The shorter the wavelength the more likely radiation damage will be. What is the objective of your research? The shortest wavelength at which radiation is present in sunlight at ground level is around 290 nm. As one can infer from the use of `germicidal' UV lamps emitting at 254 nm to sterilize lab benches used in microbiology, the emission of your light source near this region will dominate the effect you see in the response.
Yes, I would expect cell-damage from an UV radiation source emitting at wavelengths as short as 250 nm. Photons at this wavelength have enough energy to break chemical bonds. Nucleic acids and some amino acids could be affected directly by photoreactions. ROS could affect lipids. UV radiation could cause cell death depending on the length of exposure and irradiance and the organism in question.
The normal protocol in UV research is to filter UVB lamps with cellulose diacetate film (approx. 0.125 mm thick) that behaves like a long-pass filter cutting at a wavelength of approximately 285 nm. Take into account that this films degrade quickly and need to be replaced frequently (tens of hours of use). Of course one can also use optical-glass filters, which suffer very little degradation, but they are expensive. Removing short-wave UV avoids unrealistic damage. This does not mean that a big enough dose from a filtered lamp cannot cause damage, but such damage can be thought to be also `possible' under sunlight.
Other factors affect the possibility of damage. In general exposure to ultraviolet radiation in the absence of visible radiation is likely to be much more damaging than in the presence of UVA and VIS light. This is because DNA photo-repair depends on UVA and blue light.
You do not say what is the organism under study and whether you are working with cells in culture. In most cases organisms (plants and animals at least) can acclimate and attain some degree of protection. For example the UV absorbance of the epidermis of plants can increase drastically in response to blue light and UV radiation. So history of cells/organisms and protocol used also affect the degree of damage.
At the very least you have to take into account that, for example, a very small dose of UV radiation at 254 nm, can have a larger effect and cause more cell damage than a much larger dose of UV radiation at longer wavelengths.
Note 1: above I mention 254 nm as this is one of the emission lines of mercury, and is present in most UV and other fluorescent lamps unless filtered (either by the user or the manufacturer of the lamp).
Note 2: be aware that working with/near lamps emitting UV radiation can be damaging also to the health of persons using them. Proper skin and eye protection is required.
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Our work focuses on skin cells and UVB, since UVB is more mutagenic and energetic that UVA. We use a special meter to measure an approximate dose in mJ/cm2. We also use a Kodacel filter to remove all UVC and about ~90% of UVB, which allows it to resemble a model closer to that of solar exposure.
What wavelength do you want to study? UVA (320-400), UVB (280-320) and UVC (100-280) will certainly induce lots of DNA damage and cell death in your cells. If you are trying to measure for more specific UV-induced DNA damage (CPD and 6,4-PP), then it would be better to focus on UVB, as this wavelength is more readily absorbed by DNA.
That spectrum falls within UVA. Normally this wavelength isn't absorbed by DNA but it can generate ROS which indirectly damages the DNA, proteins and can cause lipid peroxidation. It has also been shown that UVA can cause the UVB signature mutations (CPD and 6,4-PP) but the mechanism of how this occurs is not well understood. You will definitely get cell death with UVA.
As you work with photocrosslinking of peptides I asume that you're asking for your skin. If you're working with any source of UV radiation you should protect your skin from it. If you are exposed, you will suffer acute skin burns. Moreover, as the exposures turns chronic, you're increasing the risk of developing an skin cancer.
I strongly suggest you to take the propper care when you handle the UV lamp.