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If you do a chemistry degree you will likely have entire modules revolving around this and various trends. The Periodic Table is actually set up extremely carefully and cleverly.

I'll give a quick overview.

4 Blocks:

S Block - (Columns 1 and 2) - Valence electrons of elements is in the S orbital.

D Block - (Columns 3 - 12) - Valence electrons of elements is in the D orbital.

P Block - (Columns 13 - 18) - Valence electrons of elements is in the P orbital.

F Block - (Those 2 rows at the bottom, separate) - Valence electrons in F orbital.

And that makes sense. S shell holds 2 electrons, it has 2 columns. P shell holds 6 electrons, gets 6 columns and etc etc. So now we can see that S block column 2 has valence S2. Row 6 is P block. Valence is s2, p4. Total of 6 electrons.

Since we can tell a LOT about an element's properties from its valence electrons, a glance at the periodic table proves to be extremely useful. The more you use it, the more obvious the trends become.

We also get trends like electronegativity increasing toward the top right...and a hundred other trends, again it only takes a quick look at the periodic table to gain important knowledge.

The rows, usually numbered down the left-side of the table show us what number our valence shell is (tells us the principle quantum number of the valence shell, n).

For example: Vanadium is in D block. It's in group 5 and row 4. Right away I know Vanadium has 3d3 4s2 valence. D-Blocks have funny little quirks with how their shells fill but don't worry too much about that. Practice a few and it'll become very easy.

The F-Block is kept well out of the way, which is a good idea considering they are generally less used...but more importantly, it keeps the table in a useful format.

Plus it groups the F-Block together, which share some chemical properties and can be useful to view as a separate group.

In almost any chemistry subject you do, there WILL be trends relating to it on the periodic table, just look for them. And good chemists can do huge amounts of work with atoms they know nothing about, using just the periodic table and some know-how.

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