Representation of Orbitals

Representation of Orbitals of Single-Electron Atoms

There are four types of sub-shells (sub-levels); s, p, d, f, which contain the orbitals

→ Shape of the

the s− orbital
the p− orbital
the d− orbital
~~the f− orbital~~

The s − orbital

The lowest energy orbital
The size of the orbital increases with n
The probability decreases to zero as r (from the nucleus) increases

The p − orbital

Electron density is concentrated on 2 regions on either sides of the nucleus, separated by a node at the nucleus.
The final picture is a dumbbell shape orbital with 2 lobes.
For the same value of (n), orbitals have the same size and shape, but different spatial orientation.
Size of the p orbitals increases with (n), i.e. 2p < 3p < 4p

The d − orbital

There are 5-d orbitals with the same energy, although they look different in shape.
The size of the d orbitals increases as (n) increases.

Many-electron Atoms

The atomic orbitals in a many-electron atom are like those of the H atom, but energetically different.
orbitals-many-electron-atoms

For a given value of (n), the energy of the orbital increases with the value of l:
s < p < d

For the same value of (l ), orbitals have the same energy. These orbitals are thus called: degenerate

Electron Spin

The electron behaves as if it were a tiny sphere spinning on its own axis.
Hence, Spin Magnetic Quantum Number (ms), where ms indicates the 2 opposite directions of spinning: +½ and − ½

Note: ms is called spin magnetic because a spinning charge produces a magnetic field

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Date of last modification: 2024