Chemistry NotesChemistry Notes

The Quantum TheoryThe Quantum Theory

The Bohr ModelThe Bohr Model

Recall: Bohr’s model describes the atom as having Recall: Bohr’s model describes the atom as having definite energy levelsdefinite energy levels ee-- will absorb a “quantized” amount of energy, which will absorb a “quantized” amount of energy, which

excites the eexcites the e--,when e,when e-- returns to its ground state it returns to its ground state it always emits light at specific wavelengthsalways emits light at specific wavelengths

These wavelengths correspond to definite changes in These wavelengths correspond to definite changes in the electrons energythe electrons energy Bohr used Max Plank’s idea: E = hc/Bohr used Max Plank’s idea: E = hc/λλ

Bohr’s model refers to quanta as packets of Bohr’s model refers to quanta as packets of energy (or particles)energy (or particles)

From Bohr to the Quantum ModelFrom Bohr to the Quantum Model

Bohr’s model had issuesBohr’s model had issuesconsiders electrons to have both a known

radius and orbitIt makes poor predictions regarding the

spectra of larger atoms. It does not predict the relative intensities of

spectral lines. The Bohr Model does not explain fine

structure in spectral lines.

From Bohr to the Quantum ModelFrom Bohr to the Quantum Model

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle: : it is it is impossible to know the exact position and the impossible to know the exact position and the exact momentum of an electron at the same exact momentum of an electron at the same time.time. (This challenged Bohr’s Model)(This challenged Bohr’s Model)

In order to know where an In order to know where an electron is we have to “see” electron is we have to “see” it. To see something it must it. To see something it must be hit by a photon. Photons be hit by a photon. Photons and electrons are roughly the and electrons are roughly the same size, when they collide same size, when they collide the electron will no longer be the electron will no longer be in the same position.in the same position.

From Bohr to the Quantum ModelFrom Bohr to the Quantum Model

Photoelectric Effect showed that r Photoelectric Effect showed that r frequency high light can eject electrons.frequency high light can eject electrons. i.e. – Light can act as a particle i.e. – Light can act as a particle See See

Physics notes Physics notes De Broglie – can quanta (particles) have De Broglie – can quanta (particles) have

wave properties? Can particles act like wave properties? Can particles act like waves?waves?Wave-particle duality Wave-particle duality

From Bohr to the Quantum ModelFrom Bohr to the Quantum Model

Erwin Schrodinger investigated the wave Erwin Schrodinger investigated the wave nature of the electronnature of the electronDeveloped a mathematical equation that Developed a mathematical equation that

related the electron's amplitude to any point in related the electron's amplitude to any point in space around the nucleusspace around the nucleus

Schrodinger's EquationSchrodinger's Equation

• Ψ is the wave function or probable position of the electron.•m is the mass of the electron.•E is the total energy of the system.•V is the potential energy and is a function of x, y and z.

The probability of finding the electron decreases as you move away from the center of the nucleus.

Schrodinger's EquationSchrodinger's Equation

The solutions of the Schrodinger equation The solutions of the Schrodinger equation can tell us things about the electron.can tell us things about the electron.The size of electron cloudThe size of electron cloudThe energy of the electron cloudThe energy of the electron cloudThe shape of the cloudThe shape of the cloud

The Quantum ModelThe Quantum Model

Summary: Quantum model Summary: Quantum model seeks to seeks to describe the behavior of subatomic describe the behavior of subatomic particles in terms of wavesparticles in terms of wavesElectrons have properties of both waves Electrons have properties of both waves

and particlesand particles

The Quantum ModelThe Quantum Model

Bohr’s model showed definite positioning Bohr’s model showed definite positioning of electrons (they were in orbits). of electrons (they were in orbits).

The Quantum model is primarily a The Quantum model is primarily a mathematical one that shows the probable mathematical one that shows the probable location of an electronlocation of an electron

Notice: the circles denote the probability of finding an electron in that region of space.

The Quantum ModelThe Quantum Model

A fuzzy cloud represents A fuzzy cloud represents the the probabilityprobability of finding of finding an electron within a an electron within a certain volume of space.certain volume of space. This Fuzzy Cloud is called This Fuzzy Cloud is called

an an orbital Denser cloud = higher Denser cloud = higher

probability of finding an probability of finding an electron electron

Less dense cloud = lower Less dense cloud = lower probability of finding an probability of finding an electronelectron

The Quantum ModelThe Quantum Model

OrbitsOrbits (Bohr’s Model)(Bohr’s Model) vs. vs. Orbitals (Quantum Model)Quantum Model)

(PATHS e- travel in (Regions of space where e- may be)(PATHS e- travel in (Regions of space where e- may be)

The Quantum ModelThe Quantum Model

Letters that denote atomic orbitals in Letters that denote atomic orbitals in sublevels:sublevels:s – spherical shaped p – dumbbell shaped (3 orbitals)d – four of the five kinds of d orbitals are

clover shaped. (5 orbitals)f – very oddly shaped (7 orbitals)

The maximum number of electrons in each The maximum number of electrons in each orbital is 2.orbital is 2.

