Orbital shapes and Energies
Textbook Readings
7.6: The Shape of Atomic Orbitals
Course Lectures
7.6 pdf Video Quantum Mechanical Atom
7.9 pdf Video* Atomic Orbitals
Objectives
1. Describe what is meant by the wavefunction.
2. Distinguish between the probability density
graph and the radial probability graph
and how they're related.
suggests about the probablity of finding an electron in an atom.
4.Interpret the radial probability graph (Ψ2r2 vs radial distance) and what it suggests
about the probablity of finding an electron in an atom.
5. Be able to identify the shapes and quantum numbers of s, p, d and f orbitals
Homework Problems
42. 1 What is the wavefunction and what is
it good for?
42.2 Probability density can be observed at
a concert. Where would you expect to
find the highest density of people in the
audience? Is that the place you'd most
likely expect to find someone wearing a
red cap?
42.3 When squared, the wavefunction for an
electron in an atom yields the probability
density (Figure at right).
Probability density is volume dependant
The rookie chemistry student might look
at the probability density graph and
suggest incorrectly the electron would be
found where in an atom?
in the quantum mechanical atom, the
probability of find an electron in the
nucleus is practically zero since the
nucleus is so small.
The Radial Probability is a graph that
includes the volume factor (figure at
right). Where would the rookie
chemistry student correctly predict the
highest likelyhood of finding an electron.
Draw this graph in your notebook and
indicate your answer.
of the time. What percent of the time would we expect to find the electron outside the orbital?
42.6 Nodes are regions within the atom where it is unlikely for an electron to be found. Nodes exist
within orbitals and are most easily seen in "s" orbitals. Use your textbook and determine
for s orbitals how the number of nodes depends on the n quantum number.
as "s", "p", "d" or "f".
42.8 For each orbital, write quantum number
combinations that could represent the
orbital n, l and ml.
(Multiple correct answers
are possible but they must follow the
quantum number rules!)
By Geek3 - Own work; created with hydrogen-cloud in PythonThis PNG graphic was created with Python., CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=69035277
42.1 The wavefunction is a solution to the Schodinger equations. The wavefunction includes the
particle and wave nature of matter and can be used to, amongst other things, predict the
probability or likelyhood of finding an electron in a specific place within an atom.
42.2 My experience is that the highest density of concert-goers is right up next to the stage. People
tend to get very tightly packed. However, if you're looking for a red hat, it is much more likely
you'll find one if you expand your search to areas away from the stage where most of the people are.
42.3 The rookie chemist would incorrectly pick the place where the curve is highest (i.e. the stage)
which is on the nucleus.
42.4 This graph incorporates density and available space. The electron would most likely be found
at the graph's peak. However, note that the graph predicts the electron can be found in other
locations with lower probability.
42.5 It is 10% likely that an electron will be found outside of the orbital.
42.6 The number of nodes for s orbitals is n - 1
42.7 a. 1s b. 2s c. 2p d. 3s e. 3p f. 3d g. 4s h. 4p i. 4d j. 4f
42.8 Answers may vary but all must follow the rules:
a. n = 1 b. l = 0 c. ml = 0
b. n = 2 b. l = 0 c. ml = 0
c. n = 2 b. l = 1 c. ml = -1
d. n = 3 b. l = 0 c. ml = 0
e. n = 3 b. l = 1 c. ml = +1
f. n = 3 b. l = 2 c. ml = -2
g. n = 4 b. l = 0 c. ml = 0
h. n = 4 b. l = 1 c. ml = 0
i. n = 4 b. l = 2 c. ml = -1
j. n = 4 b. l = 3 c. ml = +3