Final answer:
To order the atoms K and Cs according to increasing ionization energy, we look at their positions in the periodic table. Cs will have the smallest ionization energy followed by K, since Cs is located further down the same group as K.
Step-by-step explanation:
The question involves ordering atoms or ions based on their ionization energy. Ionization energy is the energy required to remove an electron from an atom or ion in the gas phase. Within the periodic table, ionization energy tends to increase from left to right across a period and from bottom to top up a group. Thus, for the alkali metals such as potassium (K) and cesium (Cs), we can predict that Cs will have the smallest ionization energy followed by K, as Cs is located below K in the same group on the periodic table. The order of increasing ionization energy for the specified elements or ions will be as follows: Cs, K.
Additionally, when we look at elements forming a rectangle in the periodic table and considering that we are looking at elements in the two far-left columns, the one at the bottom left (such as Rb) would have the lowest ionization energy, according to the trends of the periodic table.