Chapter 6Chapter 6

Electronic Structure of AtomsElectronic Structure of Atoms

• Our goal:• Understand why some substances behave as they do.

• For example: Why are K and Na reactive metals? Why do H and Cl combine to make HCl? Why are some compounds molecular rather than ionic?

• Atom interact through their outer parts, their electrons.• The arrangement of electrons in atoms are referred to as

their electronic structure.• Electron structure relates to:

• Number of electrons an atom possess.

• Where they are located.

• What energies they possess.

Electronic StructureElectronic Structure

• Study of light emitted or absorbed by substances has lead to the understanding of the electronic structure of atoms.

• Characteristics of light: • All waves have a characteristic wavelength, , and

amplitude, A.

• The frequency, , of a wave is the number of cycles which pass a point in one second.

• The speed of a wave, v, is given by its frequency multiplied by its wavelength:

• For light, speed = c.

The Wave Nature of LightThe Wave Nature of Light

c

Identifying Identifying and and

• Modern atomic theory arose out of studies of the interaction of radiation with matter.

• Electromagnetic radiation moves through a vacuum with a speed of 2.99792458 10-8 m/s.

• Electromagnetic waves have characteristic wavelengths and frequencies.

• Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).

Electromagnetic RadiationElectromagnetic Radiation

The Electromagnetic SpectrumThe Electromagnetic Spectrum

• The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?

Class Guided Practice ProblemClass Guided Practice Problem

cClass Practice ProblemClass Practice Problem

• A laser used to weld detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

• Planck: energy can only be absorbed or released from atoms in certain amounts “chunks” called quanta.

• The relationship between energy and frequency is

where h is Planck’s constant (6.626 10-34 J.s).• To understand quantization consider walking up a ramp

versus walking up stairs:• For the ramp, there is a continuous change in height whereas up

stairs there is a quantized change in height.

Quantized Energy and PhotonsQuantized Energy and Photons

hE

• Planck’s theory revolutionized experimental observations.

• Einstein:• Used planck’s theory to explain the photoelectric effect.

• Assumed that light traveled in energy packets called photons.

• The energy of one photon:

The Photoelectric EffectThe Photoelectric Effect

hE

• Calculate the energy of a photon of yellow light whose wavelength is 589 nm.

Class Guided Practice ProblemClass Guided Practice Problem

hE

Class Practice ProblemClass Practice Problem• (a)Calculate the smallest increment of energy (a

quantum) that can be emitted or absorbed at a wavelength of 803 nm. (b) Calculate the energy of a photon of frequency 7.9 x 1014 s-1. (c) What frequency of radiation has photons of energy 1.88 x 10-18 J? Now calculate the wavelength.

Line Spectra• Radiation composed of only one wavelength is called

monochromatic.• Most common radiation sources that produce radiation

containing many different wavelengths components, a spectrum.

• This rainbow of colors, containing light of all wavelengths, is called a continuous spectrum.

• Note that there are no dark spots on the continuous spectrum that would correspond to different lines.

Line Spectra and the Bohr ModelLine Spectra and the Bohr Model

Specific Wavelength “Line Spectra”Specific Wavelength “Line Spectra”

When gases are placed under reduced pressure in a tube and a high voltage is applied, radiation at different wavelengths (colors) will be emitted.

• Balmer: discovered that the lines in the visible line spectrum of hydrogen fit a simple equation.

• Later Rydberg generalized Balmer’s equation to:

where RH is the Rydberg constant (1.096776 107 m-1), h is Planck’s constant (6.626 10-34 J·s), n1 and n2 are integers (n2 > n1).

Line SpectraLine Spectra

22

21

111

nnh

RH

• Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun.

• However, a charged particle moving in a circular path should lose energy.

• This means that the atom should be unstable according to Rutherford’s theory.

• Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states. These were called orbits.

Bohr ModelBohr Model

• Colors from excited gases arise because electrons move between energy states in the atom.

Line Spectra (Colors)Line Spectra (Colors)

• Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.

• After lots of math, Bohr showed that

where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).

Line Spectra (Energy)Line Spectra (Energy)

218 1

J1018.2n

E

• Can only explain the line spectrum of hydrogen adequately.

• Electrons are not completely described as small particles.

Limitations of the Bohr Model

• Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature.

• Using Einstein’s and Planck’s equations, de Broglie showed:

• The momentum, mv, is a particle property, whereas is a wave property.

