Question

Rank the following elements by increasing atomic radius: carbon, aluminum, oxygen, potassium.

Answer 1

A chemical element's atomic radius is a measurement of the size of its atoms, generally the mean or normal distance between the nucleus's centre and the border of the surrounding electron shells. There are numerous non-equivalent definitions of atomic radius since the border is not a well-defined physical object.

Complete answer:
Typically, atomic radius is measured in a bound form because of the difficulties of isolating atoms to measure their radii individually; nevertheless, theoretical calculations are much easier when considering atoms in isolation. The interdependence of the environment, probe, and condition results in a plethora of definitions.
The fact that only two of these four elements, C and O, are in the same row (period) of the periodic table is significant; the other two, Al and K, do not share a period with C and O, nor with each other, since Al is in the third period and K is in the fourth.
Because both of the periodic patterns in atomic size are visible here, you'll be able to quickly rank them in order of increasing atomic radius.
Let's start with C and O. Because of the rise in effective nuclear charge, we know that atomic radius decreases from left to right over time.
The number of protons increases in lockstep with the number of electrons as you move to the right within a period; however, electrons are added to the same energy level across periods, which means that the increasing number of protons allows the nucleus to exert more pull on these electrons, reducing the atomic radius. Because C occurs before O in the second period, O's atomic radius will be lower than C's.
As previously stated, Al and K do not share a period. The other periodic tendencies come into play at this point. The atomic radius rises as you travel down a column (a group) of the periodic table.
Because electrons are now being added to higher energy levels, further away from the nucleus, the nucleus' attraction is weakening. The electron shielding effect, which asserts that electrons at higher energy levels are protected by those closer to the nucleus, further lowering the nucleus' force on them, is another cause for the increase in atomic radius.
As a result, Al's atomic radius will be lower than K's, but larger than C's and O's.
Hence In terms of increasing atomic radius, this is the right sequence $O < C < Al < K$

Note:
Electrons lack fixed orbits and well defined ranges. Instead, their locations must be represented as probability distributions that taper off gradually as one travels out from the nucleus, with no sudden cutoff; these are known as atomic orbitals or electron clouds. Furthermore, in condensed matter and molecules, atoms' electron clouds frequently overlap, and some electrons may travel across a broad range covering two or more atoms.