Option 1 -> "relentlessly" is an adverb meaning persistently and without stopping, perfectly describing dedicated work over ten years.
Option 2 -> "in excitement" is an adverbial phrase but doesn't fit well grammatically or meaningfully with sustained work over a decade.
Option 3 -> "in the morning every day" is overly specific and doesn't capture the intensity or dedication implied by working on research for ten years.
Option 4 -> "to and fro" means back and forth physically, which doesn't make sense with the verb "worked" in this context.
Hence, Option 1: relentlessly -> This adverb appropriately conveys the persistent, continuous, and determined manner in which someone would dedicate themselves to a long-term research study spanning ten years -> correct