Download Orbitals and Quantum Numbers

Orbitals and Quantum
Numbers
(rev. 12/04/08)
Objective

Students will be able to 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.
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)
Principle Quantum Number “n”

The principle quantum number (n)
indicates the main energy level
occupied by the electron

n can have integral values of 1, 2, 3, etc.
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
Which sublevel does each
value of “l” represent?

Value of l
0
1
2
3
letter used
s
p
d
f
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, +1/2 or -1/2
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
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?)
Problems to try


Brown & LeMay
P. 222 problems 60, 61, 62
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, l=1, ml=-2
n=3, l=2, ml=+2
n=4, l=3, ml=+3
n=5, l=2, ml=+3
Replace the ? Mark with an
appropriate quantum number.
n=3, l=1, ml=?
n=4, l=?, ml=-2
n=?, l=3, ml=?