The Courier must consume 20 doses of RadAway.
Upon completion of this challenge, RadAway will now remove an additional 10 points of radiation. This applies regardless of Hardcore mode being activated - in Hardcore mode, while RadAway will still reduce radiation over time (as opposed to all at once without Hardcore mode), the amount of radiation removed will still be 10 points higher.
Behind the scenes
The name of this perk is a reference to atoms, molecules, or ions with unpaired electrons on an open shell configuration.