AGAIN!!!AGAIN!!!

The Quantum Theory is not trying to show The Quantum Theory is not trying to show what the atom looks like. what the atom looks like.

The QT is a mathematical model The QT is a mathematical model The QT is trying to show us the probable The QT is trying to show us the probable

location of electrons in an atomlocation of electrons in an atomThe orbitals represent the probability of The orbitals represent the probability of

finding an electronfinding an electron

Describing the Distribution of Describing the Distribution of ElectronsElectrons

Quantum NumbersQuantum Numbers: : like a zip code for electronslike a zip code for electrons

nn (principle quantum number)– Indicates (principle quantum number)– Indicates principle energy level principle energy level

DescribesDescribes relative size of the electron cloudrelative size of the electron cloud Corresponds to the energy level 1,2,3,…nCorresponds to the energy level 1,2,3,…n

Describing the Distribution of Describing the Distribution of ElectronsElectrons

ll (second quantum number) – Indicates (second quantum number) – Indicates sublevel sublevel

DescribesDescribes shape of cloudshape of clouds: l = 0; p: l = 1; d: l = 2; f: l = 3s: l = 0; p: l = 1; d: l = 2; f: l = 3

Describing the Distribution of Describing the Distribution of ElectronsElectrons

mm (third quantum number) – Indicates (third quantum number) – Indicates orientation in space of the cloudorientation in space of the cloud

For the For the p orbitals p orbitals the values range from the values range from –1 to 1–1 to 1 ppxx (-1) / (-1) / ppyy (O) / (O) / ppzz (+1)(+1)

For the For the d orbitalsd orbitals the values range from the values range from –2 to 2–2 to 2 ddxx22yy22 (+2) / (+2) / ddzz22 (+1) / (+1) / dxdxyy (O) / (O) / ddxzxz (-1) / (-1) / ddyzyz (-2) (-2)

For the For the f orbitalsf orbitals the values range from the values range from –3 to 3–3 to 3 Don’t worry about it.Don’t worry about it.

Describing the Distribution of Describing the Distribution of ElectronsElectrons

s s (fourth quantum number) (fourth quantum number) - - distinguish distinguish between electrons in same orbital.between electrons in same orbital.

+1/2 denotes a clockwise spin+1/2 denotes a clockwise spin -1/2 denotes a counter clockwise spin.-1/2 denotes a counter clockwise spin.

The Pauli exclusion principal The Pauli exclusion principal says: electrons in says: electrons in the same orbital have opposite spins. (See Fig. the same orbital have opposite spins. (See Fig.

5.12 on p. 123 in book)5.12 on p. 123 in book)

Describing the Distribution of Describing the Distribution of ElectronsElectrons

What do the following numbers tell us: 4, 1, -1, +1/2 What do the following numbers tell us: 4, 1, -1, +1/2

Electron is in the 4th PELElectron is in the 4th PELElectron is in the p sublevel Electron is in the p sublevel Electron is oriented in the orbital along x-Electron is oriented in the orbital along x-

axisaxisElectron has a clockwise spinElectron has a clockwise spin

Describing the Distribution of Describing the Distribution of ElectronsElectrons

Quantum numbers are like zip codesQuantum numbers are like zip codesN N United States / PEL United States / PELL L Michigan / sublevel Michigan / sublevelM M Bridgman / orbital Bridgman / orbitalS S facing north / spin facing north / spin

See table 5.1 in book See table 5.1 in book Please read pages 109-125Please read pages 109-125

The Quantum TheoryThe Quantum Theory

SummarySummary Explain how the quantum model is part of the on Explain how the quantum model is part of the on

going development of the atomic model.going development of the atomic model. State the Heisenburg Uncertainty Principle and State the Heisenburg Uncertainty Principle and

explain how it influenced the modern view of the explain how it influenced the modern view of the atom.atom.

Explain how the Quantum Model is different than Explain how the Quantum Model is different than other views of the atom.other views of the atom.

Use quantum numbers to locate the approximate Use quantum numbers to locate the approximate location of electrons.location of electrons.