DNA data storage is a potential alternative to magnetic tape for archival storage purposes, promising substantial gains in information density. Critical to the success of DNA as a storage media is an understanding of the role of environmental factors on the longevity of the stored information. In this paper, we evaluate the effect of exposure to ionizing particle radiation, a cause of data loss in traditional magnetic media, on the longevity of data in DNA data storage pools. We develop a mass action kinetics model to estimate the rate of damage accumulation in DNA strands due to neutron interactions with both nucleotides and residual water molecules, then utilize the model to evaluate the effect several design parameters of a typical DNA data storage scheme have on expected data longevity. Finally, we experimentally validate our model by exposing dried DNA samples to different levels of neutron irradiation and analyzing the resulting error profile. Our results show that particle radiation is not a significant contributor to data loss in DNA data storage pools under typical storage conditions.