Why does a fast film respond to x-rays more quickly than a slow film?

The reason a fast film responds to x-rays more quickly than a slow film is due to the presence of larger silver halide crystals in the film's emulsion. Fast films are designed with these larger crystals, which increase the sensitivity of the film to the radiation. When x-rays hit the film, the size of the crystals allows them to capture the energy more effectively, resulting in a quicker response time and the need for shorter exposure periods.

In contrast, slow films contain smaller silver halide crystals, which means they require a greater amount of x-ray exposure to produce a comparable image. This inherent sensitivity difference is fundamental in radiography, as it impacts both the speed of the procedure and the comfort of the patient, who is exposed to radiation for less time with fast films.

The other given options do not accurately reflect the factors that determine the speed of the film. For instance, the tubehead shutter opening wider does not influence film sensitivity; exposure times being longer for fast films contradicts the definition of what "fast" means in this context; and the use of different processing chemistry is not a determining factor in the response of the film to x-rays.