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PowerPoint to accompany Chapter 5 Electronic Structure of Atoms Part-2

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Heisenberg Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely its position is known. In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

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Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics. The Energy, Momentum and Position of each electron around an atom can be expressed as the solution to a wave equation.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital is a probability function which describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Quantum Mechanics The wave equation is designated with a lower case Greek psi ( ). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. 2 = ▼H 2 Figure 5.14

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Principal Quantum Number, n The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 0. n determines the size of an atom

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Azimuthal Quantum Number, l This azimuthal quantum number defines the shape or direction of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Azimuthal Quantum Number, l Value of l0123 Type of orbitalspdf

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Magnetic Quantum Number, m l Describes the three-dimensional orientation of the orbital. Values are integers ranging from -l to l: −l ≤ m l ≤ l. Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

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Magnetic Quantum Number, m l Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells. Table 5.2

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Electron Probability Functions

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

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s Orbitals Value of l = 0 Spherical in shape Radius of sphere increases with increasing value of n Figure 5.17

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. Figure 5.16 Figure 5.20

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia p Orbitals Value of l = 1 Have two lobes with a node between them Figure 5.18

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

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d Orbitals Value of l is 2 Four of the five orbitals have 4 lobes; the other resembles a longer p orbital with a doughnut around the centre Figure 5.21

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy, i.e. they are degenerate.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Energies of Orbitals As the number of electrons increases, so does the repulsion between them. Therefore, in many- electron atoms, orbitals on the same energy level are no longer degenerate. Figure 5.22

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Spin Quantum Number, m s In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy. This led to a fourth quantum number, the spin quantum number, m s. The spin quantum number has only 2 allowed values: +½ and −½. Figure 5.23

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Spin Quantum Number, m s

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Electron Configurations Distribution of all electrons in an atom. Consist of: Number denoting the energy level. Letter denoting the type of orbital. Superscript denoting the number of electrons in those orbitals.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Orbital Diagrams Each box represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron: +½ or -½ ↓

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Periodic Table Atoms fill orbitals in increasing order of energy. Different blocks on the periodic table correspond to different types of orbitals. Figure 5.25

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

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Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Some Anomalies For instance, the electron configuration for Iron is: [Ar] 4s 1 3d 5 rather than the expected: [Ar] 4s 2 3d 4. This occurs because the 4s and 3d orbitals are very close in energy. Hund’s rule for degenerate (half filled) orbitals is to half fill each box.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Some Anomalies For instance, the electron configuration for Copper is: [Ar] 4s 1 3d 10 rather than the expected: [Ar] 4s 2 3d 9. This occurs because the 4s and 3d orbitals are very close in energy. Symmetry and similar energies for electrons fills the 3d-block first

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Some Anomalies For instance, the electron configuration for Iron is: [Ar] 4s 1 3d 5 rather than the expected: [Ar] 4s 2 3d 4. This occurs because the 4s and 3d orbitals are very close in energy. These types of anomalies occur in f- block atoms, as well.

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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia End of Chapter 5 part 2

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