Re: Hund's rule for Phosphorus(15)

Let's work through your question in stages.

Yes, the ground state electron configuration for phosphorus is 3s(2) 3p(3), which means that each p-orbital has 1 electron.

Because each p-orbital has 1 electron, they are all taken as having spin equal to +½. Therefore the spin S = 3 × ½ = ³/₂, and the superscript number in the term symbol is 2(³/₂) + 1 = 4.

The valence electrons have the following m_l values:

• Each s-electron has m_l = 0, summing to zero.
• Each p-electron has a different m_l value -- 1, 0 and -1 -- but they also add to zero.

Since L=0, the J value (the subscript in the term symbol) is equal to the spin, which is ³/₂.

Therefore, the term symbol for ground-state phosphorus is ⁴S_3/2.

ref: Wikipedia's term symbol article