Lecture 7
Monday, 20 January, 2014 11:01 AM
Today's Topics: Announcements: Homework:
Experiment 1 report (21 Jan)
Quiz 1 (21 Jan)
Practice questions (21 Jan)
Lecture Topic:
Practice problem: which of the following combinations of quantum numbers does not
describe an allowed orbital?
Option n l m(l)
1 1 1 0
2 3 0 0
3 2 1 -1
4 4 3 -2
5 4 2 0
• The answer is option 1 because the azimuthal number, l, must be at least 1 less than
the principal quantum number, n.
Orbital nodes
• A node is a region in space with zero probability of finding an electron
○ It is the result of destructive interference (in a wave)
• There are two types of nodes:
○ Angular (a)
○ Planar (b)
• To determine radial nodes, you use the equation
○ For 3s, s has an l value of 0, so the number of radial nodes would be 3 - 0 - 1
= 2 radial nodes
n = 3
l = 0
○ For 3p, it would be 3 - 1 - 1 = 1 radial nodes
• They can be graphically represented by plotting the electron density (probability of
finding an electron) on the y axis vs.orla on the x axis
○ When y = 0 there is a node
• In p orbitals, the term refers to the nodal plane (the plane where there are no
electrons to be found)
○ Ex: p xas nodal plane yz
• The d orbitals have two nodal planes
○ Ex: d xys nodal planes zx and zy
Orbital phases
• Wave functions (and therefore orbitals) have a phase:
• Orbitals change phase when they cross a node
○ Represent with a colour or sign change
The hierarchy of quantum numbers for atomic orbitals
Name, symbol (property) Allowed values Quantum numbers
Principal, n (size, energy) Positive integer (1, 2, 3…) 1
Angular momentum,l (shape) 0 to n-1 0
Magnetic, m lorientation) -l, …, 0, …, +l 0
Spin, ms -1/2, +1/2

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