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what elements is represented by each electron cofiguration

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[Ar]4s2 is Ca (calcium). 

Find argon on the periodic table. Count over 2 more elements (hence the "2").

[Kr]5s2 4d10 5p4 is Te (tellerium).

Alternatively, you could learn to identify different regions of the periodic table by their "blocks" (i.e., s-block, p-block, d-block). This website has a good image that identifies each. This element can be found by counting down five rows in the p-block (don't forget He!) and over four elements.

Just to add to Elizabeth,

The cores in your example are Argon and Krypton. Use the core a s a guide and as you add electrons to orbitals you would form new elements.

In the example, 4s1 is potassium then 4s2 is Calcium then next orbitals are the 3d orbitals and you have ten electrons total and then the 4p orbitals with 6 but you have to know what orbitals the electrons go in to correctly write the notation.



To keep it really simple, Ar has 18 electrons. Then adding the 2 electrons of the 4s orbital , we get 20 which is the atomic number of Calcium whose symbol is Ca. 

Similarly, Kr has 36 electrons. Then adding the 2 electrons of 5s, 10 electrons of 4d and 4 electrons of 5p orbitals, we get 36 + 2 + 10 + 4 = 52 and this is the atomic number of Tellurium whose symbol is Te. 

Now you could apply this to other similar questions using the periodic table.