Chapters 7 & 8

Quantum Mechanical Model; Electronic Structure

of the Atoms & Periodic Trends

Definitions

• Atoms - smallest particles of matter

• Matter - has mass, volume and specific position

• Energy - no mass; a wave function; delocalized

Einstein’s Contribution

• Energy is related to mass as seen in the equation:

E = mc2

Law of Conservation of Energy

• Energy can never be destroyed. It can only be converted from one form to another.

Forms of Energy

• Electromagnetic radiation wavelength, frequency and speed

• Light

• Heat

Electromagnetic Spectrum

• Radio Waves

• Microwaves, Radar Rays

• Infrared

• Visible

• UV

• X-rays

• Gamma Rays

The Wave Nature of LightThe Wave Nature of Light

The Wave Nature of LightThe Wave Nature of Light

Chemistry in Color

• Specific elements gave color when heated in flame.

• Continuous spectrum - e.g., rainbow

• Line Spectrum

Line Spectra

• Held the key to the structure of the atom!

The Bohr Atom

• Bohr: suggested that electrons were responsible for the line spectra.

Proposed that electrons traveled around the nucleus of the atom in shells

The Bohr Atom

• Bohr: associated each shell w/ a particular

energy level. The farther away, the higher the Energy.

Allowed electrons to jump from one shell to another. (ground state excited state)

Comparison

• Bohr Model similar to model for solar system where the planets revolve in their particular orbits.

• Difference: Electrons can jump from one shell to another. The planets do not!

Ionization

• An electron can absorb so much energy that it can jump completely from the atom!

The Photoelectric Effect and Photons• If light shines on the surface of a metal, there is a point

at which electrons are ejected from the metal.• The electrons will only be ejected once the threshold

frequency is reached.• Below the threshold frequency, no electrons are

ejected.• Above the threshold frequency, the number of

electrons ejected depend on the intensity of the light.

Quantized Energy and Quantized Energy and PhotonsPhotons

Matter and Energy

• Matter and Energy are not distinct!

• Proof: Matter can absorb or emit energy.

• Max Planck’s Postulate: Energy can be gained or lost only in whole numbers or integer multiples, h.

Wrong assumption

• Matter was assumed to transfer any amount of energy because E was continuous.

Quantum

• E can be quantized or delivered in small packets of size h, called a Quantum.

• Quanta = photon

Quantum Mechanical Model

• De Broglie and Schroedinger

• Corrected Bohr’s model

• determined that E had wave properties and mass

Quantum Mechanical Model

• re-evaluated electron as occupying volume of space instead of shells that were like orbits.

• Orbital - volume of space occupied by an electron

If we solve the Schrödinger equation, we get wave functions and energies for the wave functions.

• We call wave functions orbitals.

• Orbitals were located in levels.

Quantum Mechanics and Quantum Mechanics and Atomic OrbitalsAtomic Orbitals

Quantum Mechanical Model

• De Broglie and Schroedinger

• Corrected Bohr’s model

• determined that E had wave properties and mass

Quantum Mechanical Model

• re-evaluated electron as occupying volume of space instead of shells that were like orbits.

• Orbital - volume of space occupied by an electron

If we solve the Schrödinger equation, we get wave functions and energies for the wave functions.

• We call wave functions orbitals.

Quantum Mechanics and Quantum Mechanics and Atomic OrbitalsAtomic Orbitals

Principal Quantum Number, n

• Schrödinger’s equation requires 3 quantum numbers:

1.Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. N refers to the shell.

Azimuthal Quantum Number, l.

2. This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.

Representations of Representations of OrbitalsOrbitals

Magnetic Quantum Number, ml.

3. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

The s-Orbitals

Representations of Representations of OrbitalsOrbitals

Shape of Orbitals

• s - sphere

• p - dumbbell

• d - double dumbbell

The p-Orbitals

• There are three p-orbitals px, py, and pz.

• The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system.

• The letters correspond to allowed values of ml of -1, 0, and +1.

• The orbitals are dumbbell shaped.• As n increases, the p-orbitals get larger.• All p-orbitals have a node at the nucleus.

Representations of Representations of OrbitalsOrbitals

The p-Orbitals

Representations of Representations of OrbitalsOrbitals

The d and f-Orbitals

• There are five d and seven f-orbitals.

• Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes.

• Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes.

• Four of the d-orbitals have four lobes each.

