Question

what is the $m_{s}$ value (magnetic spin) for the electronic configuration diagram for argon?

1. sulfur, s, 16
2. argon, ar, 18
3. aluminum, al, 13
4. sodium, na, 11

+3
+1/2
-3
-1/2
+8

Explanation:

The magnetic spin quantum number \(m_s\) has only two possible values, \(+\frac{1}{2}\) (spin - up) and \(-\frac{1}{2}\) (spin - down). In a filled orbital (where there are two electrons), the electrons have opposite spins. Argon has a completely filled electron configuration. For each pair of electrons in an orbital, one has \(m_s =+\frac{1}{2}\) and the other has \(m_s =-\frac{1}{2}\). But when considering the overall spin for a closed - shell configuration (all orbitals filled), the net spin is zero. However, looking at the individual electron spin values in the diagram (since each pair of arrows in an orbital represents \(+\frac{1}{2}\) and \(-\frac{1}{2}\)), but if we assume the question is referring to the spin of an electron in a filled orbital (as all orbitals are filled in Ar), for any single electron in a filled orbital, the possible \(m_s\) values are \(+\frac{1}{2}\) or \(-\frac{1}{2}\).

Answer:

\(+\frac{1}{2}\) and \(-\frac{1}{2}\) (but if we consider the options given and the fact that in a filled orbital, electrons have these two possible spin values. If we assume the question is about the possible values for an electron in Ar's configuration, from the options, both \(+\frac{1}{2}\) and \(-\frac{1}{2}\) are correct. But if we consider the spin of an electron in a pair (since all orbitals are filled in Ar), \(+\frac{1}{2}\) and \(-\frac{1}{2}\) are the possible \(m_s\) values. Among the given options, \(+\frac{1}{2}\) and \(-\frac{1}{2}\) are valid. If we assume the question is about the spin of an electron (not the net spin of the atom), then both \(+\frac{1}{2}\) (as an option) and \(-\frac{1}{2}\) (as an option) are correct. But if we consider the spin of an electron in a pair (as per electron - pairing in orbitals), \(+\frac{1}{2}\) and \(-\frac{1}{2}\) are the possible \(m_s\) values. So the answers are \(+\frac{1}{2}\) and \(-\frac{1}{2}\) (i.e., B. \(+\frac{1}{2}\) and D. \(-\frac{1}{2}\))