ml, the magnetic quantum number

Quantum numbers are like parts of an address. Each one describes some property of the electron, just like how each part of an address gives some information about where a person lives.

ml describes the orientation of the orbital where an electron resides. In other words, while l describes the shape of the orbital, ml describes the positioning of that shape.

In a nutshell

ml describes the orientation of the orbital where an electron resides. In other words, while l describes the shape of the orbital, ml describes the positioning of that shape.

ml values visualized

(Quantum Numbers Slidedeck)

Possible values of ml

For l = 0, there is only one orientation ml = 0. This is intuitive since l = 0 has a spherical shape so it makes sense that the orbital could only have one unique orientation in space. For l = 1, there are 3 possible ml values, -1, 0, and 1. From the diagram you can see that changing ml does not affect the n-shell or shape of the electron's orbital, but only its rotation.

As the value of l increases, the shape of the orbital gets increasingly complex. As a result, there are more possible values of ml since there are more ways for the shape to be oriented.

Periodic Table Usage Explained

From the articles about n and l, you should be familiar that the n-value of the

Formulas

Values of ml for a given l:

{ -l , -(l - 1) , ..., 0 , ... , (l - 1) , l }

Number of possible value of ml for a given n:

n2

Usage with the Periodic Table

(Atomic Theory)

Practice

1) How many ml values are there for l = 4?

Answer: 9 (ml could be -4, -3, -2, -1, 0, 1, 2, 3, or 4)

2) How many possible values of ml are there for n = 2?

Answer: 4 ( 22 = 4 )

More Information

Wikipedia

Britannica

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