Final answer:
To determine the exposure in Gy needed to achieve a 40 Sv dose when exposed to α particles, we use the equation Sv = Gy × RBE with an RBE of 20 for α particles. After calculating, we find that the exposure needed is 2 Gy, which is not listed in the provided options, suggesting a potential error in the choices.
Step-by-step explanation:
To answer how many Gy of exposure is necessary to administer a dose of 40 Sv to a cancerous tumor when exposed to α (alpha) activity, we must utilize the equation Sv = Gy × RBE (RBE stands for Relative Biological Effectiveness). For α particles, the RBE is generally assumed to be around 20, because α particles cause more biological damage per Gy than x-rays or γ-rays, for which the RBE is set to 1 by definition.
To calculate the required Gy, we rearrange the equation to Gy = Sv/RBE. So, with a dose of 40 Sv using α particles that have an RBE of 20, the equation becomes Gy = 40 Sv / 20.
By performing this calculation, we find that the exposure in Gy is 40 Sv / 20 = 2 Gy, which is equivalent to 2000 mGy. Therefore, the correct exposure required to give a cancerous tumor a dose of 40 Sv if it is exposed to α activity is 2 Gy, which isn’t one of the listed options, so there might be an error in the given options.