• One d-orbital has two lobes and a collar.

Representations of Representations of OrbitalsOrbitals

Pauli Exclusion Principle

• An orbital can only hold 2 electrons and they must have opposite spins!

• Example: px, py, pz

Rules for Occupancy and Pairing

• Opposite spins pair up.

• Hund’s Rule: For the same sublevel, each orbital must be occupied singly before pairing can occur. This is the lowest E for an atom configuration.

Heisenberg Uncertainty Principle

• “There is a fundamental limitation as to how precisely we can determine the position and momentum of a particle at a given time.”

• 90-95% probability of finding the electron in the orbital

Magnetic Spin Quantum Number, ms

• Gives insight into the spin of the electron

• 2 Possible Values: ½ and – ½

Orbitals and Their Energies

• Orbitals of the same energy are said to be degenerate.

• For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other.

• Therefore, the Aufbau diagram looks slightly different for many-electron systems.

Many-Electron Atoms Many-Electron Atoms

Energy Levels

• The electrons are found at a certain distance from nucleus in their shell(s).

• energy level = shell (interchangeable terms)

• Electrons in the same shell have the same E.

Heisenberg Uncertainty Principle

• “There is a fundamental limitation as to how precisely we can determine the position and momentum of a particle at a given time.”

• 90-95% probability of finding the electron in the orbital

Shorthand Notation

• Uses the closest noble gas before the given element to represent the inner electrons.

• Al = 13 electrons 1s2 2s2 2p6 3s2 3p1

• Shorthand Notation: [Ne] 3s2 3p1

– Neon represents the 10 inner electrons

Sample Problems

• Give the electronic configuration of:

• a.) Ob.) Mg

c.) Ca

Periodicity

• Valence electrons determined the position of the atoms in the periodic table and predicted the reactivity of the elements.

Periodic Table

• Organized according to Electronic Configuration of elements

• Based on the Aufbau Principle of building up the number of electrons and protons

Definitions

• Core Electrons - inner electrons

• Valence Electrons - electrons on the outermost energy level of an atom

Valence Electrons

• Are the electrons in the outermost shell

• Determines the group where the element belongs in the periodic table.

• For ex., 1s22s22p3 = element belongs to Grp V. Outermost level is 2. Add the electrons in 2s and 2p orbitals.

Sample Problem

• What is the largest principal quantum number in the ground state electron configuration of iodine ?

For electron configurations ending in d or f

• When the outermost orbitals are d or f, only count the electrons in the d or f orbitals. This number of electrons determines the Group. However, the group will be B.

• Ex. 1s22s22p63s23p64s23d4 = Group IVB.

• Even though highest level is 4, only consider the d or f electrons.

Sample Problem

• What is the azimuthal quantum number for the orbitals being filled in the Lanthanide series?

Sample Problem

• What is the azimuthal quantum number for the orbitals being filled in Group II?

Sample Problem

• What is the azimuthal quantum number for the orbitals being filled in Group VII?

Sample Problem

• How many electrons have quantum numbers 4,2,1,-1/2.

• How many orientations have n=5 and l=2?

• How many electrons have n=5 and l=2?

Transition Metals• Electron configuration of transition metals

differ from that of regular A-block elements.

• Preference for half-filled and totally filled d-orbitals.

• Transition metals do not like the d4 and d9 configuration. They borrow one electron from the closest s orbital (before the d orbital) to make d5 or d10.

• Lanthanides and Actinides do not like ending the electron configuration in f6 and f13. They borrow one electron from the closest s orbital (before the f orbital) to make f7 or f14.

Sample Problem

• Write the electronic configuration of Molybdenum?

• Write the abbreviated electronic configuration of Molybdenum.

Trends

• Atomic Size

• Ionization Energy

• Electron Affinity

Sample Problem

• Arrange the following in order of increasing atomic radii.

• A.) Ba, Sr, S, Pb, V• B.) Au, Cd, Tl, In, Te

Sample Problem

• Arrange the following elements in order of increasing ionization energies.

• A.] Ca, Mg, F, B, Br• B.] Kr, O, Se, Tl, Na

General Trend

• As you go across the periodic table, electron affinity increases.

• As you go down the periodic table, electron affinity decreases. (too far away for nucleus to have much of an effect)

Sample Problem

• Arrange the following in order of increasing electron affinity.

• Ba, Sn, C, Pd, Fe