Download Orbitals and Quantum Numbers

Orbitals and Quantum
Numbers
(
Drill

If the frequency of radiation is
4.68 x 10 -3 Hz. What is the wavelength
of light in cm?
Objectives




iWBAT
Distinguish between the 4 quantum numbers.
describe the quantum numbers n, l, and ml
used to define an orbital in an atom, and list
the limitations placed on the values each may
have.
Assign quantum numbers to specific electrons
in atoms
What is an orbital?


An orbital is an allowed energy state of
an electron in the quantum-mechanical
model of the atom
the term orbital is also used to describe
the spatial distribution of the electron.

Defined by the values of 4 quantum
numbers: n, l, and ml , ms
4 Quantum Numbers

Reminder:
quantum numbers specify the
properties of atomic orbitals and the
properties of electrons in orbitals
Principal Quantum Number “n”

The principal quantum number (n)
indicates the main energy level
occupied by the electron

n can have integral values of 1, 2, 3, etc.
The Large Numbers Represent the Principal Quantum Numbers
Principal Quantum Numbers
http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/quantum_table1.gif
http://library.thinkquest.org/15567/lessons/sublevels.jpg
Azimuthal Quantum Number

The angular momentum (or azimuthal)
quantum number (symbolized by “l “)
indicates the shape of the orbital

“l “ can take on integral values from
0 to n -1
for each value of n
L is Mistral font
Which sublevel does each
value of “l ” represent?

Value of l
0
1
2
3
letter used
s
p
d
f
http://chemwiki.ucdavis.edu/@api/deki/files/4826/=Single_electron_orbitals.jpg
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/imgqua/hydco5.gif
Magnetic Quantum Number

The magnetic quantum number ( ml )
describes the orientation of the orbital
in space



It can take on values from “l to –l ”
For example:
If “l ” is 2 then ml could be 2, 1, 0, -1, -2
Electron Spin Quantum Number
Electron Spin Quantum Number (ms )


This number indicates the two fundamental
spin states of an electron in an orbital
This quantum number can only have two
possible values, + ½ or - ½
http://www.brooklyn.cuny.edu/bc/ahp/LAD/C3/graphics/C3_quant_04.gif
http://quantumanthropology2.files.wordpress.com/2012/04/picture-paul-40.png
Pauli Exclusion Principle


Pauli Exclusion Principle
states that no two electrons in an atom
can have the same set of 4 quantum
numbers n, l, ml, and ms
http://www.chemistryland.com/CHM130W/10-ModernAtom/Spectra/PeriodicTableWithQuantumNumbers.jpg
http://wps.prenhall.com/wps/media/objects/3081/3155040/blb0605/blb06t02.gif
http://atomicstructureforelectrons.webs.com/quantum-number-pic.gif
Practice Problem #1


For n=4, what are the possible values
of l ?
Answer on next slide.
Answer

l = 0,1,2,3

(what do these values correspond to?)
Practice Problem #2


For l =2, what are the possible values
of ml ?
Answer on next slide.
Answer

ml = 2,1,0,-1,-2

(what do these values correspond to?)
Can an e- be described by the following
set of quantum numbers?
n=2, l=1, ml=-1
All quantum numbers are allowed values
Can an e- be described by the following
set of quantum numbers?
n=1, l=1, ml=+1
Not possible.
The value of l must be less than the value
of n.
Can an e- be described by the following
set of quantum numbers?
n=7, l=3, ml=+3
All the quantum numbers are allowed
values.
Can an e- be described by the following
set of quantum numbers?
n=3, l=1, ml=-3
Not possible.
The value of ml must be in the range
-l to +l
Can an e- be described by the following
set of quantum numbers?
n=2,
n=3,
n=4,
n=5,
l=1,
l=2,
l=3,
l=2,
ml=-2
ml=+2
ml=+3
ml=+3
Replace the ? Mark with an
appropriate quantum number.
n=3, l=1, ml=?
n=4, l=?, ml=-2
n=?, l=3, ml=?