Quantum Numbers.ppthhhhhhhhhhhhhhhhhhhhhhh

Dr. S. B Maulage
Dept of Chemistry

The 4 quantum numbers are like a zip
code for the electron.
THE QUANTUM NUMBERS

They specify an atomic orbital, a region in
space where there is high probability of
finding an electron with a characteristic
energy, and the number of electrons which
can occupy the orbital.

A) The Principal Quantum Number – n
The modern equivalent of n in the Bohr
Theory. It describes the main energy
level. It can have the values of the
positive integers: 1, 2, 3, 4, 5,....
It is related to the average distance of the
electron from the nucleus. The energy of
the electron depends principally on n.
Orbitals of the same quantum number n,
belong to the same shell.

B) Angular momentum quantum number
- azimuthal or subsidiary quantum
number - distinguishes orbitals of a given n
having different shapes. Other synonyms
are sublevel and subshell. There are n
different kinds of orbitals each with a
distinctive shape denoted by .

 has values from 0 to n-1. (It is important
to remember that in this case 0 does not
mean nothing.)
When n = 1,  can only equal 0 - only one
subshell
When n = 2,  can equal 0 and 1 - two
subshells
When n = 3,  can equal 0, 1, and 2 - three
subshells

Associated with each value of  is a letter
related to a shape which is a region of
space with an approximate 90% occupancy
rate by an electron of a specified energy.
When = 0, the letter designation is s and
the shape is spherical.
When = 1, the letter designation is p and
the shape is dumbbell shaped.
When  = 2, the letter designation is d and
the shape is a cloverleaf and another
shape.

designations used are 1s, 2s, 2p, 3s, 3p, 3d,...

C) m is the magnetic quantum number
which distinguishes orbitals of given n and .
It specifies the orientation in space of the
atomic orbital.
The number of different orientations in
space depends on the subshell designated.
The allowed values are integers from - 
through 0 to +  giving 2  +1 possibilities.
When n = 1;  = 0; m  = 0 - only 1
orientation possible - a sphere.

When n = 2;  = 0; m = 0 - only 1
When n = 2;  = 1; m  = -1, 0, +1 - 3
orientations are possible – one dumbbell
along each of the three axes, x, y and z.

When n = 3; = 0; m  = 0 - only 1
When n = 3; = 1; m  = -1, 0, +1 The 3
orientations which are possible are one
dumbbell along each of the three axes, x,
y, z.
When n = 3; = 2; m = -2 -1, 0, +1 +2
There are 5 orientations possible – four
cloverleafs and 1 other shape. One is
along the xy axes, three between the axes,
and the special one is along the z axis.

Quantum Numbers.ppthhhhhhhhhhhhhhhhhhhhhhh

D) ms is the spin quantum number. An
electron has magnetic properties that
correspond to a charged particle spinning
in its axis. Either of 2 spins are possible???
2 values are possible - +½ and -½ for every
set of n,  , m - this gives two as the
number of electrons which can occupy
each orbital.
2 e's in the 1s orbital - "zip code" 1,0,0,+ ½
and 1,0,0,- ½ .

2 e's in the 2s orbital - "zip code" 2,0,0,+ ½
and 2,0,0,- ½ .
2 e's in each 2p orbital - "zip code" 2,1,-1,+½;
2,1,-1,- ½; 2,1,0,+ ½; 2,1,0, -½; 2,1,+1,+ ½;
2,1,+1- ½ .

CAPACITIES OF PRINCIPAL
LEVELS, SUBLEVELS, AND
ORBITALS
A) Each principal level of quantum
number n can hold 2(n2
) electrons.
level 1 can hold 2e (2 X 12
)
)
)

B) Each principal level of quantum number
n can contain a total of n sublevels.
level 1 has 1 sublevel - s
level 2 has 2 sublevels - s and p
level 3 has 3 sublevels - s, p, and d
level 4 has 4 sublevels - s, p, d and f

C) Each sublevel of quantum number 
can contain a total of 2  + 1 orbitals.
= 0 there are (2 x 0 + 1) orbitals, 1 orbital
called s.
 = 1 there are (2 x 1 + 1) orbitals, 3
orbitals called p.
 = 2 there are (2 x 2 + 1) orbitals, 5 orbitals
called d.
D) Each orbital can contain only 2
electrons.

Quantum Numbers.ppthhhhhhhhhhhhhhhhhhhhhhh

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