Download Notes: Assigning Quantum Numbers

Notes: Assigning Quantum Numbers
What are quantum numbers? – Quantum numbers are a set of four numbers that scientists use to identify the properties
of an electron in an atom. A good analogy is to think of the quantum numbers as an "address" of the electron in the atom.
Principal Quantum Number – symbolized n, indicates the main energy levels or shells surrounding a nucleus.
 quantum theory equivalent of Bohr orbits
 values of n are whole numbers only (i.e. 1, 2, 3, 4, ...)
Azimuthal Quantum Number – symbolized l, indicates the shape of the orbital
 within each main energy level (beyond the first) orbitals of different shapes occupy different regions referred to as
sublevels or subshells
 the first four azimuthal quantum numbers are designated in ascending order (of energy) by the letters s, p, d and f
or the numbers 0, 1, 2, and 3
s orbitals: l = 0; spherical
p orbitals; l = 1; dumbbell shape
d orbitals; l = 2; have four lobes (except for one)
f orbitals; l = 3; very complex
 in the nth main energy level, n sublevels are allowed
when n = 1, 1 sublevel (or shape) is allowed
when n = 2, 2 sublevels (or shapes) are allowed
when n = 3, 3 sublevels (or shapes) are allowed
when n = 4, 4 sublevels (or shapes) are allowed
 values of l are whole numbers up to n-1 (i.e. 0, 1, 2, 3, . . . (n-1))
Magnetic Quantum Number – symbolized ml, indicates the orientation of an orbital about the nucleus
 s orbital has only 1 possible orientation (ml = 0)
 p orbitals have 3 possible orientations (ml = -1, 0, +1)
 d orbitals have 5 possible orientations (ml = -2, -1, 0, +1, +2)
 f orbitals have 7 possible orientations (ml = -3, -2, -1, 0, +1, +2, +3)
 values of ml are whole numbers with values in the range of –l to +l
Magnetic Spin Quantum Number – symbolized ms, indicates the spin of the electron
 ms has only two possible values, +½ or -½
 by convention the first electron placed in the orbital is designated +½ and the second electron is designated -½
Summary of the first seven energy levels
n
1
2
3
4
5
6
7
l
0
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
2
3
4
5
0
1
2
3
4
5
6
ml
0
0
-1,0,+1
0
-1,0,+1
-2,-1,0,+1,+2
-1,0,+1
-2,-1,0,+1,+2
-3,-2,-1,0,+1,+2,+3
0
-1,0,+1
-2,-1,0,+1,+2
-3,-2,-1,0,+1,+2,+3
-4.-3,-2,-1,0,+1,+2,+3,+4
0
-1,0,+1
-2,-1,0,+1,+2
-3,-2,-1,0,+1,+2,+3
-4.-3,-2,-1,0,+1,+2,+3,+4
-5,-4.-3,-2,-1,0,+1,+2,+3,+4,+5
0
-1,0,+1
-2,-1,0,+1,+2
-3,-2,-1,0,+1,+2,+3
-4.-3,-2,-1,0,+1,+2,+3,+4
-5,-4.-3,-2,-1,0,+1,+2,+3,+4,+5
-6,-5,-4.-3,-2,-1,0,+1,+2,+3,+4,+5,+6
ms
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½
-½ or +½