Question

you are a scientists trying to develop a technology that can be used to power wrist watches what type of electromagnetic wave would be most useful to investigate

Answer 1

Well, we have a big, free and constant source of electromagnetic waves: the sun.

The sun's black body spectrum might give you a hint as to which sort of electromagnetic wave is most abundant (so most useful).

You might also want to consider the work function of materials that exhibit the photoelectric effect. It sets a minimum frequency for useful light.