Quantum
numbers
The simplest definition of Quantum mechanics is that quantum mechanics is the part of science that explain the
distribution of the electrons around the nucleus and calculate the energy of
electrons.
There are four quantum numbers used to describe the distribution of
the electrons in any atom. These numbers are derived from the mathematical
solution of the Schrödinger equation for the hydrogen atom. The four quantum
numbers are called:
a- The principal quantum number
b. The angular momentum quantum number
c. The magnetic quantum number
d. The spin quantum number
The first three are used to describe atomic orbitals and to label
electrons that reside in them. The fourth quantum number describes the behavior
of a specific electron and completes the description of electrons in atoms.
a. The Principal Quantum Number (n)
The principal quantum number (n) have to be an integer
number (1, 2, 3,…….). For hydrogen atom only, the value of n determines
the energy of an orbital. The principle quantum number can give information
about the average distance of the electron from the nucleus is a particular
orbital. The larger n is, the greater the average distance of an
electron in the orbital from the nucleus and therefore the larger the orbital.
The Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) give information
about the “shape” of the orbitals. From the value of “n” we can
determine the number of ‘l” value. For a given value of n, l
has possible integral values from 0 to ( n -1). For example, If n =
1, there is only one possible value of l; ( l = n - 1 = 1 -
1 = 0). Another example, if n = 2, there are two values of l (l
= 0 and 1). If n = 3, there are three values of l (l= 0,
1, and 2). The value of l is generally designated by the letters s ,
p , d , f, and so on.
l
|
0
|
1
|
2
|
3
|
4
|
5
|
Name
of orbital
|
s
|
p
|
d
|
f
|
g
|
h
|
If n=1, l= 0 we have s orbital
If n=2, l=0 and 1 we have s and p orbitals
If n=3, l=0, 1 and 2 we have s, p and d orbitals and so on……………
( “s” stand for the spectral lines of atomic emission
spectra, “p” stand for the strong emission of principal lines, “d”
for the diffuse of the atomic emission spectra, and “f” for
fundamental atomic spectra emission). After letter “f” the naming
of orbital followed alphabetical order.
A collection of orbitals “l” with the same value of “n”
is frequently called a shell. If one or more orbitals with the same “n”
and “l” values are referred to as a subshell. For example,
the shell with n= 2 is composed of two subshells, l= 0 and 1 (the
allowed values for n= 2). These subshells are called the 2s and 2p
subshells where 2 denotes the value of n , and s and p denote
the values of l.
The principle quantum no.
|
The Angular Momentum Quantum Number (l)
|
Orbital
|
Subshell
|
n=1
|
l=0
|
s
orbital
|
1s
|
n=2
|
l=
0 and 1
|
s
and p orbitals
|
1s,
2s, 2p
|
The Magnetic Quantum Number (ml)
The magnetic quantum number (ml) describes the
orientation of the orbital in space. Within a subshell, the value of ml
depends on the value of the angular momentum quantum number, l.
For a certain value of l, there are (2l+1) integral
values of ml as follows:
- l, (-l+1),
0, (+l-1), + l
Example: for l=0 ml=0
If l =1 then no. of ml= (1X2)+1=3 ml will have three values=
-1, 0, 1
If l=2, then no. of ml = (2X2)+1 = 5 values, ml
= -2, -1, 0 ,1, 2.
The number of ml values indicates the number of
orbitals in a subshell with a particular l value.
The Electron Spin Quantum Number (ms )
The electromagnetic theory postulated that, a spinning charge generates
a magnetic field, and it is this motion that causes an electron to behave like
a magnet. The two possible spinning motions of an electron, one clockwise and
the other counter clockwise.
The fourth quantum number, called the electron spin quantum number
(ms ), which has a value of +½ , -½
Otto
Stern and Walther Gerlach in 1924 experiment showed that the interaction
between an electron and the magnetic field causes the atom to be deflected from
its straight-line path. Because the spinning motion is completely random, the
electrons in half of the atoms will be spinning in one direction, and those
atoms will be deflected in one way; the electrons in the other half of the
atoms will be spinning in the opposite direction, and those atoms will be
deflected in the other direction. Thus, two spots of equal intensity are
observed on the detecting screen.
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