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3.7 Quantum Numbers
Quantum numbers are required to describe the distribution of
electron density in an atom.
There are three quantum numbers necessary to describe an atomic
orbital.
 The principal quantum number (n) – designates size
 The angular moment quantum number (l) – describes shape
 The magnetic quantum number (ml) – specifies orientation
Quantum Numbers
The principal quantum number (n) designates the size of the
orbital.
Larger values of n correspond to larger orbitals.
The allowed values of n are integral numbers: 1, 2, 3 and so forth.
The value of n corresponds to the value of n in Bohr’s model of the
hydrogen atom.
A collection of orbitals with the same value of n is frequently called
a principle energy level or shell.
Quantum Numbers
The angular moment quantum number (l) describes the shape of
the orbital.
The values of l are integers that depend on the value of the
principal quantum number
The allowed values of l range from 0 to n – 1.
 Example: If n = 2, l can be 0 or 1.
l
0
1
2
3
Orbital designation
s
p
d
f
A collection of orbitals with the same value of n and l is referred to
as a subshell.
Quantum Numbers
The magnetic quantum number (ml) describes the orientation of
the orbital in space.
The values of ml are integers that depend on the value of the
angular moment quantum number:
– l,…0,…+l
Quantum Numbers
Quantum numbers designate shells, subshells, and orbitals.
Worked Example 3.8
What are the possible values for the magnetic quantum number (ml) when the
principal quantum number (n) is 3 and the angular quantum number (l) is 1?
Strategy Recall that the possible values of ml depend on the value of l, not on
the value of n.
Setup The possible values of ml are – l,…0,…+l.
Text Practice: 3.81 3.82
Quantum Numbers
The electron spin quantum number (ms ) is used to specify an
electron’s spin.
There are two possible directions of
spin.
Allowed values of ms are +½ and −½.
Quantum Numbers
A beam of atoms is split by a magnetic field.
Statistically, half of the electrons spin clockwise, the other half spin
counterclockwise.
Quantum Numbers
To summarize quantum numbers:
principal (n) – size
angular (l) – shape
Required to describe an atomic orbital
magnetic (ml) – orientation
principal (n = 2)
2px
related to the magnetic
quantum number (ml )
angular momentum (l = 1)
electron spin (ms) direction of spin
Required to describe an
electron in an atomic orbital
3.8
Atomic Orbitals
All s orbitals are spherical in shape but differ in size:
1s < 2s < 3s
principal quantum
number (n = 2)
2s
angular momentum
quantum number (l = 0)
ml = 0; only 1 orientation
possible
Atomic Orbitals
The p orbitals:
Three orientations:
l = 1 (as required for a p orbital)
ml = –1, 0, +1
Atomic Orbitals
The d orbitals:
Five orientations:
l = 2 (as required for a d orbital)
ml = –2, –1, 0, +1, +2
• http://mw.concord.org/modeler/showcase/simulation.html?s=http://mw2.concord.org
/public/student/quantumchemistry/atomicorbitals.html
Energies of Orbitals
The energies of orbitals in the hydrogen atom depend only on the
principal quantum number.
3s subshell
3;
l = 0)
3rd shell (n
(n ==3p
3)subshell
(n3d
= subshell
3; l = 1) (n = 3; l = 2)
2s
2ndsubshell
shell (n = 2)2p subshell (n = 2; l = 1)
(n = 2; l = 0)
Worked Example 3.9
List the values of n, l, and ml for each of the orbitals in a 4d subshell.
Strategy Consider the significance of the number and the letter in the 4d
designation and determine the values of n and l. There are multiple values for ml,
which will have to be deduced from the value of l.
Text Practice: 3.86 3.90
Study Guide for sections 3.7-3.8
DAY 6, Terms to know:
Sections 3.7-3.8 quantum numbers, orbitals, Pauli exclusion principle
DAY 6, Specific outcomes and skills that may be tested on exam 1:
Sections 3.7-3.8
•Given a set of quantum numbers, be able to describe the energy level, subshell (s,
p, d, or f), and spin state for an electron
•Given information about the principle energy level or shell, subshell (s, p, d, or f),
and orbital, be able to determine a set of 4 possible quantum numbers for an
electron
•Be able to recognize that no two electrons in the same atom can have the same
values for each of the 4 quantum numbers
•Be able to describe an experiment that could be used to show that half of the
electrons in an atom have a spin = ½ and the other half have a spin = -½.
•Be able to draw a figure that shows the shape and location of nodes in any orbital
in the 1st, 2nd, or 3rd energy level of an atom
•Be able to rank the relative energies of any two orbitals in the 1st, 2nd, or 3rd energy
levels of an atom and explain WHY
Extra Practice Problems for sections 3.7-3.8
Complete these problems outside of class until you are confident you have learned
the SKILLS in this section outlined on the study guide and we will review some of
them next class period. 3.75 3.77 3.83 3.85 3.89 3.123
Prep for day 7
Must watch videos:
http://www.learnerstv.com/video/Free-video-Lecture-3349-Chemistry.htm (electron configurations)
http://www.learnerstv.com/video/Free-video-Lecture-3350-Chemistry.htm (more on electron
configurations)
http://www.learnerstv.com/video/Free-video-Lecture-3351-Chemistry.htm (more electron
configuration examples)
Other helpful videos:
http://echem1a.cchem.berkeley.edu/modules/module-3/ (UC-Berkeley watch lesson 8)
http://ocw.mit.edu/courses/chemistry/5-111-principles-of-chemical-science-fall-2008/video-lectures/
(MIT lecture 8)
Read sections 3.9-3.10
We will review for exam 1 during the next class, so practice as many example problems
from chapters 1-3 as you can before then so you can ask questions about them in the next
class period.