The chemical element Hydrargyrum (Hg) has two names in English: Quicksilver and Mercury.
Can these two words be used interchangeably? Is one of them more appropriate for a professional context?
No, they are not interchangeable, and yes, one is definitely more appropriate.
To begin with, in any scientific or technical context, do not use quicksilver. It is an archaic term that will reflect badly on whatever it is you have to say precisely because it is archaic. (It would be somewhat similar to "See, the quicksilver doth pour forth out of the vessel. And if thou touchest it, that insidious substance, verily thou shalt become mad.") It would place doubts into the minds of your readers: "Why does this guy use THESE words? Does he really know what he's talking about?" Use mercury unless there's a very specific reason to refer to the element by its Latin name.
In poetic writing, on the other hand, quicksilver is fine. It's very descriptive and puts nice pictures into peoples' minds when they read it. (It's a truly beautiful substance, even if it is poisonous.)
TL;DR: Any of the words for the element may be used in a poetic or casual context. Use mercury anywhere you want to be taken "seriously" in a scientific/technical context.