PhysicsLAB: Orbitals

Orbitals

Pauli's Exclusion Principle states that no two electrons may be in the same quantum state and that the orbitals will be filled in order of increasing energy.


Images courtesy of Wikipedia and Oleg Alexandrov. They were programmed using MATLAB.
Shown above are vibrating drum heads that illustrate the three modes of vibration for the 1S, 2S, and 3S orbitals.

Note the similarity to vibrating strings having one, two, and three loops.

The three probability functions (Ψ²) for these orbitals are shown on Mark Winter's ORBITRON website sponsored by the University of Sheffield in England.

When electrons begin filling in the "shells" or orbitals to create each successive element, Hund's rule is used: "every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin."

To show how the orbitals are filled, here are orbital diagrams of the first 10 elements.


Hydrogen 1S¹	Helium 1S²	Lithium 2S¹	Beryllium 2S²	Boron 2P¹

Carbon 2P²	Nitrogen 2P³	Oxygen 2P⁴	Fluorine 2P⁵	Neon 2P⁶

To see how an atom of Neon "looks" once it has been built, click here for an animation from YouTube. Note the alignment of the three 2P orbitals: one along the x-axis, one on the y-axis and one on the z-axis. Also note the shape of the P-orbitals which Dr. Winter states should be more like flat lobes with NO sharp points converging at r = 0 (the nucleus).

Quantum Numbers

To completely describe an "orbiting" electron four quantum numbers are required.

the principal quantum number, n

The principal quantum number is sometimes known as the shell. The larger its value, the greater the radius of the electron cloud and the more energy the electron possesses. These numbers are always positive integers.
the angular quantum number, l

The angular momentum quantum number is sometimes referred to as the subshell. It describes the shape of the electron cloud. These numbers are non-negative integers greater than or equal to 0; l = n-1.
the magnetic quantum number, m

The magnetic quantum number describes the orientation of the subshell or orbital. These numbers are between -l < m < l.
and the spin quantum number, s

The spin quantum number represents a spin of either +½ or -½.

Z	name	n	l	m	s	orbital notation	ORBITRON gallery
1	Hydrogen	1	0	0	+½
2	Helium	1	0	0	-½
3	Lithium	2	0	0	+½
4	Beryllium	2	0	0	-½
5	Boron	2	1	-1	+½
6	Carbon	2	1	0	+½
7	Nitrogen	2	1	1	+½
8	Oxygen	2	1	-1	-½
9	Fluorine	2	1	0	-½
10	Neon	2	1	1	-½