Potassium is a highly reactive metal while argon is an inert gas. How can you explain this difference based on their electronic configurations?

Hint: Potassium is the element of group 1 and period 4, so its atomic number is 19, therefore there are 19 electrons. Argon is the element of group 18 and period 3, so its atomic number is 18, therefore there are 18 electrons.

Complete answer: Potassium is the element of group 1 and period 4, so its atomic number is 19, therefore there are 19 electrons. Argon is the element of group 18 and period 3, so its atomic number is 18, therefore there are 18 electrons.
We know that each element or compound wants to be stable and according to the electronic configuration we can decide the stability by the octet rule.
Now, we can see the electronic configuration of potassium. There are 19 electrons in it:
$1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{1}}$
Now, let us see the electronic configuration of argon. There are 18 electrons in it:
$1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}$
We can see that the 3^rd shell of the argon is filled because there are 8 electrons in it, so it does not react with other elements and remains stable.
In potassium, the last electron enters the 4s orbital, and if this electron is removed then it will have a stable configuration like argon. So, potassium is very reactive because this electron in the 4s will take place in reactions easily.

Note: There is a series in which the electrons are filled in the orbitals and these orbitals are arranged in the increasing order of energy. The series is:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p