• de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

The Wave Behavior of MatterThe Wave Behavior of Matter

m

h

The Uncertainty Principle• Heisenberg’s Uncertainty Principle: on the mass scale

of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.

• For electrons: we cannot determine their momentum and position simultaneously.

• If x is the uncertainty in position and mv is the uncertainty in momentum, then

The Wave Behavior of MatterThe Wave Behavior of Matter

4

hmx

• Schrödinger proposed an equation that contains both wave and particle terms.

• Solving the equation leads to wave functions. • The wave function gives the shape of the electronic

orbital.• The square of the wave function, gives the probability of

finding the electron,• that is, gives the electron density for the atom.

Quantum Mechanics and Atomic Quantum Mechanics and Atomic OrbitalsOrbitals

Electron Density Distribution Electron Density Distribution

Probability of finding an electron in a hydrogen atom in its ground state.

1. Schrödinger’s equation requires 3 quantum numbers:

2. 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 = 1, 2, 3…)

2. Azimuthal Quantum Number, l. 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. (l = 0, 1, 2…n-1). Defines the shape of the orbitals.

3. Magnetic Quantum Number, ml. 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 in space. (m = -l…0…+1)

The Three Quantum Numbers

Orbitals and Quantum Numbers

Class Guided Practice Problem• (a) For n = 4, what are the possible values of l? (b) For l

= 2. What are the possible values of ml? What are the representative orbital for the value of l in (a)?

• (c) How many possible values for l and ml are there when (d) n = 3; (b) n = 5?

Class Practice Problem

• All s-orbitals are spherical.• As n increases, the s-orbitals get larger.• As n increases, the number of nodes increase.• A node is a region in space where the probability of

finding an electron is zero.• At a node, 2 = 0 • For an s-orbital, the number of nodes is (n - 1).

Representations of Orbitals Representations of Orbitals The s-Orbitals

The s-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.

The p-Orbitals

The p-Orbitals

Electron-distribution of a 2p orbital.

• 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.

The d and f-Orbitals

• Orbitals can be ranked in terms of energy to yield an Aufbau diagram.

• As n increases, note that the spacing between energy levels becomes smaller.

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

Orbitals and Quantum Numbers

Orbitals and Their Energies

• Line spectra of many electron atoms show each line as a closely spaced pair of lines.

• Stern and Gerlach designed an experiment to determine why.

• A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected.

• Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction.

Electron Spin and the Pauli Exclusion Principle

Electron Spin and the Pauli Exclusion Principle

• Since electron spin is quantized, we define ms = spin quantum number = ½.

• Pauli’s Exclusions Principle:: no two electrons can have the same set of 4 quantum numbers.• Therefore, two electrons in the same orbital must have

opposite spins.

Electron Spin and the Pauli Exclusion Principle

• Electron configurations tells us in which orbitals the electrons for an element are located.

• Three rules:• electrons fill orbitals starting with lowest n and moving

upwards;

• no two electrons can fill one orbital with the same spin (Pauli);

• for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule).

Electron Configurations:Electron Configurations: Hund’s Rule

• The periodic table can be used as a guide for electron configurations.

• The period number is the value of n.• Groups 1A and 2A (1 & 2) have the s-orbital filled.• Groups 3A - 8A (13 - 18) have the p-orbital filled.• Groups 3B - 2B (3 - 12) have the d-orbital filled.• The lanthanides and actinides have the f-orbital filled.

Electron Configurations and the Electron Configurations and the Periodic TablePeriodic Table

Class Guided Practice Problem• Write the electron configurations for the following

atoms: (a) Cs and (b) Ni

Class Practice Problem

• Write the electron configurations for the following atoms: (a) Se and (b) Pb

• Neon completes the 2p subshell.• Sodium marks the beginning of a new row.• So, we write the condensed electron configuration for

sodium as

Na: [Ne] 3s1

• [Ne] represents the electron configuration of neon.• Core electrons: electrons in [Noble Gas].• Valence electrons: electrons outside of [Noble Gas].

Condensed Electron Configurations

• After Ar the d orbitals begin to fill.• After the 3d orbitals are full, the 4p orbitals begins to fill.• Transition metals: elements in which the d electrons are

the valence electrons.

Transition Metals

• From Cs onwards the 4f orbitals begin to fill.• Note: La: [Xe]6s25d14f0

• Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

• Elements Th - Lr have the 5f orbitals filled and are called actinides.

• Most actinides are not found in nature.

Lanthanides and Actinides