AtomsFirst2e_day6_sec3.7-3.8_CHMY171_fall_2015.ppt

Quantum number

1. Quantum Numbers
Quantum numbersare required to describe the distributionof
electron densityin 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 (m
l) –specifies orientation
3.7

2. Quantum Numbers
The principal quantum number (n) designates the sizeof the
orbital.
Larger values of ncorrespond to larger orbitals.
The allowed values of nare integral numbers: 1, 2, 3 and so forth.
The value of ncorresponds to the value of nin Bohr’s model of the
hydrogen atom.
A collection of orbitals with the same value of nis frequently called
a principle energy level or shell.

3. Quantum Numbers
The angular moment quantum number(l) describes the shapeof
the orbital.
The values of lare integers that depend on the value of the
principal quantum number
The allowed values of lrange from 0 ton –1.
Example: If n= 2, l can be 0 or 1.
A collection of orbitals with the same value of nand l is referred to
as a subshell.
l 0123
Orbital designationspdf

4. Quantum Numbers
The magnetic quantum number (m
l) describes the orientationof
the orbital in space.
The values of m
lare integers that depend on the value of the
angular moment quantum number:
–l,…0,…+l

5. Quantum Numbers
Quantum numbers designate shells, subshells, and orbitals.

6. Worked Example 3.8
StrategyRecall that the possible values of m
ldepend on the value of l, not on
the value of n.
What are the possible values for the magnetic quantum number (m
l) when the
principal quantum number (n) is 3 and the angular quantum number (l) is 1?
SetupThe possible values of m
lare –l,…0,…+l.
Text Practice: 3.81 3.82

7. Quantum Numbers
The electron spin quantum number(m
s ) is used to specify an
electron’s spin.
There are two possible directions of
spin.
Allowed values of m
sare +½ and −½.

8. Quantum Numbers
A beam of atoms is split by a magnetic field.
Statistically, half of the electrons spin clockwise, the other half spin
counterclockwise.

9. Quantum Numbers
To summarize quantum numbers:
principal (n) –size
angular (l) –shape
magnetic (m
l) –orientation
electron spin (m
s) direction of spin
Required to describe an atomic orbital
Required to describe an
electron in an atomic orbital
2p
x
principal (n = 2)
angular momentum (l= 1)
related to the magnetic
quantum number (m
l)

10. Atomic Orbitals
All s orbitalsare spherical in shape but differ in size:
1s< 2s< 3s
2s
angular momentum
quantum number (l= 0)
m
l= 0; only 1 orientation
possible
principal quantum
number (n = 2)
3.8

11. Atomic Orbitals
The p orbitals:
Three orientations:
l= 1 (as required for a porbital)
m
l= –1, 0, +1

12. Atomic Orbitals
The d orbitals:
Five orientations:
l= 2 (as required for a dorbital)
m
l= –2, –1, 0, +1, +2
•http://mw.concord.org/modeler/showcase/simulation.html?s=http://mw2.concord.org
/public/student/quantumchemistry/atomicorbitals.html

13. Energies of Orbitals
The energies of orbitals in the hydrogen atom depend only on the
principal quantum number.
2
nd
shell (n= 2)
3dsubshell (n= 3; l= 2)
2psubshell (n = 2; l= 1)
3
rd
shell (n= 3)
2ssubshell
(n= 2; l= 0)
3psubshell (n= 3; l= 1)3ssubshell (n= 3; l= 0)

14. Worked Example 3.9
StrategyConsider the significance of the number and the letter in the 4d
designation and determine the values of nand l. There are multiple values for m
l,
which will have to be deduced from the value of l.
Text Practice: 3.86
List the values of n, l, and m
lfor each of the orbitals in a 4dsubshell.

15. Study Guide for sections 3.7-3.8
DAY 6, Terms to know:
Sections 3.7-3.8quantum 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 1
st
, 2
nd
, or 3
rd
energy level of an atom
•Be able to rank the relative energies of any two orbitals in the 1
st
, 2
nd
, or 3
rd
energy
levels of an atom and explain WHY

16. 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

17. 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.