Chapter 5: Periodicity and Atomic Structure 4/27/2017 Copyright © 2008 Pearson Prentice Hall, Inc.

Light and the Electromagnetic Spectrum Chapter 5: Periodicity and Atomic Structure 4/27/2017 Light and the Electromagnetic Spectrum Electromagnetic energy (“light”) is characterized by wavelength, frequency, and amplitude. Copyright © 2008 Pearson Prentice Hall, Inc.

Light and the Electromagnetic Spectrum Chapter 5: Periodicity and Atomic Structure 4/27/2017 Light and the Electromagnetic Spectrum l n Wavelength and frequency are inversely proportional to each other. Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Light and the Electromagnetic Spectrum Chapter 5: Periodicity and Atomic Structure 4/27/2017 Light and the Electromagnetic Spectrum Wavelength x Frequency = Speed l n c x = s 1 s m m c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light. s m c = 3.00 x 108 Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 5: Periodicity and Atomic Structure 4/27/2017 Examples 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? You could compare this numerical value to the visible spectrum to show the students that it matches, color-wise. Copyright © 2008 Pearson Prentice Hall, Inc.

– Particlelike Properties of Electromagnetic Radiation: The Planck Equation FIGURE 5.6 Atomic line spectra.

The energy level of Hydrogen

Particlelike Properties of Electromagnetic Energy Chapter 5: Periodicity and Atomic Structure 4/27/2017 Particlelike Properties of Electromagnetic 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. The book uses a nice analogy of the effect of throwing a thousand ping-pong balls at a window versus 1 baseball. Copyright © 2008 Pearson Prentice Hall, Inc.

Particlelike Properties of Electromagnetic Energy Chapter 5: Periodicity and Atomic Structure 4/27/2017 Particlelike Properties of Electromagnetic Energy The book uses a nice analogy of the effect of throwing a thousand ping-pong balls at a window versus 1 baseball. Copyright © 2008 Pearson Prentice Hall, Inc.

Particlelike Properties of Electromagnetic Energy Chapter 5: Periodicity and Atomic Structure 4/27/2017 Particlelike Properties of Electromagnetic Energy Einstein explained the effect by assuming that a beam of light behaves as if it were a stream of particles called photons. E = hn ν E Electromagnetic energy (light) is quantized. Energy and frequency are directly proportional to each other. h (Planck’s constant) = 6.626 x 10-34 J s Copyright © 2008 Pearson Prentice Hall, Inc.

Emission of Energy by Atom How does atom emit light? Atoms absorbs energy Atoms become excited Release energy Higher-energy photon –>shorter wavelength Lower-energy photon -> longer wavelength

Examples What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108 Hz? What is the energy (in kJ/mol) of photons of an X-ray with λ = 3.44 x 10-9 m?

Particlelike Properties of Electromagnetic Energy Chapter 5: Periodicity and Atomic Structure 4/27/2017 Particlelike Properties of Electromagnetic 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. This is often called the “planetary model.” A major problem which had to be overcome was that bodies in orbit constantly radiate energy in classical mechanics. Think about what eventually happens to satellites as they orbit the Earth. Copyright © 2008 Pearson Prentice Hall, Inc.

Wavelike Properties of Matter Chapter 5: Periodicity and Atomic Structure Wavelike Properties of Matter 4/27/2017 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. mv h l = 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. Copyright © 2008 Pearson Prentice Hall, Inc.

Examples What is the de Broglie wavelength (in meters) of a small car with a mass of 11500 kg traveling at a speed of 55.0 mi/h (24.6 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 Uncertainty Principle Chapter 5: Periodicity and Atomic Structure 4/27/2017 Quantum Mechanics and the Heisenberg Uncertainty 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. What would be needed to “see” an electron? Light would have to interact with the electron. But this interaction would affect the electron and thus changes it. Copyright © 2008 Pearson Prentice Hall, Inc.

Quantum Mechanics and the Heisenberg Uncertainty 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 small ii. Δ x (position of the electron) is large 4. If the exact position of the electron is known i. Δmv is large ii. Δ x (position of the electron) is small

