Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency 8.00 × 1014 hz?

The answer is just the wavelength of that light. You cannot resolve details smaller than the wavelength of light you are using to observe. This is why blue ray discs can hold more information than regular red laser CD's. blue lasers make a smaller point, and so you can fit more data on a disc.

The smaller the wavelength, the better the resolution. To find the wavelength simply divide the speed of light by the frequency shown:

2.9 x10^8 / 8 x10^14 = 0.0000003625m
or 3.625 x10^-7m
or 362.5 x10^-9m
or 362.5nm

This did i unseated, sorry