What is the least abundant element on the earth's atmosphere?

The order of elements in the atmosphere is nitrogen (78.1%), oxygen (20.9%), argon (0.96%), followed by (in uncertain order) carbon and hydrogen. The carbon and hydrogen concentrations are variable for a number of reasons, including human activity. Sulfur, phosphorus, and all other elements are present in significantly lower proportions.

According to the above graphic, argon, a significant if not major component of the atmosphere, does not appear in the crust at all.

https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elements#Atmosphere

Difficult to answer this; all those that do not occur at all I suppose, like iron, uranium, gold, etc.

A difficult question to answer because there are a lot of "trace elements" in the atmosphere, which without our help would not normally be there.

Francium is the least abundant element on earth because it is the most unstable. It has a half-life of 22 minutes and estimates suggest that only one atom of naturally occurring Francium exsists on the Earth at any one time. If this were to get into the atmosphere, theres the answer!