The Half-Value layer thickness of a material varies with:

The Half-Value Layer (HVL) thickness of a material primarily varies with the energy of the radiation. This relationship is based on the principle that higher energy radiation is more penetrating and, therefore, requires a thicker layer of material to reduce its intensity by half. As the energy increases, the ability of the material to attenuate the radiation decreases, resulting in a larger HVL.

Understanding that HVL is a measure of how much material is needed to reduce the radiation intensity to half is key. The dependence on energy means that different types of radiation, such as gamma rays or X-rays, will have varying HVL measurements based on their specific energy levels.

While distance and intensity are important concepts in radiation physics, they do not directly affect the HVL of a material in the same manner that energy does. The square of the distance relates more to the inverse square law governing radiation intensity, while the square of intensity pertains to how intensity diminishes with distance or attenuation. However, these principles do not influence the material's HVL directly. Thus, the answer regarding energy reflects the core concept of how HVL behaves with respect to radiation characteristics.