The electrons around every element are arranged in energy levels: a maximum of 2 electrons in the first level, a maximum of 8 in the second energy level, and a maximum of 8 in the third energy level. If an element has an outermost energy level that is not at the maximum it will combine with other elements by gaining, losing, or sharing electrons so the outside energy level is complete.
Now look at the electron arrangement for Argon. Argon has an atomic number of 18 which means it has 18 protons in the nucleus and 18 electrons surrounding the nucleus. The first energy level will take 2 electrons, leaving 16. The second energy level will take 8, leaving 8. The third energy level will take the final 8 electrons and is full. Because all energy levels are full, Argon will not combine with other elements to form chemical bonds.
Argon is a very unreactive element as it already has a full outer shell.
Here is the concept of electron shells for elements:
An element would have a full inner or first shell with a maximum of two electrons. The second shell would have a maximum of eight shells, as with the third shell too and so on. If an element does not have full electron shells, it would either give or take electrons (ionic bonding) or share electrons (covalent bonding).
Argon has an atomic number of 18 which means that it has 18 electrons. This means that it has a full outer shell and thus would not have to bond or share with other elements to gain or lose any more electrons. Argon is one of the six unreactive elements which have full outer shells: helium, neon, argon, krypton, xenon and radon, which are the noble gases in Group VIII of the periodic table.