CHEM 100 Chapter 5: Quantum Theory of the Atom PDF

CHEM 100 Chapter 5: Quantum Theory of the Atom Dr. Doris HOMSI EL MURR Quantum Numbers and Atomic Orbitals According to quantum mechanics, each electron in an atom is described by four different quantum numbers, three of which (n, l, and ml) specify the wave function that g...

CHEM 100 Chapter 5: Quantum Theory of the Atom Dr. Doris HOMSI EL MURR Quantum Numbers and Atomic Orbitals According to quantum mechanics, each electron in an atom is described by four different quantum numbers, three of which (n, l, and ml) specify the wave function that gives the probability of finding the electron at various points in space. A wave function for an electron in an atom is called an atomic orbital. A fourth quantum number (ms) refers to a magnetic property of electrons called spin. We first look at quantum numbers, then at atomic orbitals. Chapter 5 2 Quantum Numbers and Atomic Orbitals Quantum Numbers The principle quantum number (n) The angular momentum quantum number (l) The magnetic quantum number (ml) The spin quantum number (ms) Chapter 5 3 Quantum Numbers The principal quantum number (n) ▪ The principal quantum number (n) has integral values: 1, 2, 3,.. ▪ higher values mean orbital has higher energy ▪ higher values mean orbital has farther average distance from the nucleus Chapter 5 4 Quantum Numbers and Atomic Orbitals The angular momentum quantum number (l) The angular momentum quantum number (l) has integral values from 0 to n - 1 for each value of n (0 ≤ l ≤ n-1). Within each shell of quantum number n, there are n different kinds of orbitals (subshells), each with a distinctive shape. This quantum number is related to the shape of atomic orbitals. For example, if an electron has a principal quantum number of n= 3, the possible values for l are 0, 1, and 2. Thus, within the 3rd shell n = 3, there are three kinds of orbitals, each having a different shape for the region where the electron is most likely to be found. Chapter 5 5 Quantum Numbers and Atomic Orbitals The angular momentum quantum number (l) Although the energy of an orbital is principally determined by the n quantum number, the energy also depends somewhat on the l quantum number : For a given n, the energy of an orbital increases with l. To denote a subshell within a particular shell, we write the value of the n quantum number for the shell, followed by the letter designation for the subshell. For example, 2p denotes a subshell with quantum numbers: n = 2 and l =1. Chapter 5 6 Quantum Numbers and Atomic Orbitals The magnetic quantum number (ml) The magnetic quantum number (ml) has integral values between l and -l , including zero (-l ≤ ml ≤ l). It gives the number of orbitals l=0 ml = 0 (1 orbital) l =1 ml = -1 ; 0 ; 1 (3 orbitals) l=2 ml = -2 ; -1 ; 0 ; 1 ; 2 (5 orbitals) There are 2l+1 integral values of ml Chapter 5 7 Quantum Numbers and Atomic Orbitals Chapter 5 8 Quantum Numbers and Atomic Orbitals The electron spin quantum number (ms) Electrons act like tiny magnets. They are spinning around their own axes. ms=1/2 or -1/2 Chapter 5 9 Quantum Numbers and Atomic Orbitals Each subshell contains one or more orbitals: s = 1 orbital p = 3 orbitals d = 5 orbitals f = 7 orbitals Each type of sublevel has a different shape and energy Chapter 5 10 Quantum Numbers and Atomic Orbitals Atomic Orbital Shapes The relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen Chapter 5 11 Quantum Numbers and Atomic Orbitals Atomic Orbital Shapes The three 2p orbitals: (a) 2px, (b) 2pz, (c) 2py There are three p orbitals in each p subshell. All p orbitals have the same basic shape but differ in their orientations in space. Chapter 5 12 Quantum Numbers and Atomic Orbitals Atomic Orbital Shapes The shapes and labels of the five 3d orbitals Chapter 5 13 Quantum Numbers and Atomic Orbitals Atomic Orbital Shapes The shapes and labels of the seven 4f orbitals Chapter 5 14 Exercises Chapter 5 15 Exercises Chapter 5 16 Exercises Chapter 5 17 Exercises Chapter 5 18 End of Chapter 5 Chapter 5 19