TLDR: A beta emitting sample will likely produce more damage than a gamma emitting sample due to the associated quality factors. An alpha emitting sample will do zero damage.
A question like this is quite nuanced, so let’s dive in.
Radiation that is made of charged particles (like alpha and beta) behave differently than radiation that is made up of neutral particles (like gamma). Charged particles are characterized by their “range”, which describes how far that particle can go through a medium (like air) before they lose their kinetic energy and become harmless. Alpha particles are relatively heavy and have a range of 1-10 cm in air at atmospheric pressure, so a sample that is an alpha emitter placed on the opposite side of the room will have exactly zero potential of dealing damage to you. You’re simply too far away. For a beta emitter, the range of beta particles is about 4 meters per MeV (a measure of the particle’s energy). This means that a low energy beta can reach you from across the room, and higher energy betas can easily reach you.
Neutral particles are not characterized by ranges, as they interact with matter differently. Instead, they are characterized by “half-thicknesses” based on an exponential attenuation function. The half-thickness of a material is the thickness of the material needed to reduce the intensity of the gamma rays to one-half the original intensity. Because of this, a gamma emitting sample will easily be able to affect you just like a beta sample would be. We now have to use something else to determine which will be worse.
In radiative studies, there exists a parameter for radiation types called the “quality factor”, which adjusts the value for radiation doses to account for the biological impact of each type of radiation. For example, if you were exposed to two different types of radiation with the exact same dose but one had a quality factor of one and the other had a QF of ten, then the radiation with a QF of ten did essentially ten times more damage than the other. Gamma rays have a quality factor of 1, whereas beta rays can have a QF anywhere from 1-20 based on their energy (higher energy = higher QF). Because of this, the beta emitter will likely do more damage than the gamma emitter.
Hope this helps!
