The formula presented (S = n/2) is a simplification and potentially misleading. The spin quantum number (s) is an intrinsic property of elementary particles and is not calculated in the same way as other quantum numbers like the principal quantum number (n). Its value is inherent to the particle.
Here's a more accurate explanation:
-
Spin Quantum Number (s): This number describes the intrinsic angular momentum of a particle, which is quantized. It's a fundamental property, like mass or charge.
-
Possible Values: For fundamental particles like electrons, protons, and neutrons, the spin quantum number (s) is either 1/2 or an integer. The most common value you'll encounter in chemistry is s = 1/2 for electrons.
-
Spin Angular Momentum: The magnitude of the spin angular momentum (S) is given by:
S = ħ√(s(s+1))
where:
- S is the spin angular momentum
- ħ (h-bar) is the reduced Planck constant (h/2π)
- s is the spin quantum number
-
Spin Magnetic Quantum Number (ms): This quantum number describes the orientation of the spin angular momentum in a magnetic field. For a given value of s, ms can have values ranging from -s to +s in integer steps. For an electron (s = 1/2), ms can be either +1/2 (spin up) or -1/2 (spin down).
Why the S = n/2 is Incorrect:
The formula 'S = n/2' provided in the reference is highly misleading and is not the standard or correct way to determine spin quantum numbers. 'n' usually represents the principal quantum number which describes the energy level of an electron. These are entirely different concepts.
Example:
For an electron, s = 1/2. Therefore:
S = ħ√(1/2(1/2+1)) = ħ√(3/4) = (ħ√3)/2
ms = +1/2 (spin up) or ms = -1/2 (spin down)
In Summary: You don't calculate the spin quantum number (s) for fundamental particles. It's a fundamental property. You are more likely working with it as s=1/2 for electrons to understand spin angular momentum (S) and the spin magnetic quantum number (ms).
