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Question

What is the range of magnetic quantum number ?

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Solution

The range of magnetic quantum number depends on the azimuthal quantum number.
For a certain value of azimuthal quantum number (l) the magnetic quantum number will have all the values between -l. to +l including zero
Azumuthal quantum number indicates the orbital (s,p,d,f) while magnetic quantum number indicates the sub orbital.
The following table indicates the range of magnetic quantum number for various azimuthal quantum number and their significance.
azimuthal quantum number orbital magnetic quantum number sub orbital
0 s 0 s
1 p -1 0 +1 px, py, pz
2 d -2, -1, 0, 1, 2 dxy, dyz, dxz, dx2-y2, dz2

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