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×27th Jan 2020 @ 3 min read

The magnetic quantum number is a set of integers that determine the spatial orientation of an orbital. It defines the orbital and is unique to each orbital for a given value of the azimuthal quantum number. It is symbolized as *m _{l}*.

The number along with the principal quantum number, azimuthal quantum number, and spin quantum number is used to identify each and every electron in an atom. It was introduced by Arnold Sommerfeld, a German theoretical physicist, who also proposed the azimuthal quantum number.

It determines the direction of the orbital angular momentum. The magnetic quantum number does not decide the energy of an orbital. However, it affects the energy of an orbital in the presence of an external static magnetic field. The magnetic quantum number together with the spin quantum number contributes to the magnetic moment of an electron.

The values of the magnetic quantum number are restricted by the azimuthal quantum number *l*. For a given value of *l*, we can have 2*l* + 1 possible values of *m _{l}*, ranging from −

For *l* = 0, *m _{l}* = 0. This represents an s orbital, which is spherical in shape. For an s orbital, the orbital angular momentum is zero and it does not point in any specific directions.

For *l* = 1, *m _{l}* = {−1, 0, 1}. Each value represents a p orbital. When

*l* = 2 is the d subshell and it has five orbitals. The magnetic quantum numbers for d subshell are −2, −1, 0, 1, and 2. *m _{l}* = 0 is the d

*l* for f subshell is 3 and its has seven orbitals: f_{z3}, f_{xz2}, f_{yz2}, f_{xyz}, f_{z(x2 − y2)}, f_{x(x2 − 3y2)}, and f_{y(3x2 − y2)}. And the magnetic quantum number associated with these orbitals are −3, −2, −1, 0, 1, 2, and 3.

Similarly for g orbital, *m _{l}* = −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, and 5.

Each orbital can hold utmost two electrons. Thus, every *m _{l}* can have two electrons; however, it cannot distinguish those two electrons. They can only be identified by the spin quantum number.

The magnetic quantum number *m _{l}* depends on the azimuthal quantum number

Therefore, *n*^{2} values of *m _{l}* are possible for every

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Thanks for your response!

Kalyani

27th Mar 2020

27th Mar 2020

For p_{x} and p_{y}, how do we decide which one will have 1 or −1 value? Is there any order?
Reply:
No, there is no order. For p_{z}, it is clear: *m*_{l} = 0. But for p_{x} and p_{y}, it is wrong to assign 1 or −1 to anyone.

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