An element has four quantum numbers associated with it. We have
1. principal quantum number (
)
2. azimuthal quantum number (
)
3. magnetic quantum number (
)
4. spin quantum number (
)
To look for each quantum number of Chlorine (Cl), we mus first recall its electronic configuration:
.
1. For
, we need to look for its highest energy level or by simply checking the period that the element belongs to. So for this case, it's
.
2. For
, we need to look for the sublevel where the last electron was assigned. The sublevels, p, d, f are assigned to a value of 0, 1, 2, and 3, respectively. Since the last electron was assigned in p, then
.
3. And for
, the number of orbitals present in Cl is
. The possible magnetic quantum numbers for
are -1, 0, +1. Since there 5 electrons we count starting at -1. So, we have
, we need to determine the spin. Since we have 5 electrons, all the arrows upward are filled in. That means the fifth electron has a spin of +1/2.
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