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What is the dose in mSv for: (a) a 0.1 Gy x-ray? (b) 2.5 mGy of neutron exposure to the eye? (c) 1.5 mGy of $\alpha$ exposure?
Question by OpenStax is licensed under CC BY 4.0.
1. $100\textrm{ mSv}$
2. $80\textrm{ mSv}$
3. $23\textrm{ mSv}$
Note: the video has an error in the calculation for part (c). The working is correct, but the final answer should be $23 \textrm{ mSv}$
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 32, Problem 8 (Problems & Exercises) (2:08)

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This is College Physics Answers with Shaun Dychko. Part (a) of this question is asking what is the dose equivalent in millisieverts of 0.1 grays of x-rays? So the grays is a unit to describe the amount of energy absorbed per kilogram of tissue but it doesn't take into account the type of ionizing radiation and different types have different amounts of effect indicated by this relative biological effectiveness. So the dose equivalent in millisieverts is the absorbed dose in milligrays multiplied by the relative biological effectiveness. So we have 0.1 grays and we have to multiply that by 1000 milligrays for every gray if we want to have our units of millisieverts in our answer then we multiply by RBE of x-rays, which is 1 and so we have 100 millisieverts then is the dose equivalent. In part (b), we have 2.5 milligrays of neutrons to the eye and the dose equivalent then is going to be 2.5 milligrays multiplied by the RBE and the RBE is a little bit hard to know what it should be because we have neutrons that are thermal to slow which have RBE of 2 to 5 or neutrons that are fast, which for the eye would be 32. So are these fast neutrons or are they slow ones? Well since the question specifically says "eyes," I think what they are getting at is this number here so 32 is the number that we will use. So we have 32 times 2.50 milligrays gives 80 millisieverts. Part (c) says we have 1.50 milligrays of alpha particles and so the dose equivalent then is 1.5 milligrays times the RBE for alpha particles, which is between 10 and 20 so I just took 15— taking the middle of that range for the relative biological effectiveness— and this gives an answer of 38 millisieverts is the dose equivalent.