Quantum Numbers:
The possibility of finding electrons is maximum in orbitals. The space between two orbitals has no electrons. This region of atom is called nodal plane or nodal surface.
Fig. Px Py Pz
Shape Of f-orbital
The number that fully explains An electron
Or the number that tells all features e.g. size , energy , shape , orientation of an orbit is called Quantum Number.An electron in an atom is fully explained
by its four quantum numbers. For Example; a complete address of a person comprises his name, the city in which he lives, the town, block, street and the house number. In the same way, quantum
numbers serve as numbers or labels, which completely describe an electron. These
quantum numbers locate the position of electron in an atom.
The quantum numbers are calculated by Schrodinger Wave Equation.
There are four types of Quantum Number.
1. Principal Quantum Number (n)
2. Azimuthal Quantum Number (l)
3. Magnetic Quantum Number (m)
4. Spin Quantum Number (s)
1. Principal Quantum Number
This quantum number tells us about the number of shell in which electrons exist. This quantum number is represented by n.
n is 1 for K Shell, n is 2 for L Shell, n is 3 for M shell , n is 4 for N shell and so on...
2.Azimuthal Quantum Number
This quantum number tells us about the shape of subshell in which electrons exist.
The values of azimuthal quantum number l are
l= 0, 1, 2, 3, ...........(n-1)
Its value depends upon the principal Quantum Number (n). These values represent diferent subshells, represented
by small letters, s, p, d, f. The s stands for sharp, p for principal, d for diffused and f for fundamental.
These are the spectral terms used to describe the series of lines observed in the atomic spectrum.
A subshell may have diferent shapes depending upon the value of l. It may be spherical,
dumb-bell, or some other complicated shapes. The values of azimuthal quantum number always start from zero.
This quantum number also tells us the number of electrons in subshell by follow formula,
Total number of electrons=2(2l+1)
l is 0 for s subshell, so ne=2(2(0)+1), ne=2 so s-subshell has 2 electrons.
l = 1 for p-subshell so p-subshell has 6 electrons.
l=2 for d-subshell so d-subshell has 10 electrons.
l= 3 for f-subshell so f has 14 electrons
Magnetic Quantum Number
This quantum number describes the orientation of orbitals in three dimensional space.
It's value Depends on the value of azimuthal Quantum Number l.
m = 0, ± 1, ± 2, ± 3,....
It's value is calculated from l by following formula:
m= (2l+1)
m = 1 when l is 0. It means that s has only one orientation in space.
m= 3 when I is 1 for p orbital. It means that p has 3 orientations in space that are Px, Py, and Pz..
m= 5 when I is 2 for d orbital. It means that d has 5 orientations in space that are dxy, dyz, dzx, dx2-dy2, dz2.
Because this quantum number explains the orientation of orbitals that's why it's also named as orbital orientation quantum number
Spin Quantum Number
This quantum number explains the rotation of electrons in an orbital.
This is represented by s. There are two types of rotations of electrons i.e. clockwise and anticlockwise. When an electron rotates it creates two kinds of fields i.e. electric field and magnetic field. These two fields are at right angle to each other. There are only two possible values of s i.e
, ±1/2.
+1/2 for clockwise rotation and -1/2 for anticlockwise rotation. The spin Quantum Number also explains the magnetic behavior of an atom.
If there are two unpaired electrons in two orbitals they will always have rotation in same direction and they will be attracted towards magnet. This is called paramagnetic behave of electrons.If there is pair of electron in an orbital these electrons will always have rotation in opposite directions. And atom will not be attracted by a magnet. This is called diamagnetic behavior of electrons.
Shapes Of Orbitals
In above section we have studied that there are four values of Azimuthal Quantum Number i.e, l=0,1,2,3,
So there are four types of subshells s,p,d and f. Now we will discuss their shapes in detail.
Shape Of s-orbital
s-orbital has spherical shape and represented by a circle. As the value of principal quantum number n increases the size of s orbital also increases.
Shapes Of p-orbitals
According to magnetic quantum number there are 3 values of m for p-subshell. It means that p-subshell has only three orientations in space, these Px, Py and Pz along x-axis, y-axis and z-axis respectively. p-orbital has dumb-bell shape.
Shape Of d-orbital
According to magnetic quantum number there are five orientations of d-subshell in space. Value of l is 2 for d-subshel.
m=(2l+1), so m=(2(2)+1), m=4+1, m= 5 , and it's written as m = 0, ± 1, ± 2.
So d-subshell has five orientations in space and they are dxy, dyz, dzx, dx2-dy2, dz2. First four of the five d orbitals are cloverleaf shaped.The fifth d orbital dz2 is shaped like an elongated dumbbell which has a doughnut around its middle.
Orbital f has no defite shape. It's shape is very complex, we can't determine it's shape clearly. According to magnetic quantum number there are seven space orientations of f-subshell.
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