Which unit measures the absorbed radiation that accounts for biological damage?

The unit that measures absorbed radiation accounting for biological damage is the REM (Roentgen Equivalent Man). The REM is specifically designed to quantify the biological effects of ionizing radiation on human tissues, taking into account not just the amount of radiation absorbed but also the type of radiation and its potential to cause harm. This is essential in radiation protection because different types of radiation (such as alpha particles, beta particles, and gamma rays) have varying capacities to cause damage to biological systems.

In practice, while the Gray measures the physical amount of radiation energy absorbed by tissue (1 Gray = 1 joule per kilogram), it does not address the varying biological impacts different radiation types may have. The REM, on the other hand, utilizes a quality factor to adjust for these differences, thus providing a more accurate representation of potential biological effects.

The other units listed, such as Becquerel (which measures radioactivity) and Coulomb/kilogram (which measures ionization in air), do not provide a direct measure of the biological impact of radiation exposure on human health. Hence, REM is the most appropriate answer in the context of assessing radiation safety and potential biological damage.