Final answer:
Based on the criterion that tissue damage is directly proportional to the charge of the irradiating particle, gamma rays, which are uncharged, would cause the least damage to the tissue compared to alpha, beta, and positron radiation.
Step-by-step explanation:
When considering types of radiation and their potential to cause damage to tissue, it is essential to take into account their ability to penetrate material and the charge on the irradiating particle. Alpha particles possess a relatively high charge (+2e) and are massive, thus they have a high ionizing power and the greatest capacity to damage tissue if they are inside the body. However, due to their size, they have very low penetration power and can be blocked by something as simple as a sheet of paper or the outer layer of skin. Beta particles (electrons) and positrons (anti-electrons) have a single negative or positive charge (-e or +e), respectively, and are lighter than alpha particles, meaning they have a greater ability to penetrate tissues but cause less damage per particle due to their lower charge. Finally, gamma rays are uncharged and can penetrate tissues and materials very effectively, but since the damage is directly proportional to the charge of the irradiating particle, and gamma rays are uncharged, they will cause the least damage based on the specific criterion provided in the question.