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Ch 43: Nuclear Physics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
43장, 문제 37

A 6767-kg person accidentally ingests 0.350.35 Ci of tritium.
(a) Assume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of 5.05.0 keV of energy from the electrons emitted in the decay. The half-life of tritium is 12.312.3 y, and the RBE of the electrons is 1.01.0. Calculate the absorbed dose in rad and the equivalent dose in rem during one week.
(b) The β\(\beta\)^{-} decay of tritium releases more than 5.05.0 keV of energy. Why is the average energy absorbed less than the total energy released in the decay?

검증된 단계별 안내
1
Step 1: Understand the problem and identify the given data. The person has ingested 0.35 Ci of tritium, which spreads uniformly throughout their body. Each decay releases 5.0 keV of energy absorbed by the body. The half-life of tritium is 12.3 years, and the RBE (Relative Biological Effectiveness) is 1.0. We need to calculate the absorbed dose in rad and the equivalent dose in rem for one week. Additionally, we need to explain why the average energy absorbed is less than the total energy released in the decay.
Step 2: Convert the activity from curies (Ci) to disintegrations per second (Bq). Use the conversion factor: 1 Ci = 3.7 × 10^10 Bq. Multiply the given activity (0.35 Ci) by this factor to find the activity in Bq.
Step 3: Calculate the total number of decays in one week. Use the formula for activity: \( N = A \cdot t \), where \( A \) is the activity in Bq and \( t \) is the time in seconds. Convert one week into seconds (1 week = 7 days × 24 hours/day × 3600 seconds/hour). Multiply the activity by the time to find the total number of decays.
Step 4: Calculate the total energy absorbed by the body. Multiply the total number of decays by the average energy absorbed per decay (5.0 keV). Convert the energy from keV to joules using the conversion factor: 1 eV = 1.602 × 10^-19 J. Then, divide the total energy by the mass of the person (67 kg) to find the absorbed dose in rad. Note: 1 rad = 0.01 J/kg.
Step 5: Calculate the equivalent dose in rem. Multiply the absorbed dose in rad by the RBE (1.0 in this case). Finally, for part (b), explain that the average energy absorbed is less than the total energy released because not all the energy from the decay is absorbed by the body. Some energy is carried away by neutrinos or escapes the body as radiation.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha, beta, and gamma decay. In the case of tritium, beta decay occurs, where a neutron is converted into a proton, emitting an electron and an antineutrino. Understanding this process is crucial for calculating the energy released and the biological effects of radiation exposure.
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Absorbed Dose and Equivalent Dose

The absorbed dose is a measure of the energy deposited by ionizing radiation in a given mass of tissue, typically expressed in grays (Gy) or rads. The equivalent dose accounts for the biological effect of the radiation type, using a quality factor known as the Relative Biological Effectiveness (RBE). This is expressed in sieverts (Sv) or rems. These concepts are essential for assessing the potential health risks associated with radiation exposure.
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Energy Transfer in Radiation

When radiation interacts with matter, not all the energy released during decay is absorbed by the surrounding tissue. Factors such as the range of the emitted particles, their energy, and the material properties influence how much energy is actually transferred. In the case of tritium's beta decay, while the total energy released is higher, the average energy absorbed is lower due to these interactions, which must be considered in dose calculations.
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