The energy state of an electron in an atom may be described
by a set of four quantum numbers. Quantum numbers describe the orbital the
electron occupies in terms of: 1) distance from the nucleus; 2) shape; 3)
position with respect to the three axes in space; and 4) the direction of the
electron on the orbital.
1.
Principle quantum number (n)
This is the main energy level
n will equal positive whole numbers
ex:
n=2 indicates that the electron being described is in the second energy level
note: The number of possible orbital shapes in an energy
level is equal to the value of the principal quantum number (n)
ex: the
third energy level can contain three differently shaped types of orbitals
first energy level- only has an s orbital
second
energy level- has s and p orbitals
third
energy level- has s, p, and d orbitals
fourth
energy level- has s, p, and d orbitals
2.
Orbital
Quantum Numbers ( l )
this indicates the shape of the orbital
which the electron occupies
l=
0,1,2,3,… where l= 0 indicates the electron is in an s orbital
l= 1 indicates the electron is in a p orbital
l= 2 indicates the electron is in a d orbital
l= 3 indicates the electron is in an f orbital
n=
3 l=
2 indicates the electron being
describes is in a d orbital in the
third energy level
Note: -there is 1 s
orbital per energy level
-if an
energy level has p orbitals (level 2
and above) then it will have three p
orbitals in that energy level
-if an
energy level has d orbitals (level 3
and above) then it will have five d
orbitals in that energy level
-if an
energy level has f orbitals (level 4
and above) then it will have seven f
orbitals in that energy level
3.
Magnetic
quantum number (m)
-This indicates the position about the
three axes in space by indicating which orbital of a particular shape the
electron is in
-for the single s orbital is in an energy level m=0
s
orbital __ If l=
0 then m= 0
0
-for the three p in an energy level m= -1, 0, +1
p
orbitals __ __ __ If l= l then m= -1, 0, +1
-1
0 +1
- for the
five d orbitals in an energy level m=
-2, -1, 0, +1, +2
d orbitals __ __ __ __ __ If l= 2 then m= -2, -1, 0, +1, +2
-2 -1
0 +1 +2
- for the
seven f orbitals in an energy level
m= -3, -2, -1, 0, +1, +2, +3
f
orbitals __ __ __ __ __ __ __ If l=
3 then m= -3, -2, -1, 0, +1, +2, +3
-3 -2 -1 0 +1 +2 +3
Note: each line represents an orbital
4.
Spin
quantum number (s)
This represents a quantity which can be
thought of as the electron spinning on its axis;
There are two possibilities, clockwise and
counterclockwise.
S=
+½ or –½ represent the two possibilities
Note: -an orbital can
hold a maximum of two electrons (if it has two they must have opposite spins)
-the
orbitals fill one electron at a time before pairing
-no two
electrons within an atom can be described by the same four quantum numbers
-the total
number of orbitals in an energy level equals n2
Ex.
Third energy level n= 3 n2= 9
1
s orbital
3
p orbitals
5
d orbitals
9
orbitals total
-the total number of electrons which an energy level can
hold equals 2n2
Ex. Third energy
level n=3 9 total orbitals, each with a
maximum of two electrons
2
x 9= 18 or 2(3)2=18
Questions: For
odd numbers, circle the electron indicated, identify element. For even numbers,
draw orbital notation and assign quantum numbers to the last electron
represented.
1) 2 ↑_ __ __ __ n=2
1
↑↓ l =0
s p m=0
s
= +½
element=
___
2) 2 __ __
__ __ n=
1 __
l=
s
p m=
s
=
element=
Ne
3) 2 ↑↓ ↑_ ↑_ ↑_ n=
2
1 ↑↓ l = 1
s p m= +1
s
= +½
element=
___
4) 2 __ __
__ __ n=
1 __ l =
s
p m=
s
=
element=
Be
5) 3 ↑↓ ↑_ __ __ __
__ __ __ __ n= 2
2 ↑↓ ↑↓ ↑↓ ↑↓ l = 1
1 ↑↓ m=
0
s
p d s
= +½
element=
6) 3 __ __
__ __ __ __ __ __ __ n=
2 __ __ __ __ l =
1 __ m=
s
p d s=
element=
S
7) 4 ↑↓ ↑_ ↑_ __ __
__ __ __ __ __ __ __ __ __ __
__ n=3
3 ↑↓ ↑_ __ __ __ __ __ __ __ l = 2
2 ↑↓ ↑↓ ↑↓ ↑↓ m= -1
1 ↑↓ s = +½
s
p d
f element=
8) 4 __ __
__ __ __ __ __ __ __ __ __ __ __ __ __ __ n=
3 __ __ __ __ __
__ __ __ __ l =
2 __ __ __ __ m=
1 __ s
=
s
p d f element= Mn
No comments:
Post a Comment