The key difference between magnetic quantum number and spin quantum number is that magnetic quantum number is useful in differentiating orbitals available within subshells, whereas spin quantum number describes the energy, shape and orientation of an orbital.
Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. There are four specific quantum numbers: principal quantum number, angular quantum number, magnetic quantum number and spin quantum number.
CONTENTS
1. Overview and Key Difference
2. What is Magnetic Quantum Number
3. What is Spin Quantum Number
4. Side by Side Comparison – Magnetic Quantum Number vs Spin Quantum Number in Tabular Form
5. Summary
What is Magnetic Quantum Number?
Magnetic quantum number differentiates orbitals available within subshells. The symbol for this value is mi. According to its definition, this quantum number states that the electrons in each particular subshell have angular quantum numbers that range from –l to +l plus zero. Therefore, s, p, d and f subshells contain different numbers of orbitals. The following table shows the number of orbitals present in each subshell.
| Subshell | Values for magnetic quantum number | Number of orbitals |
| s | mi=0 | 1 |
| p | mi=-1,0,+1 | 3 |
| d | mi=-2,-1,0,+1,+2 | 5 |
| f | mi=-3,-2,-1,0,+1,+2,+3 | 7 |
The magnetic quantum number determines the energy shift of an orbital that occurs due to the magnetic field applied externally. We call this effect the “Zeeman effect”. The actual magnetic moment arises from two factors: electron angular moment and electron spin, which are described from the magnetic quantum number.
What is Spin Quantum Number?
Spin quantum number describes the energy, shape and orientation of an orbital. The symbol for this value is “s”. The spin quantum number is a parameter of the intrinsic angular momentum of an atom. The spin angular momentum of an electron in an orbital is given as s=1/2.
Figure 02: Effect of an External Magnetic Field on an Electron
An orbital can contain a pair of electrons; hence, the two electrons have s=-1/2 and s=+1/2 spin quantum numbers. It refers to the “spin-up” and “spin-down” orientations of electrons. The quantum number specifies the quantum state of a particular electron of an atom. Furthermore, we can give a “total spin quantum number” (S), which couples the spins of several unpaired electrons of some certain atoms.
What is the Difference Between Magnetic Quantum Number and Spin Quantum Number?
Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. The key difference between magnetic quantum number and spin quantum number is that magnetic quantum number is useful in differentiating orbitals available within subshells, whereas spin quantum number describes the energy, shape and orientation of an orbital. The values for magnetic quantum number is given as –l, 0 and +l. The symbol for this value is mi. But, the spin quantum number is given as -1/2 and +1/2. The symbol for this value is “s”.
Moreover, a further difference between magnetic quantum number and spin quantum number is that the magnetic quantum number describes the energy shift of an orbital that occurs due to the magnetic field applied externally, while the spin quantum number describes the intrinsic angular momentum of an atom.
Summary – Magnetic Quantum Number vs Spin Quantum Number
Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. The key difference between magnetic quantum number and spin quantum number is that magnetic quantum number is useful in differentiating orbitals available within subshells, whereas spin quantum number describes the energy, shape and orientation of an orbital.
Reference:
1. “Quantum Numbers for Atoms.” Chemistry LibreTexts, Libretexts, 27 Sept. 2019, Available here.
2. “Magnetic Quantum Number.” Wikipedia, Wikimedia Foundation, 16 Nov. 2019, Available here.
3. “Spin Quantum Number.” Wikipedia, Wikimedia Foundation, 1 Sept. 2019, Available here.
4. Helmenstine, Anne Marie. “Spin Quantum Number Definition.” ThoughtCo, Dec. 7, 2018, Available here.
Image Courtesy:
1. “Atomic orbitals spdf m-eigenstates” By Geek3 – Own work, Created with hydrogen 1.1 (CC BY-SA 4.0) via Commons Wikimedia
2. “Two negatively charged particles spinning in a magnetic field” By CK-12 Foundation – File:High School Chemistry.pdf, page 280 (CC BY-SA 3.0) via Commons Wikimedia