Transcript Quantum Numbers

The Four Quantum Numbers
In the quantum mechanical model of the atom, each electron is described
by four quantum numbers, and no two electrons in an atom can have the
same numbers.
The quantum numbers are:
n: the principle quantum number. n = 1, 2, 3, 4…
l: the angular quantum number. It describes the ‘shape’ of the
orbital…the electronic distribution about the nucleus. l = n-1, n-2,… to 0
If l = 0, it’s an s orbital
If l = 1, it’s a p orbital
If l = 2, it’s a d orbital
If l = 3, it’s an f orbital (and so on)
ml: the magnetic quantum number. It describes the orientation of the
orbital on an xyz-coordinate axis. ml = -l…0…+l in integral values.
ms: the spin quantum number. It equals +½ or -½. Conventionally, the
+½ is always given first.
n Orbital types
One s-orbital
One s-orbital
Three p-orbitals
One s-orbital
Three p-orbitals
Five d-orbitals
One s-orbital
Three p-orbitals
Five d-orbitals
Seven f-orbitals
Within an energy level (n = 1, 2, 3, 4…), there exists n types of
orbitals and n2 sublevels.
A few examples:
(all ms’s are ± ½, so won’t be shown here)
n
l
ml
1
0
0
2
1
-1, 0, 1
2
0
0
3
2
-2, -1, 0, +1, +2
3
1
-1, 0, +1
3
0
0
Notes
The 1s orbital
The three 2p orbitals.
The 2s orbital
The five 3d orbitals.
The three 3p orbitals.
The 3s orbital
Notice that n = # of subshells present and that n2 = total
number of orbitals for a particular energy level.
The three p-orbitals are oriented along the x, y and z axes
and can hold a maximum of 2 electrons each.
z
z
y
y
x
px
z
y
x
pz
x
py
It’s been suggested that the p-orbitals look like peanuts if that
helps you to remember their shape.
The d-orbitals
dxy
dxz
dyz
d x2-y2
dz 2
Even though the d-orbitals look like two p-orbitals, it is
important to remember that each orbital can hold a
maximum of 2 electrons regardless of how many lobes it has.
The freaky (or flowery) f-orbitals
Examples
1. (a) What is the designation for the subshell with n = 5 and l =
1? (b) How many orbitals are in this subshell? (c) Indicate the
values of ml for each of these orbitals.
(a) l = 1 is a p-orbital, so it is a 5p subshell
(b) There are three p-orbitals
(c) ml = -1, 0, 1
3. (6.54) Which of the following are permissible sets of quantum
numbers for an electron in a hydrogen atom: (a) n = 2, l = 1,
ml = 1; (b) n = 1, l = 0, ml = −1; (c) n = 4, l = 2, ml = −2; (d) n
= 3, l = 3, ml = 0? For those combinations that are
permissible, write the appropriate designation for the
subshell to which the orbital belongs (that is, 1s, and so on).
(a) 2px
(c) 4dx2-y2