## Definition of Orbital

**Orbital** in chemistry or physics defines a three-dimensional region where the probability of finding an electron is maximum. The wave function suggests that the probability of finding an electron in three-dimensional space around the nucleus involves two aspects, radial probability, and angular probability.

- The square of the radial part of the wave function indicates the probability of finding the electron at any distance r from the nucleus.
- The square of the angular part of the wave function gives the probability of finding an electron in a particular direction from the nucleus.
- If the radial and angular dependence of wave function is taken together, it defines the three-dimensional standing electron wave or cloud or orbital which predicts the size shape, and orientation of atomic orbitals.

The pictorial representation of an orbital in two-dimensional space is difficult. It is generally represented by a shaded picture in which the intensity of shading is proportional to the portability of finding the electron at that location.

## Quantum Number Orbital Diagram

In order to describe the size, shape, and orientation of the orbital, three quantum number is necessary. These quantum numbers are

- Principal (n) quantum number
- Azimuthal quantum number (l)
- Magnetic quantum number (m)

In the study chemistry, the relation between quantum number and orbital designation is represented in the below table.

Principal quantum number (n) | Azimuthal quantum number (l) | Magnetic quantum number (m) |

n=1 (K-shell) | l = 0 (1s) | m = 0 (2s) |

n = 2 L-shell | l = 0 (2s) | |

l = 1 (2p) | m = 0 (2p_{x}) | |

m = +1 (2p_{y)} | ||

m = −1 (2p_{z}) | ||

n =3 M-shell | l = 0 (3s) | m = 0 (3s) |

l = 1 (3p) | m = 0 (3p_{x}) | |

m = +1 (3p_{y)} | ||

m = −1 (2p_{z}) | ||

l = 2 (3d) | m = 0 (3d_{xy}) | |

m = +1 (3d_{yz}) | ||

m = −1 (3d_{xz}) | ||

m = +2 (3d_{x2-y2}) | ||

m = −2 (3d_{z2}) |

### Shape of s-orbital

From the above table, we have seen that for s-orbitals l = 0 and m = 0. It indicates that the s-orbital has only one orientation in space with a spherically symmetrical shape.

The electron cloud density in s-orbitals is not concentrated in any particular direction. Therefore, an equal chance of finding the electron density in any direction with respect to the nucleus of an atom.

### Shape of p-orbitals

For p-orbital l = 1 and m = +1, 0, −1. Three values of magnetic quantum number (m) define the three orientations along the x, y, and directions. Therefore, p-orbitals are designated as p_{x}, p_{y}, and p_{z}.

In the absence of a magnetic or electric field, these three orbitals are equivalent in energy and are said to be three-fold degenerate or triply degenerate energy levels.

The three p-orbitals are dumb-bell shape which is perpendicular to each other. Each of the three p-orbitals has two lobes touching each other at the origin and these lobes are completely symmetrical along any of the three-axis. For example, the p_{x}-orbital is symmetrical to the x-axis.

The plane which separated the two lobes of the p-orbital is called the nodal plane. The electron density on the nodal plane is zero. For p_{x}-orbital, yz-plane is the nodal plane.

### Shape of d-orbitals

d-orbital arises when n = 3 and m = +2, +1, 0, −2, −1 or it starts with the 3rd main energy level. The azimuthal quantum number indicates that d-orbitals have five orientations in space.

Five orientations along the x, y, and z-axis are named d_{xy}, d_{xz}, d_{yz}, d_{x2-y2,} and d_{z2}.

- The three orbitals namely d
_{xy}, d_{yz}and d_{xz}have their lobes lying symmetrically between their respective coordinate axis. For example, the lobes of the d_{xy}orbital lie between the x and y-axis. This set of three orbitals is known as the t_{2g}set non-axial set. - The lobes of d
_{x2-y2}are lying along the x and y-axis and the lobes of d_{z2}are lying along the z-axis. This set of two orbitals is called e_{g}set or axial set.