Download Quantum Numbers “Where are the Electrons?”

Quantum Numbers
“Where are the Electrons?”
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An orbital is a three-dimensional region around the nucleus that indicates the probable location of an
electron.
Quantum numbers are used to describe atomic orbitals and the electrons in them. There are 4 quantum
numbers:
o The principal quantum number (n), indicates the main energy level occupied by the electron.
 n = a whole number such as 1, 2, 3, 4
 n tells the distance from the nucleus and the energy of an electron in that main energy level
(electrons in n=1 are closest to the nucleus and have the lowest energy)
 There can be more than one orbital in a main energy level.
 The total number of orbitals that exist in a given energy level is equal to n2
 The total number of electrons that can be found in a given main energy level is 2n2
o
Main energy levels can have sublevels. The angular momentum quantum number (l), describes
the sublevels:
 the number of sublevels = n (the main energy level)
 Letters (s, p, d, f) are used to indicate the shape of the orbitals in the sublevel.
 s orbitals are spherical
 p orbitals are dumbbell-shaped
 d orbitals are double-dumbbells
 f orbitals are very complex
o
The magnetic quantum number (m), indicates the number of orbitals in a sublevel:
o
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The s sublevel consists of one s orbital.
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The p sublevel consists of three p orbitals.
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The d sublevel consists of five d orbitals.
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The f sublevel consists of seven f orbitals.
The spin quantum number indicates the direction each electron is spinning:
 Each electron spins clockwise or counterclockwise as it moves around the nucleus
 This is indicated by spin values of +½ or -½
 A single orbital can hold a maximum of two electrons, which must have opposite
spins.
Main Energy
Level
(n)
Sublevels
Available
Number of
Orbitals
per
sublevel
1
s
1
2
2
s
p
1
3
2
6
8
s
p
d
s
p
d
f
s
p
d
f
g*
s
p
d
f*
g*
h*
1
3
5
1
3
5
7
1
3
5
7
9
1
3
5
7
9
11
2
6
10
2
6
10
14
2
6
10
14
18
2
6
10
14
18
22
18
2
3
4
5
6
Total electrons
Total electrons
possible for
possible in the
energy level
sublevel
(2n2)
*These orbitals are not used in the ground state of any known element.
32
50
72