.remaining electrons.

The Apparent ContradictionThe Apparent Contradiction

Waves can act as particles, and Waves can act as particles, and particles can act as wavesparticles can act as waves

Bohr’s atomic model explained light in Bohr’s atomic model explained light in terms of particle properties. terms of particle properties.

ElectronsElectrons (like light) have properties of (like light) have properties of both waves and particlesboth waves and particles

Wave-particle duality of natureWave-particle duality of nature applies applies to all waves and all particlesto all waves and all particles

Electron ConfigurationElectron Configuration

When we write the electron configuration for a When we write the electron configuration for a specific atom, we must specify the energy specific atom, we must specify the energy level (principal quantum number, 1,2,3,...), level (principal quantum number, 1,2,3,...), the sublevel (angular momentum quantum the sublevel (angular momentum quantum number, s, p, d, f) and the number of number, s, p, d, f) and the number of electrons in each sublevel (indicated via a electrons in each sublevel (indicated via a superscript).superscript).

Electron ConfigurationElectron Configuration

For example, the electron configuration for For example, the electron configuration for magnesium (which has 12 electrons) is:magnesium (which has 12 electrons) is:

1s1s222s2s222p2p663s3s22

When you add up all the exponents, you should When you add up all the exponents, you should get the total number of electron for that get the total number of electron for that particular atom (in this case, 2 + 2 + 6 + 2 = 12)particular atom (in this case, 2 + 2 + 6 + 2 = 12)

Modern Atomic StructureModern Atomic Structure

1. The division between matter and energy is 1. The division between matter and energy is becoming even less clear.becoming even less clear.

2. de Bröglie Hypothesis (1923) led the way to 2. de Bröglie Hypothesis (1923) led the way to the present theory of atomic structure.the present theory of atomic structure.

Electron Dot DiagramsElectron Dot Diagrams>>>Rules <<<>>>Rules <<<

The elemental symbol represents the The elemental symbol represents the nucleus and all electrons not in the nucleus and all electrons not in the outer shellouter shell

Write out the electron configuration Write out the electron configuration (1s(1s222s2s22…) selecting those electrons in …) selecting those electrons in the outer energy level onlythe outer energy level only

Each side represents an orbital. Draw Each side represents an orbital. Draw dots to represent electrons in that orbitaldots to represent electrons in that orbital

Quantum TheoryQuantum Theory

The quantum theory describes the behavior of the The quantum theory describes the behavior of the electrons.electrons.

There are four quantum numbers needed to There are four quantum numbers needed to describe the electron in an electron (n, describe the electron in an electron (n, ll, m, s), m, s)

No two electrons can have the same four quantum No two electrons can have the same four quantum numbersnumbers

Principal Quantum Number, nPrincipal Quantum Number, n

Represents the “Represents the “sizesize” of the energy level ” of the energy level (orbital)(orbital)

Energy Sublevels,Energy Sublevels, ll

Describes the “Describes the “shapeshape” of the orbital ” of the orbital

These are multiple energy states that are These are multiple energy states that are grouped very close togethergrouped very close together

The number of sublevels (for each level) = nThe number of sublevels (for each level) = n

n=1n=1 1 sublevel1 sublevel

n=2n=2 2 sublevels2 sublevels

n=3n=3 3 sublevels3 sublevels

n=4n=4 4 sublevels4 sublevels

Orbital Quantum Number, mOrbital Quantum Number, m

Describes the Describes the orientationorientation of the orbital in of the orbital in space; the direction in which it points.space; the direction in which it points.

Degenerate orbitals: those orbitals with Degenerate orbitals: those orbitals with the same size (n) and shape (the same size (n) and shape (ll) which ) which have the same energy. e.g.,have the same energy. e.g., the three 2p orbitalsthe three 2p orbitals the five 3d orbitals the five 3d orbitals

Electron Spin Quantum Number, sElectron Spin Quantum Number, s

Electrons can Electrons can spinspin either clockwise or either clockwise or counterclockwisecounterclockwise

““s” will have one of two values depending on s” will have one of two values depending on the direction of rotation: +1/2 or -1/2the direction of rotation: +1/2 or -1/2

Distribution of ElectronsDistribution of ElectronsHow are electrons distributed among the energy How are electrons distributed among the energy

levels?levels?In a neutral atom:In a neutral atom:

#e#e--’s = # protons = atomic no.’s = # protons = atomic no.Electrons always fill the energy level and Electrons always fill the energy level and

sublevel to produce the lowest energy sublevel to produce the lowest energy arrangementarrangement

No two electrons can have the same 4 quantum No two electrons can have the same 4 quantum numbersnumbers (Pauli Exclusion Principle)(Pauli Exclusion Principle)

The max. no. of eThe max. no. of e-- in energy level “n” = 2n in energy level “n” = 2n22

Aufbau PrincipleAufbau Principle

Build up the electrons from the bottomBuild up the electrons from the bottom ““The Aufbau Hotel”The Aufbau Hotel”

Hund’s RuleHund’s Rule

Add one electron to each orbital of degenerate Add one electron to each orbital of degenerate orbitals until all orbitals have at least one orbitals until all orbitals have at least one electron. electron. ThenThen start pairing up the remaining start pairing up the remaining electronselectrons..

Pauli Exclusion PrinciplePauli Exclusion Principle

No two electrons can have the same set of No two electrons can have the same set of four (4) quantum numbersfour (4) quantum numbers

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

It is not possible to know precisely the position It is not possible to know precisely the position of an electron and its momentum (velocity) of an electron and its momentum (velocity) at the same instant.at the same instant.