if yeast cells are put under UVB radiation how long does it take for the cells to mutate and die?

Answer 1

There is no single answer to this question. When you put the cells under the radiation, there are many cells, and some die immediately, while others can remain unaffected for long periods of time. Generally, scientists determine "dose response" curves (based on the "dose" of UVB radiation) and "survival" curves in looking at the entire population they have to study.
"The major lethal and mutagenic effects of UV radiation to marine organisms results from damage to DNA. The type and extent of damage to DNA is a function of the wavelength and intensity of the exposure. UV-A generally causes indirect damage to DNA through the formation of chemical intermediates such as oxygen and hydroxyl radicals which interact with DNA to form strand breaks, alkali labile sites and DNA protein crosslinks (Peak and Peak, 1989). Conversely, adsorption of energy from UV-B induces direct damage to DNA. The two major lesions induced by UV-B radiation are the cyclobutane pyrimidine dimer and the pyrimidine-pyrimidone (6-4) photoproduct. These photoproducts may be detected and quantified using specific radioimmunoassays (Mitchell et al., 1985)."

Answer 2

Obviously depends on the wavelength and the UV intensity. For saccharomyces cerevisiae with UVC (250nm) the lethal dose is about 13mJ/cm^2. What you need to do is find out the effective intensity of your UV source is at a given range. Say you have 2mW/cm^2 at this distance, then using E=P*t > t=13mJ/2mW=6.5sec. Don't think it kills all the buggers though. Would suspect though that the same dose over a longer time would give the yeast time to self-repair. Dunno if some of the critturs contain multiple back-up copies of their own genome just in case of this very eventuality