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An organic sample of mass \(4.00 \mathrm{~kg}\) absorbs \(2.00 \mathrm{~mJ}\) via slow neutron radiation \((\mathrm{RBE}=5) .\) What is the dose equivalent (mSv)?

Short Answer

Expert verified
The dose equivalent is 2.50 mSv.

Step by step solution

01

Understand the given data

We are given an organic sample with a mass of \(4.00 \mathrm{~kg}\), and it absorbs \(2.00 \mathrm{~mJ}\) of energy. The relative biological effectiveness (RBE) for the radiation is 5. We need to find the dose equivalent in millisieverts (mSv).
02

Convert energy to joules

The energy absorbed by the sample is given in millijoules (mJ). We first convert this energy into joules (J) for easier calculations:\[ 2.00 \; \mathrm{mJ} = 2.00 \times 10^{-3} \; \mathrm{J} \]
03

Calculate absorbed dose (Gray)

The absorbed dose \(D\) is calculated by dividing the energy absorbed \(E\) by the mass \(m\) of the sample using the formula:\[ D = \frac{E}{m} = \frac{2.00 \times 10^{-3} \; \mathrm{J}}{4.00 \; \mathrm{kg}} = 5.00 \times 10^{-4} \; \mathrm{Gy} \]
04

Calculate dose equivalent (mSv)

The dose equivalent \(H\) is calculated by multiplying the absorbed dose \(D\) by the RBE value. Since we need the answer in mSv, and 1 Sv = 1000 mSv:\[ H = D \times \text{RBE} = 5.00 \times 10^{-4} \; \mathrm{Gy} \times 5 = 2.50 \times 10^{-3} \; \mathrm{Sv} = 2.50 \; \mathrm{mSv} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Organic Sample
An organic sample refers to a material that is composed of carbon-based compounds. Organic samples are commonly found in both biological systems and synthetic materials. In our context, the organic sample being considered has a mass of 4.00 kg. This aspect is crucial in calculating radiation doses because the mass of the material impacts the total energy absorbed. Understanding the composition and mass of the sample is essential for accurately assessing the effects of radiation. It’s important to remember that in radiation physics, the properties of the material, such as being organic, can influence how radiation is absorbed. While the calculations focus on the mass, there are additional considerations about how the radiation could interact differently compared to inorganic materials.

Overall, knowing that the sample is organic sets the groundwork for determining both the absorbed dose and the dose equivalent.
Relative Biological Effectiveness (RBE)
Relative Biological Effectiveness (RBE) is a measure of the potency of different types of radiation in causing biological damage. RBE is a critical factor when assessing the potential health effects of radiation. For different types of radiation, RBE values can vary significantly. The RBE value provided in this exercise is 5, indicating that slow neutron radiation is five times more effective in causing damage than standard X-ray or gamma-ray radiation.

RBE is used to adjust the absorbed dose value to reflect the actual biological risk accurately. This adjustment is necessary because just knowing the amount of energy absorbed (measured in Grays) without accounting for the type of radiation might not adequately represent the risk to living tissues. In summary, RBE is essential for translating physical measurements into meaningful biological impacts.
Dose Equivalent (mSv)
The dose equivalent is an important measure in radiation protection and health physics. It is expressed in units of millisieverts (mSv) and considers both the energy absorbed and the biological impact of that energy, based on RBE. In our exercise, we calculated the dose equivalent as 2.50 mSv. To arrive at this value, we multiplied the absorbed dose (0.0005 Gy) by the RBE factor (5) to get 0.0025 Sv, which converts to 2.50 mSv.

Dose equivalent helps compare different types of radiation exposure and assess the potential risk to human health. It is widely used in regulatory standards for radiation exposure. Understanding the dose equivalent can be crucial for evaluating exposure limits, planning safety measures, and ensuring health protection in environments where radiation is present.
Absorbed Dose (Gray)
The absorbed dose is a measure of the amount of energy deposited by radiation in a specific mass of material, and is a key factor in radiation dosimetry. It is measured in Grays (Gy), which is the absorption of one joule of radiation energy per kilogram of matter. In the exercise, the absorbed dose was determined to be 0.0005 Gy. This calculation is performed using the formula:\[ D = \frac{E}{m} \]where \(E\) is the energy absorbed (2.00 mJ converted to 0.002 J), and \(m\) is the mass of the sample (4.00 kg).

The absorbed dose alone doesn’t tell the complete story of the biological impact, as it does not consider the type of radiation or its biological effect. However, it is instrumental in the initial stages of radiation dose calculations. Grasping the concept of absorbed dose is fundamental for deeper insights into radiation exposure levels.

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Most popular questions from this chapter

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