The radiation dose received by an object is measured in units of grays (Gy), where 1 Gy = 1 J/kg. A technician uses a proton beam that delivers energy at a rate of 1 × 1016 eV/s to treat a 50 g region of tissue. If the beam runs for 1 min, what is the dose received by the tissue?A.0.03 GyB.0.2 GyC.2 GyD.100 Gy
Question
The radiation dose received by an object is measured in units of grays (Gy), where 1 Gy = 1 J/kg. A technician uses a proton beam that delivers energy at a rate of 1 × 1016 eV/s to treat a 50 g region of tissue. If the beam runs for 1 min, what is the dose received by the tissue?A.0.03 GyB.0.2 GyC.2 GyD.100 Gy
Solution
First, we need to convert everything to the same units.
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Convert the energy rate from eV/s to J/s. We know that 1 eV = 1.6 x 10^-19 J. So, 1 x 10^16 eV/s = 1 x 10^16 * 1.6 x 10^-19 J/s = 1.6 x 10^-3 J/s.
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Convert the time from minutes to seconds. We know that 1 min = 60 s. So, 1 min = 60 s.
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Calculate the total energy delivered by the proton beam. Energy = power x time = 1.6 x 10^-3 J/s x 60 s = 0.096 J.
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Convert the mass of the tissue from g to kg. We know that 1 g = 0.001 kg. So, 50 g = 0.05 kg.
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Calculate the radiation dose received by the tissue. Dose = Energy/Mass = 0.096 J / 0.05 kg = 1.92 Gy.
So, the dose received by the tissue is closest to 2 Gy. Therefore, the answer is C. 2 Gy.
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