Quantum Mechanics College Chemistry

Heisenberg’s Uncertainty Principle The position and the momentum of a moving object cannot be simultaneously known exactly – really just for small particles http://www.youtube.com/watch?v=KAZzv8Yh8Ho Our wavelength is too small Try it…. l = h/mu

Quantum Mechanics New “idea” of a model that takes into account the fact: 1. energy of an atom is quantized 2. electrons exhibit wavelike behavior 3. it is impossible to know an electron’s exact position and momentum at the same time

Orbitals We know electrons are more likely to hang out in certain areas more than others – high electron density Atomic orbital – region of high probability for the electron to occur

Orbitals and Energy Principal energy levels (n)– quantum numbers, main levels Values of 1,2,3, etc. NO ZERO! n, relates to the distance from the nucleus The grater n is, the further from the nucleus you are

Orbitals and Energy principal energy levels are divided into sublevels called angular momentum quantum number (l) Tells us the shape of the orbital s (l = 0), p (l = 1), d (l = 2), and f (l = 3) Values of l depend on n Possible values 0  (n -1)

ORBITALS AND ENERGY In addition to n orbitals, each principle energy level is divided into one or more sublevels Sublevels referred to as s, p, d, f s has the lowest energy and f has the greatest energy Energy increases with increasing atomic orbital and sublevel

ORBITALS AND ENERGY Each sublevel (s, p,d, and f) can hold a specified number of electrons s holds 2 p holds 6 d holds 10 f holds 14 Each orbital can hold 2 electrons

“S” ORBITAL Holds only 2 electrons Shaped like a sphere

“P” ORBITAL Each “p” orbital holds 6 electrons Shaped like a dumbbell

“D” SUBSHELL Holds 10 electrons shaped like a flower

“F” ORBITALS Hold 14 electrons very interesting, odd shape

Orbitals and Energy Magnetic quantum number, ml – describes the orientation of the orbital in space Depends on the angular momentum number, for a certain value of l, there are (2l + 1) values Ex: if l = 1, there are 2(1) + 1 = 3 values  -1, 0, -1

Orbitals and Energy Electron spin quantum number (ms) – electrons “spin” on their own axis, each pair of electrons must spin in opposite directions  + ½ and – ½

Orbitals and Energy

Example 7.6 What are the values of n, l, ml, and ms in the 4d subshell? n = 4 l = 2 (d orbitals = 2) ml = -2, -1, 0, 1, or 2 ms = +1/2 and -1/2

Example 7.7 What is the total number of orbitals associated with the principal quantum number n = 3 We need to find the values of l first: l = 0,1, and 2 So one 3s orbital (l = 0, ml = 0) Three 3p orbitals (l = 1, ml = -1, 0, 1) Five 3d orbitals (l = 2, ml = -2, -1, 0, 1, 2) So 1 + 3 + 5 = 9

Can the following exist? (2, 0, 0, +1/2) yes (2, 2, 0, -1/2) No, l cannot be the same as n