1. Quantum Mechanics
College Chemistry

2. Heisenberg’s Uncertainty Principle
The position and the momentum of a moving object cannot be simultaneously known exactly – really just for small particles
Our wavelength is too small
Try it…. l = h/mu

3. 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

4. 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

5. 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

6. 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)

7. 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

8. 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

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

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

11. “D” SUBSHELL
Holds 10 electrons
shaped like a flower

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

13. 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

14. 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

15. Orbitals and Energy

16. 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

17. 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 = 9

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