You are a scientist trying to develop a technology that can be used to power wrist watches. which type of electromagnetic wave would be most useful to investigate? gamma rays, because they are powerful and safe. infrared waves, because they do not produce heat and have high energy. ultraviolet waves, because they have moderate energy and are abundant. microwaves, because they are powerful and available.

Well I don't know.  Let's examine the choices one at a time:

-- Gamma rays ... NO, they are NOT safe.

-- Infrared waves ... NO, they DO produce heat.

-- Ultraviolet waves ... Maybe.  They have plenty of energy, and they're abundant in sunlight.  But unrestricted exposure to them is somewhat dangerous.  

-- Microwaves ... Maybe.  They can be generated with plenty of energy, with inexpensive devices. (They're even used, in most homes, to warm up leftover meatloaf.)  They're safe at moderate power levels, and they're actually all over the place right now.

I think my personal choice is microwaves.