1. Chemistry 141 Friday, November 3, 2017 Lecture 25 H Atom Orbitals
Chemistry 11 - Lecture 11
9/30/2009
Chemistry 141
Friday, November 3, 2017
Lecture 25
H Atom Orbitals

2. Matter Waves
Scientists at IBM accidentally observed standing waves from the interference of electrons on a copper surface with defect sites
They then decided to intentionally create electron standing waves by arranging iron atoms in a ring, thereby confining the space the electrons can roam in, and forming standing waves
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3. A very deep question:
Waves do not have a location. If a small particle (i.e. an electron) behaves like a wave, can we specify its location?

4. Heisenberg’s Uncertainty Principle
The Uncertainty Principle (Heisenberg, 1927) states:
There is an inherent uncertainty in our ability to specify an electron’s exact location
there is a fundamental limit to our ability to describe the properties of particles that are very small
Instead of certainty, we must rely on probabilities to tell us the likely location of these small particles

5. When does the uncertainty principle matter?
What is the uncertainty in the position of an electron (mass = 9.11x10-31 kg) moving with a speed of 5x106 m/s? Assume the uncertainty in the speed is 1%.

6. When does the uncertainty principle matter?
What is the uncertainty in the position of a baseball (mass = kg) moving with a speed of 18 m/s? Assume the uncertainty in the speed is 1%.

7. The Founders of Quantum Mechanics on Their Creation
Anyone who is not shocked by quantum theory has not understood it.
-- Neils Bohr
I don’t like it, and I’m sorry I ever had anything to do with it.
-- Erwin Schrödinger
[I] think I can safely say that nobody understands quantum mechanics.
-- Richard Feynman
Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing.
-- Albert Einstein
God does not play dice with the universe
-- Albert Einstein

8. Wave Functions Wave function ()
A mathematical description of the electron accounting for dual wave/particle nature – an ORBITAL
 can have positive or negative values; the sign of  is called the phase
The points at which =0 are called nodes
 has no direct physical interpretation, but the square of the wave function gives us the electron density, or probability of finding the electron at a given location

9. H-atom quantum numbers
For each wavefunction () or orbital there are three quantum numbers that characterize that wavefunction
The principal quantum number, n quantization of energy
can take on integer values (n = 1, 2, 3, …)
determines the energy associated with the wavefunction
determines the size of the orbital (smaller n means smaller size)
determines the total number of nodes (# total nodes = n – 1)

10. H-atom quantum numbers
The angular momentum quantum number, l
quantization of angular momentum
can have integer values from 0 to n – 1
n = 4
determines the number of angular nodes (# angular nodes = l) and therefore shape
l = 0: spherically symmetric
l = 1: 1 planar node dumb-bell orbital
higher l: 2 or more planar nodes more complex shapes
From rules for n and l, # radial nodes = n – l - 1
each value of l is assigned a letter:
for H atoms, energy does not depend on l
l = 0, 1, 2, 3

11. H-atom quantum numbers
The magnetic quantum number, ml
quantization of the z-component of the angular momentum
can have values from –l to +l
l = 2
Therefore, for each l, there are 2l + 1 values of ml
1 s, 3 p’s, 5 d’s, etc.
determines the orientation of an orbital
ml = 0: orbital is oriented along the z axis
energy does not depend on ml
ml = -2, -1, 0, +1, +2

12. H-atom quantum numbers
Each set of three quantum numbers (n, l, ml) defines a unique wavefunction or orbital
n = 1, 2, 3, …
l = 0, 1, 2, …, n – 1
ml = -l, … -1, 0, 1, … +l
nodes n l ml
name
energy
total
angular
radial 1 1s
E1=-2.18×10-18 J 2 2s
E2=¼ E1
2pz +1 -1 3 3s
E3=1/9 E1
0, ±1
3px,y,z E3
0, ±1, ±2 3d
n2 = 1
n2 = 4
2px, 2py
n2 = 9

13. Hydrogen atom energy levels
The energy is determined only by the principle quantum number, n
For each energy (each n), there are n2 wave functions (orbitals)
excited states
all orbitals with the same n have the same energy
ground state

14. What is an orbital? http://www.falstad.com/qmatom/

15. s Orbitals (l = 0)

16. s Orbitals (l = 0) # nodes = n -1 # “bumps” = n
most probable distance from nucleus increases 

17. p Orbitals (l = 1) two lobes divided by a planar node
n = 3 and higher p orbitals also have radial nodes

18. d Orbitals (l = 2)
four lobes divided by 2 planar nodes

19. Energies of Orbitals
Hydrogen Atom
Multi-electron Atom

20. Spin Quantum Number, ms
An electron has a “spin” – either “up” or “down”, which describes its magnetic field
Indicated by the spin quantum number, ms, which has only two allowed values, +½ and –½.
Pauli Exclusion Principle
No two electrons in the same atom can have the same 4 quantum numbers.

21. Electron Configurations
1s2 2s1

22. Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”