using the trends in the periodic table, rank the following atoms in order of increasing electronegativity. k, rb,

The trend for electronegativity in the periodic table generally increases from left to right across a period and decreases from top to bottom within a group.

K (Potassium) is in Group 1 (alkali metals) and has an electronegativity of 0.82 on the Pauling scale.
Rb (Rubidium) is also in Group 1 and has a slightly higher electronegativity of 0.82 as well.

Since both atoms are in the same group, they have similar electronegativities and it is difficult to determine which one is higher.

Therefore, the ranking in increasing electronegativity is:
K = Rb