Z component of spin angular momentum quantum number values

In summary, the quantum number S_z is limited to non-zero values in nonrelativistic quantum mechanics, but can have a value of zero for a spin 1 particle in a relativistic context. However, for a spin 1/2 particle, the quantum number can have values of -1/2, 0, and 1/2, indicating the orientation of the angular momentum in the xy plane. This is a consequence of the 1/2 angular momentum itself.
  • #1
LostConjugate
850
3
Hello,

What prevents the S_z quantum number from having a value of zero? With a standard angular momentum system the quantum number can have values between -l and +l.
 
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  • #2
Technically, in nonrelativistic QM a spin 1 particle can have m_s = 0. However, a particle with spin 1 is properly described in a relativistic context, where m_s loses its nonrelativistic meaning and the concept of helicity steps in.
 
  • #3
What about spin of 1/2? It should still be able to have -1/2, 0, and 1/2. Zero in the z component as a quantum number just means that the angular momentum cone is roughly pointing somewhere in the xy plane.
 
  • #4
No, no, the weights must differ by 1, so it's -1/2, then +1/2.
 
  • #5
dextercioby said:
No, no, the weights must differ by 1, so it's -1/2, then +1/2.

Oh, so it is a consequence of the 1/2 angular momentum itself. How is a general direction of the angular momentum in the xy plane represented then?
 

FAQ: Z component of spin angular momentum quantum number values

1. What is the Z component of spin angular momentum quantum number?

The Z component of spin angular momentum quantum number, often denoted as ms, is a quantum number that describes the orientation of the electron's spin in a magnetic field. It can have values of +1/2 or -1/2, representing the electron's spin being aligned with or against the magnetic field, respectively.

2. How is the Z component of spin angular momentum quantum number related to the spin quantum number?

The spin quantum number, denoted as s, represents the magnitude of the electron's spin. It is related to the Z component of spin angular momentum quantum number through the equation ms = s(s+1)ħ, where ħ is the reduced Planck's constant.

3. How does the Z component of spin angular momentum quantum number affect the energy levels of an atom?

The Z component of spin angular momentum quantum number affects the energy levels of an atom through the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers. This means that electrons with different ms values will have slightly different energy levels.

4. Can the Z component of spin angular momentum quantum number be measured?

Yes, the Z component of spin angular momentum quantum number can be measured through certain experimental techniques, such as electron spin resonance (ESR) spectroscopy. This technique involves applying a magnetic field to the electron and measuring the energy difference between the two spin states, which is proportional to the Z component of spin angular momentum quantum number.

5. How does the Z component of spin angular momentum quantum number affect an atom's chemical properties?

The Z component of spin angular momentum quantum number does not directly affect an atom's chemical properties. However, it indirectly affects the atom's chemical behavior by determining the electron's spin state, which can affect the strength of the electron's interactions with other atoms and molecules. This can ultimately impact the atom's reactivity and chemical properties.

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