Download SCHRODINGER`S QUANTUM MECHANICS

QUANTUM NUMBERS
“Energy changes within an atom are simply the result of an electron changing from a
wave pattern with one energy to a wave pattern with a different energy” (Schrodinger)
Electron waves are standing waves, which are called orbitals. Each orbital has a
characteristic energy.
1) Principal Quantum Number (n)
All orbitals having the same “n” are said to be in the same shell
“n” primarily describes the energy and size of the orbital (wave)
As “n” increases the energy of the orbital increases also.
n = 1
2
3
4
5…….
2) Secondary Quantum Number (l)
Each energy level is divided into sublevels.
Each sublevel is represented by a particular value of “l”. “l” describes the shape of an
orbital
Each sublevel has a different shape and amount of energy. The higher the “l” value the
greater the energy.
The number of sublevels is equal to “n”
l” values ranges from 0 to n -1
e.g.
if n = 1
if n = 2
if n = 5
then
then
then
l=0
l = 0 or 1
l = 0, 1, 2, 3, or 4
There is one sublevel
There are two sublevels
There are five sublevels
the values of “l” have letter designations:
l
0
letter s
shape?
1
p
2
d
3
f
4
g
5…
h
3. Magnetic Quantum Number (m)
Each sublevel is subdivided into orbitals. Each orbital has a specific orientation in
space represented by “m”. “m” also give the number of orbitals in a sublevel.
“m” values range from “– l to +l”
e.g.
if l = 0, the s sublevel, Then m = 0 There is 1 orbital; 1 possible orientation in
space
if l = 1, the p sublevel, Then m = -1, 0 +1. There are 3 orbitals; 3 possible
orientations in space
if l = 2 , the d sublevel, Then m = -2, -1, 0, +1, +2. There are 5 orbitals; 5
possible orientations in space
NOTE: Each orbital holds two electrons and occupies as much space as possible.
sublevel
s
p
d
f
# of orbitals
one
three
five
seven
Maximum # of electrons
2
2,2,2 = 6
2, 2, 2, 2, 2 = 10
2, 2, 2, 2, 2, 2 = 14
Note: The principal quantum number(n) = the # of sublevels in an energy level
= the # of orbitals in an energy level
n2
2
= the total # of electrons/energy level
2n
e.g. For n = 2, there are two types of sublevels (two “l” values ) Î s, p
Since there are three “p” orbitals; we have a total of 4 orbitals (22 = 4)
Since each orbital can hold a maximum of 2 electrons, we would have a total
of 8 electrons in the second shell (2 * 22 = 8)
4. Spin Quantum Number (s)
“s” indicates the direction of spin for the electron. There are only two directions, so s =
+1/2 or –1/2
EXAMPLE: Write the complete set of quantum numbers that are possible for the
electrons found in the 2p sublevel
n = 2; l = 1; ml = -1, 0, 1;
2,
2,
2,
2,
2,
2,
NOTE:
1,
1,
1,
1,
1,
1,
ms = +1/2; -1/2
-1, +1/2
-1, -1/2
0, +1/2
0, -1/2
1, +1/2
1, -1/2
Every electron in an atom has it’s own unique set of quantum
numbers (its own address)