Which type of ionizing radiation travels in torturous paths as it passes through an absorbing material?

The type of ionizing radiation that travels in tortuous or erratic paths as it passes through absorbing materials is beta particles. This is primarily due to the interaction characteristics of beta particles, which are high-energy electrons. As these particles move through matter, they experience a series of scattering events due to their charge and relatively low mass compared to alpha particles.

Unlike alpha particles, which are much heavier and can be stopped by a sheet of paper or even the outer layer of skin, beta particles can penetrate deeper into materials but still interact with the electrons in the absorbing material. This interaction results in a deviation from a straight-line path, causing the beta particles to follow a convoluted trajectory.

Gamma rays and X-rays, being electromagnetic radiation, typically travel in more linear paths and are less likely to be deflected significantly by matter compared to charged particles. Thus, while they may experience some scattering, it is not as pronounced or tortuous as the paths taken by beta particles.