chap06_bch1049_07Electronic Structure of Atom

chap06_bch1049_07Electronic Structure of Atom - Electronic...

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1 Electronic Structure of Atoms Electronic Structure of Atoms (Chapter 6) What’s Ahead: 1. Atomic Orbitals and Quantum Mechanics Atomic Orbitals and Quantum Mechanics 2. 2. Representations of Atomic Orbitals Representations of Atomic Orbitals 3. Electron Configurations and Electron Configurations and Hund ’s Rule Rule 4. Relationship to Periodic Table Relationship to Periodic Table Electronic Structure of Atoms Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated: quantum mechanics . • The wave equation is designated with a lower case Greek psi ( ψ ). • The square of the wave equation, 2 , gives a probability density map of where an electron is statistically likely to be found at any given time (shown for H).
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2 Electronic Structure of Atoms Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals , and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers : n , l and m l . Electronic Structure of Atoms Relationship between n , l and m l Orbitals with the same value of n form a shell . Different orbital types within a shell are subshells . 1. An n shell consists of n subshells. 2. Number of m l equals 2 l + 1. 3. Total number of orbitals in shell is n 2 (1, 4, 9, 16).
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3 Electronic Structure of Atoms 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. •A s n increases, the orbital becomes larger. The electron spends more time farther from the nucleus, has higher energy and is less tightly bound. Electronic Structure of Atoms Azimuthal Quantum Number, l • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n 1 for each value of n . • Use letters s, p, d, and f to identify different values of l and, therefore, the shapes and types of orbitals . f d p s Type of orbital 3 2 1 0 Value of l
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4 Electronic Structure of Atoms Magnetic Quantum Number, m l • Describes the three-dimensional orientation of the orbital. • Values are integers ranging from l to l (total: 2 l + 1): l m l l • Therefore, for any given energy level, there are one s orbital, three p orbitals, five d orbitals, seven f orbitals, etc. [for l = 0, 1, 2, 3 respectively] SAMPLE EXERCISE 6.6 Subshells of the Hydrogen Atom (a) Without referring to the table, predict the number of subshells in the fourth shell, that is, for n = 4. (b) Give the label for each of these subshells. (c) How many orbitals are in each of these subshells? Analyze and Plan : We are given the value of the principal quantum number, n .
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chap06_bch1049_07Electronic Structure of Atom - Electronic...

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