The document discusses atomic orbitals. It defines orbitals as representing the probability of finding an electron in a certain region of space and describes the main types of orbitals - s, p, d, and f orbitals. S orbitals are spherical shapes centered around the nucleus, while p orbitals have dumbbell shapes with lobes on either side of a nodal plane through the nucleus. D and f orbitals have more complex lobe structures determined by quantum numbers. The document provides examples of specific d and f orbitals to illustrate their shapes and nodal features.

1. Atomic Orbitals
Prepared by
Dr. Umakant Shrivastava,
Assistant Professor, Physics,
Dr. C. V. Raman University, Bilaspur, C.G.

2. Contents
1. Objective
2. Some related Definitions
3. Types of orbital.

3. 1. Objective
It is to understand the atomic
orbitals and to know about
them through bond
formation.

4. 2. Some related Definitions
 Orbitals : They represents the probability of finding an electron in any one place. They
responds to different energies and forces. Thus we can say that an electron in an
orbital has definite energy. They can be best explained by using quantum mechanics.
 Atomic Orbitals: It is that region just outside the nucleus of an atom where the
probability of finding electrons is highest about 95 %.
 Electron Density: It is the measure of the probability of finding an electron in an
orbital.
 Wave Function: It is the mathematical description of volume of space occupied by an
electron having a certain amount of energy.
 Node: In orbital node is a place where a crest and a trough meets.

5. 3. Types of Atomic orbitals
The energy levels about the nucleus contains group of these atomic orbitals. Each orbitals
has a unique energy associated with it, and can contain a maximum of two electrons and
varies in shape and orientation. We can mainly concentrate on s and p orbitals as most of
the organic molecules have their electrons in these orbitals. Where as d and f orbitals are
utilized by the elements which are down in the periodic table.
There are various types of atomic orbitals. Some of them are:
 s-orbital
p-orbital
d-orbital
f-orbital

6. S - Orbital
1s 2s 3s
The s orbital is spherical like a fuzzy hollow ball with its centre at the nucleus of the atom.
The s orbitals are spherically symmetrical around the nucleus. For any atom there is only
one 1s orbital. The 1s orbital contains no nodes because it is closest to the nucleus.
There can be only one 2s orbital in an atom and it is similar to 1s orbital except that the
region where the probability of finding electron is most is far away from nucleus.
For any atom there is only one 3s orbital. The intensity of colouration shows the positions
where the electron is likely to be found on any plane cutting through the nucleus. There
are two spherical nodes in the 3s orbital.
There are three p orbitals of equal energy designated by Px, Py, Pz. Each p is dumbbell
shaped. Each contains of two lobes with atomic nucleus lying between them and each has
a nodal plane at the nucleus, where the probability of electron is zero.

7. p - Orbital
There are three p orbitals of equal energy designated by Px, Py, Pz. Each p is dumbbell
shaped. Each contains of two lobes with atomic nucleus lying between them and each has
a nodal plane at the nucleus, where the probability of electron is zero.
The three p- orbitals in the second shell of electrons are totally different from 1s and 2s
orbitals. Each p-orbital consist of a “dumbbell” and “teardrop” shape on either side of
nodal plane that runs through the centre of the nucleus.
Their orientation is 90⁰ from each other in the three spatial direction and have identical
energies and shapes.
They are also known as degenerate orbitals as the electrons in the three 2p orbitals are
farther from the nucleus than those in the 2s orbitals, they are at the higher energy levels.
Px Py Pz

8. d - Orbital
dxy dyz dxz dx2-y2 d z
2

9. f - Orbital
4fy3-3x2y
1.
4fxyz
2.
4f5yz2-yr2 4fz3-3zr2 4fzx2-zy2
4f5xz2-xr2 4fx3-3xy2
3.
4. 5. 6. 7.
The 4fy3-3x2y orbital corresponds to n=4, n=3 and m = -3. six lobes point to the corners of a regular
hexagon in the xy plane, with one pair of lobes along the x-axis. Three nodal planes pass between the
lobes and intersect at the z-axis.
The 4f xyz orbital corresponds to n=4, n=3 and m= -2. Eight lobes point to the corners of a cube, with
four lobes above and four lobes below the xy-plane. The x and y-axis pass through the centers of four of
the cube’s faces (between the lobes). The three nodal planes are defined by the x, y and z-axis.
The 4f5yz2-yr2 orbital corresponds to n=4, n=3 and m= -1. Six lobes point to the corner of the regular
hexagon in the xy-plane, with one pair of lobes along the x-axis. The three nodal planes pass between
the lobes and intersect at the y-axis.
The 4fz3-3zr2 orbital corresponds to n= 4, n=3 and m= 0. Two lobes point along the z-axis , with two
bowl-shaped rings above and below the xy -plane. The nodal surface are the xy-plane and a conical
surface passing through the nucleus and between the rings and the lobes.
The 4f5xz2-xr2 orbital corresponds to n=4, n=3 and m=+1. Six lobes point to the corners of a regular
hexagon in the xz-plane, with one pair of lobes along the y-axis. The three nodal planes pass between the
lobes and intersect at the x-axis.
The 4fzx2-zy2 orbital corresponds to n=4, n=3 and m = +2. It has the same shape as the 4fxyz orbital,
but the corners of the cube are in the planes defined by x, y and z-axis and the three nodal planes cut
between the lobes and intersect along the z-axis.
The 4fx3-3xy2 orbital corresponds to n=4, n=3 and m=+3. it is identical to the orbital with m_= -3
except that a lobe lies along the y-axis instead of along the x-axis.