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It's determined by the number of electrons Zinc and the order of atomic orbitals.

Zinc has an atomic number of 30 which means it has 30 protons and 30 electrons.

From there, you keep in mind the rules for filling up atomic orbitals with electrons.

  1. S-orbitals can contain a maximum of 2 electrons
  2. P-orbitals can contain a maximum of 6 electrons
  3. D-orbitals can contain a maximum of 10 electrons
  4. F-orbitals can contain a maximum of 14 electrons

From there you must know the order of these orbitals based on increasing energy.

:

You just write down that chart, and point arrows diagonally downward from left to right. That will give you the order no matter how high you go.

I used to write down that chart on scrap paper next t my tests so I could just do the configurations effortlessly.

So getting back to Zinc, you start with the order and then occupy until you have a total of 30 electrons accounted for:

The order, based on the chart is:

1s 2s 2p 3s 3p 4s 3d 4p 5s ..... etc.

Luckily that's all we have to know. Now we fill in based on the occupancy rules. You start with the lowest energy one, 1s and start filling each orbital to the MAX so 1s can only have a maximum of 2 electrons. Then we continue, 2s can have only 2 but 2p can have 6 so we just put all we can because the number 30 hasn't been reached yet.

1s2 2s2 2p6 3s2 3p6 4s2 3d10

Checking our work: (2+2+6+2+6+2+10) = (4+6)+(8+2)+10 = 30

That means all electrons are accounted for and all orbitals are completely filled.

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