Chapter 5Periodicity and Atomic Structure

Light and the Electromagnetic Light and the Electromagnetic SpectrumSpectrum

Electromagnetic energy (“light”) is characterized by wavelength, frequency, and amplitude.

Light and the Electromagnetic SpectrumLight and the Electromagnetic Spectrum

Light and the Electromagnetic SpectrumLight and the Electromagnetic Spectrum

Light and the Electromagnetic SpectrumLight and the Electromagnetic SpectrumWavelength x Frequency = Speed

=

m

s

m

s

1

cx

c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light.

c = 3.00 x 108

s

m

ExamplesExamples◦The light blue glow given off by

mercury streetlamps has a frequency of 6.88 x 1014 s-1 (or, Hz). What is the wavelength in nanometers?

Chapter 5/7 © 2012 Pearson Education, Inc.

Electromagnetic Energy and Atomic Electromagnetic Energy and Atomic Line SpectraLine Spectra

Chapter 5/8 © 2012 Pearson Education, Inc.

Electromagnetic Energy and Atomic Electromagnetic Energy and Atomic Line SpectraLine Spectra

Line Spectrum: A series of discrete lines on an otherwise dark background as a result of light emitted by an excited atom

Electromagnetic Radiation and Atomic Electromagnetic Radiation and Atomic SpectraSpectra

Individual atoms give off light when heated or otherwise excited energetically

◦ Provides clue to atomic makeup

◦ Consists of only few λ◦ Line spectrum – series of

discrete lines ( or wavelengths) separated by blank areas

E.g. Lyman series in the ultraviolet region

Chapter 5/10 © 2012 Pearson Education, Inc.

Electromagnetic Energy and Atomic Electromagnetic Energy and Atomic Line SpectraLine Spectra

Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen.

1 = R

n2

1

m2

1-

Johann Balmer in 1885 discovered a mathematical relationship for the four visible lines in the atomic line spectra for hydrogen.

1 = R

n2

1

22

1-

R (Rydberg Constant) = 1.097 x 10-2 nm-1

The energy level of HydrogenThe energy level of Hydrogen

Particlelike Properties of Particlelike Properties of Electromagnetic EnergyElectromagnetic Energy

Photoelectric Effect: Irradiation of clean metal surface with light causes electrons to be ejected from the metal. Furthermore, the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal.

ExamplesExamples

Solar energy, which is produced by photovoltaic cells.These are made of semi-conducting material which produce electricity when exposed to sunlight

it works on the basic principle of light striking the cathode which causes the emmision of electrons, which in turn produces a current.

Particlelike Properties of Particlelike Properties of Electromagnetic EnergyElectromagnetic Energy

Particlelike Properties of Particlelike Properties of Electromagnetic EnergyElectromagnetic Energy

Ephoton = hνE

Electromagnetic energy (light) is quantized.

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

Einstein explained the effect by assuming that a beam of light behaves as if it were a stream of particles called photons.

* 1mol of anything = 6.02 x 1023

Emission of Energy by AtomEmission of Energy by AtomHow does atom emit light?

◦Atoms absorbs energy ◦Atoms become excited◦Release energy ◦Higher-energy photon –>shorter

wavelength◦Lower-energy photon -> longer

wavelength

ExamplesExamplesWhat is the energy (in kJ/mol) of

photons of radar waves with ν = 3.35 x 108 Hz?

Calculate the wavelength of light that has energy 1.32 x 10-23 J/photon

Calculate the energy per photon of light with wavelength 650 nm

Particlelike Properties of Particlelike Properties of Electromagnetic EnergyElectromagnetic Energy Niels Bohr proposed in 1914 a model of the hydrogen

atom as a nucleus with an electron circling around it. In this model, the energy levels of the orbits are

quantized so that only certain specific orbits corresponding to certain specific energies for the electron are available.

Niels Bohr ModelNiels Bohr Model

In each case the wavelength of the emitted or absorbed light is exactly such that the photon carries the energy difference between the two orbits

Excitation by absorption of light and de-excitation by emission of light

Wavelike Properties of MatterWavelike Properties of Matter

The de Broglie equation allows the calculation of a “wavelength” of an electron or of any particle or object of mass m and velocity v.

mvh =

Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light.

In other words, perhaps matter is wavelike as well as particlelike.

ExamplesExamples Calculate the de Broglie wavelength of the “particle”

in the following case◦ A 25.0 bullet traveling at 612 m/s

What velocity would an electron (mass = 9.11 x 10-

31kg) need for its de Broglie wavelength to be that of red light (750 nm)?

Quantum Mechanics and the Heisenberg Quantum Mechanics and the Heisenberg Uncertainty PrincipleUncertainty Principle

In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron.

In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.

