^{{ar} 4s2
}

{kr} 5s^{2 4d}_{ }^{10 5p4}

^{{ar} 4s2
}

{kr} 5s^{2 4d}_{ }^{10 5p4}

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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 http://www.chemprofessor.com/periodicqm.htm 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, 4s^{1} is potassium then 4s^{2} 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.

Art

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.

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