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How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to $\alpha$ activity?
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$2.7\textrm{ Gy}$
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OpenStax College Physics for AP® Courses Solution, Chapter 32, Problem 10 (Problems & Exercises) (0:54)

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Video Transcript
This is College Physics Answers with Shaun Dychko. What is the absorbed dose in grays for a dose equivalent of 40 sieverts to a tumor that's being hit with alpha radiation? So the dose equivalent in sieverts is the absorbed dose in grays multiplied by the relative biological effectiveness of the type of radiation. So we can divide both sides by the RBE to solve for the absorbed dose in grays. So the absorbed dose is the dose equivalent divided by RBE and we are told that dose equivalent is 40 sieverts and so we have to look up the relative biological effectiveness of alpha radiation. So alpha rays have an RBE between 10 and 20 so I am gonna take 15 in the middle of that range as the RBE. So 40 divided by 15 is 2.7 grays.