Wave Functions and Quantum Numbers Chapter 5: Periodicity and Atomic Structure 4/27/2017 Wave Functions and Quantum Numbers Probability of finding electron in a region of space (Y 2) Wave equation Wave function or orbital (Y) solve A wave function is characterized by three parameters called quantum numbers, n, l, ml. Since we can’t ever be certain of the electron’s position, we work with probabilities. Copyright © 2008 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chapter 5: Periodicity and Atomic Structure 4/27/2017 Wave Functions and Quantum Numbers 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 Copyright © 2008 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chapter 5: Periodicity and Atomic Structure 4/27/2017 Wave Functions and Quantum Numbers Angular-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) After f, the series goes alphabetically (g, h, etc.). Copyright © 2008 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chapter 5: Periodicity and Atomic Structure 4/27/2017 Wave Functions and Quantum Numbers Magnetic 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. Copyright © 2008 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chemistry: McMurry and Fay, 6th Edition Chapter 5: Periodicity and the Electronic Structure of Atoms 4/27/2017 11:23:37 AM Wave Functions and Quantum Numbers Copyright © 2011 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chemistry: McMurry and Fay, 6th Edition Chapter 5: Periodicity and the Electronic Structure of Atoms 4/27/2017 11:23:37 AM Wave Functions and Quantum Numbers Copyright © 2011 Pearson Prentice Hall, Inc.

Wave Functions and Quantum Numbers Chapter 5: Periodicity and Atomic Structure 4/27/2017 Wave Functions and Quantum Numbers 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: n = 2, l = 1, ml = 1 b) n = 4, l = 3, ml =-2 Give the possible combinations of quantum numbers for the following orbitals: A 3s orbital b) A 4d orbital Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 5: Periodicity and Atomic Structure 4/27/2017 The Shapes of Orbitals Node: A surface of zero probability for finding the electron. s orbitals are spherical and penetrate closer to the nucleus. Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 5: Periodicity and Atomic Structure 4/27/2017 The Shapes of Orbitals p orbitals are dumbbell-shaped with a nodal plane running through the nucleus. Introductory Physical Chemistry courses often explore the mathematical relationships which define the regions of space (or shape). Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 5: Periodicity and Atomic Structure 4/27/2017 Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Spin and the Pauli Exclusion Principle Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Spin and the Pauli Exclusion Principle Electrons have spin which gives rise to a tiny magnetic field and to a spin quantum number (ms). Another way to think about it is that 2 electrons in an orbital must be spin-paired. Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers. Copyright © 2008 Pearson Prentice Hall, Inc.

Orbital Energy Levels in Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Orbital Energy Levels in Multielectron Atoms Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Effective Nuclear Charge (Zeff): The nuclear charge actually felt by an electron. Zeff = Zactual - Electron shielding Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Electron Configuration: A description of which orbitals are occupied by electrons. Degenerate Orbitals: Orbitals that have the same energy level. For example, the three p orbitals in a given subshell. Ground-State Electron Configuration: The lowest-energy configuration. Aufbau Principle (“building up”): A guide for determining the filling order of orbitals. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Rules of the aufbau principle: Lower-energy orbitals fill before higher-energy orbitals. An orbital can only hold two electrons, which must have opposite spins (Pauli exclusion principle). 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. Electrons repel each other. Electrons in different orbitals (and thus different spatial regions) will experience fewer repulsive forces than electrons placed into the same orbital. Copyright © 2008 Pearson Prentice Hall, Inc.

Chapter 5: Periodicity and Atomic Structure 4/27/2017 Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Electron Configuration H: 1s1 1 electron s orbital (l = 0) n = 1 Electron configurations show the distribution of the electrons between the subshells. Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Electron Configuration H: 1s1 He: 1s2 2 electrons s orbital (l = 0) n = 1 An s subshell can hold 2 electrons since there is only 1 orbital. Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations of Multielectron Atoms Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations of Multielectron Atoms Electron Configuration H: 1s1 1s2 He: Lowest energy to highest energy Li: Fill up the subshell before moving to the next one. You can refer to the orbital filling diagram but it’s easier to use the periodic table as described in section 5.14 of the text. 1s2 2s1 1 electrons s orbital (l = 0) n = 2 Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations and the Periodic Table Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations and the Periodic Table Valence Shell: Outermost shell. Li: 2s1 Na: 3s1 For main-group atoms, the column number (using the US standard numbering system) is equivalent to the number of valence electrons. Cl: 3s2 3p5 Br: 4s2 4p5 Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations and the Periodic Table Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations and the Periodic Table Give expected ground-state electron configurations 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) Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations and Periodic Properties: Atomic Radii Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations and Periodic Properties: Atomic Radii column radius radius row Atomic radii increases down a column because successively larger valence-shell orbitals are occupied. Atomic radii decreases from left-to-right because the effective nuclear charge increases. Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Electron Configurations and Periodic Properties: Atomic Radii Chapter 5: Periodicity and Atomic Structure 4/27/2017 Electron Configurations and Periodic Properties: Atomic Radii Copyright © 2008 Pearson Prentice Hall, Inc. Copyright © 2008 Pearson Prentice Hall, Inc.

Examples Which atom in each of the following pairs would you expect to be larger? Mg or Ba W or Au