Quantum Mechanics and the Heisenberg Quantum Mechanics and the Heisenberg Uncertainty PrincipleUncertainty Principle

Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision

1. (Δx) (Δmv) > h 4π

2. Cannot know both the position and the momentum of an electron with a high degree of certainty

3. If the momentum is known with a high degree of certainty

i. Δmv is smallii. Δ x (position of the electron) is large

4. If the exact position of the electron is knowni. Δmv is largeii. Δ x (position of the electron) is small

Wave Functions and Quantum NumbersWave Functions and Quantum Numbers

Probability of findingelectron in a regionof space (2)

Waveequation

Wave functionor orbital ()

solve

A wave function is characterized by three parameters called quantum numbers, n, l, ml.

Wave Functions and Quantum Wave Functions and Quantum NumbersNumbers

Principal Quantum Number (n)• Describes the size and

energy level of the orbital

• Commonly called shell• Positive integer (n = 1,

2, 3, 4, …)• As the value of n

increases:• The energy increases• The average distance

of the e- from the nucleus increases

Wave Functions and Quantum NumbersWave Functions and Quantum NumbersAngular-Momentum Quantum Number (l)

• Defines the three-dimensional shape of the orbital• Commonly called subshell• There are n different shapes for orbitals

• If n = 1 then l = 0• If n = 2 then l = 0 or 1• If n = 3 then l = 0, 1, or 2• etc.

• Commonly referred to by letter (subshell notation)• l = 0 s (sharp)• l = 1 p (principal)• l = 2 d (diffuse)• l = 3 f (fundamental)• etc.

Wave Functions and Quantum NumbersWave Functions and Quantum NumbersMagnetic Quantum Number (ml )• Defines the spatial orientation of the orbital• There are 2l + 1 values of ml and they can

have any integral value from -l to +l• If l = 0 then ml = 0• If l = 1 then ml = -1, 0, or 1• If l = 2 then ml = -2, -1, 0, 1, or 2• etc.

Wave Functions and Quantum NumbersWave Functions and Quantum Numbers

Wave Functions and Quantum Wave Functions and Quantum NumbersNumbers

Identify the possible values for each of the three quantum numbers for a 4p orbital.

Give orbital notations for electrons in orbitals with the following quantum numbers:

a) n = 2, l = 1, ml = 1 b) n = 4, l = 0, ml =0

Give the possible combinations of quantum numbers for the following orbitals: A 3s orbital b) A 4f orbital

The Shapes of OrbitalsThe Shapes of Orbitals

Node: A surface of zero probability for finding the electron.

The Shapes of OrbitalsThe Shapes of Orbitals

Electron Spin and the Pauli Exclusion Electron Spin and the Pauli Exclusion PrinciplePrinciple

Electrons have spin which gives rise to a tiny magnetic field and to a spin quantum number (ms).

Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers.

Orbital Energy Levels in Multielectron Orbital Energy Levels in Multielectron AtomsAtoms

Electron Configurations of Multielectron Electron Configurations of Multielectron AtomsAtomsEffective Nuclear Charge (Zeff): The nuclear charge actually felt by an electron.

Zeff = Zactual - Electron shielding

Electron Configurations of Multielectron Electron Configurations of Multielectron AtomsAtoms

Electron Configuration: A description of which orbitals are occupied by electrons.

1s2 2s2 2p6 ….

Degenerate Orbitals: Orbitals that have the same energy level. For example, the three p orbitals in a given subshell.

2px 2py 2pz

Ground-State Electron Configuration: The lowest-energy configuration.

1s2 2s2 2p6 ….

Orbital Filling Diagram: using arrow(s) to represent occupied in an orbital

s px py pz

Electron Configurations of Multielectron Electron Configurations of Multielectron AtomsAtoms

Aufbau Principle (“building up”): A guide for determining the filling order of orbitals.

Rules of the aufbau principle:1. Lower-energy orbitals fill before higher-energy

orbitals.2. An orbital can only hold two electrons, which must

have opposite spins (Pauli exclusion principle).3. If two or more degenerate orbitals are available,

follow Hund’s rule.Hund’s Rule: If two or more orbitals with the same energy are available, one electron goes into each until all are half-full. The electrons in the half-filled orbitals all have the same spin.

Electron Configurations of Multielectron Electron Configurations of Multielectron AtomsAtoms

n = 1

s orbital (l = 0)

1 electron H: 1s1

ElectronConfiguration

1s2

n = 1

s orbital (l = 0)

2 electronsHe:

Electron Configurations and the Periodic Electron Configurations and the Periodic TableTable

Valence Shell: Outermost shell or the highest energy .

Br: 4s2 4p5

Cl: 3s2 3p5

Na: 3s1

Li: 2s1

Electron Configurations and the Electron Configurations and the Periodic TablePeriodic Table

Give expected ground-state electron configurations (or the full electron configuration) for the following atoms, draw – orbital filling diagrams and determine the valence shell◦ O (Z = 8)◦ Ti (Z = 22)◦ Sr (Z = 38)◦ Sn (Z = 50)

Electron Configurations and Periodic Electron Configurations and Periodic Properties: Atomic RadiiProperties: Atomic Radii

radiusrow

radiuscolumn

Electron Configurations and Periodic Electron Configurations and Periodic Properties: Atomic RadiiProperties: Atomic Radii

ExamplesExamples

Arrange the elements P, S and O in order of increasing atomic radius