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Chapter 43: Problem 32

A person exposed to fast neutrons receives a radiation dose of 300 rem on part of his hand, affecting \(25 \mathrm{~g}\) of tissue. The \(\mathrm{RBE}\) of these neutrons is \(10 .\) (a) How many rad did he receive? (b) How many joules of energy did he receive? (c) Suppose the person received the same rad dosage, but from beta rays with an RBE of 1.0 instead of neutrons. How many rem would he have received?

Short Answer

Expert verified
The answers are: (a) The person received 30 rad. (b) The person received 0.0075 J of energy. (c) The person would have received 30 rem from beta rays.

Step by step solution

01

Calculate RAD

The person's dose of radiation is given in rem, while the RBE of the neutrons is also given. RAD can be calculated using the formula \[ \text{RAD} = \frac{\text{Rem}}{\text{RBE}} \]. Substituting the values, we have \[ \text{RAD} = \frac{300 \text{ rem}}{10} = 30 \text{ rad} \]. So the person received 30 rad of radiation.
02

Calculate Energy

The person's energy received can be calculated using the formula \[ \text{Energy(J)} = \text{RAD} (Gy) \times \text{Mass(kg)} \times 0.01 \]. In this formula, RAD is to be converted to Gy by multiplying with 0.01 because 1 rad = 0.01 Gy, and mass is to be converted to kg. Substituting the values, we have \[ \text{Energy(J)} = 30 \text{ rad} \times 0.01 \times 25 \text{ g} \times 0.001 = 0.0075 \text{ J} \]. Therefore, the person received 0.0075 J of energy.
03

Calculate REM received from beta rays

The formula mentioned in step 1 can also be used to calculate Rem from Rad: \[ \text{Rem} = \text{RAD} \times \text{RBE} \]. If the person received the same rad dosage from beta rays with an RBE of 1.0, the rem received would be \[ \text{Rem} = 30 \text{ rad} \times 1.0 = 30 \text{ rem} \]. So the person would have received 30 rem from beta rays.

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Key Concepts

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

Radiation Dose
Understanding radiation dose is crucial for assessing the risks associated with exposure to ionizing radiation, whether it's for medical professionals, nuclear power plant workers, or patients undergoing radiological procedures. A radiation dose is a measure of the amount of energy absorbed by the body from ionizing radiation. It indicates the potential for causing damage to the living tissues and is expressed using various units such as grays (Gy) and rads.

When someone receives a dose of radiation, it's essential to know the type, energy, and duration of the exposure to evaluate the potential impacts adequately. These doses can lead to biological effects ranging from negligible to severe, depending on the situation, the type of radiation, and the part of the body exposed.
RAD (Radiation Absorbed Dose)
RAD stands for Radiation Absorbed Dose, which is a unit of measurement used to quantify the energy imparted by ionizing radiation to a given mass of tissue. It is defined as the absorption of one hundredth of a joule of radiation energy by one kilogram of tissue.

This is key to calculating and comparing the absorbed doses from different types of radiation, as not all radiation has the same biological impact. For instance, in the provided exercise, a dose of 300 rem could be equated to 30 rad when considering the RBE of the radiation. This calculation helps in assessing the overall risk and potential damage caused by radiation exposure.
RBE (Relative Biological Effectiveness)
Relative Biological Effectiveness (RBE) is a factor that compares the biological effectiveness of different types of radiation. It accounts for the differing abilities of radiation to cause damage in living organisms. Essentially, RBE is used to compare the potential harm caused by different radiation types, taking into account each type's energy and penetration properties.

In practical terms, if a certain amount of radiation dose from one type causes the same biological effect as a higher dose from another type, the first type has a higher RBE. As evidenced by the original exercise, fast neutrons with an RBE of 10 would necessitate lower physical doses (rad) to produce the same effect as a radiation type with an RBE of 1, such as beta rays.
Joules of Energy from Radiation
When discussing radiation exposure, it's informative to convert the absorbed dose into a more tangible form of energy鈥攋oules. Joules are the standard unit of energy in the International System of Units (SI). Since radiation doses are normally given in units that reflect energy per unit mass (like rads or grays), the conversion to joules requires us to know the mass of tissue affected.

In our exercise, the energy received by the person's hand can be calculated by multiplying the absorbed dose (in grays, with 1 rad equals to 0.01 gray) by the mass of the affected tissue (in kilograms). This calculation provides a concrete physical understanding of the amount of energy actually absorbed. Having a clear concept of the energy transferred to human tissue helps in visualizing the potential for biological changes and for making informed decisions on safety and medical interventions.

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Most popular questions from this chapter

How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, \(\frac{28}{14} \mathrm{Si} ;\) (b) rubidium, \({ }_{37}^{85} \mathrm{Rb} ;\) (c) thallium, \({ }^{205} \mathrm{Tl} ?\)

The radioactive isotope \({ }_{7}^{12} \mathrm{~N}\) undergoes \(\beta^{+}\) decay. The energy released in the decay of one nucleus is \(16.316 \mathrm{MeV}\). What is the mass, in amu, of a neutral \({ }_{7}^{12} \mathrm{~N}\) atom? Give your answer to eight significant figures.

Radiation Overdose. If a person's entire body is exposed to \(5.0 \mathrm{~J} / \mathrm{kg}\) of \(\mathrm{x}\) rays, death usually follows within a few days. (a) Express this lethal radiation dose in Gy, rad, Sv, and rem. (b) How much total energy does a \(70.0 \mathrm{~kg}\) person absorb from such a dose? (c) If the \(5.0 \mathrm{~J} / \mathrm{kg}\) came from a beam of protons instead of \(\mathrm{x}\) rays, what would be the answers to parts (a) and (b)?

Energy from Nuclear Fusion. Calculate the energy released in the fusion reaction $$ { }_{2}^{3} \mathrm{He}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+{ }_{1}^{1} \mathrm{H} $$

In the 1986 disaster at the Chernobyl reactor in eastern Europe, about \(\frac{1}{8}\) of the \({ }^{137} \mathrm{Cs}\) present in the reactor was released. The isotope \({ }^{137} \mathrm{Cs}\) has a half-life of \(30.07 \mathrm{y}\) for \(\beta\) decay, with the emission of a total of \(1.17 \mathrm{MeV}\) of energy per decay. Of this, \(0.51 \mathrm{MeV}\) goes to the emitted electron; the remaining \(0.66 \mathrm{MeV}\) goes to a \(\gamma\) ray. The radioactive \({ }^{137} \mathrm{Cs}\) is absorbed by plants, which are eaten by livestock and humans. How many \({ }^{137} \mathrm{Cs}\) atoms would need to be present in each kilogram of body tissue if an equivalent dose for one week is 3.5 Sv? Assume that all of the energy from the decay is deposited in \(1.0 \mathrm{~kg}\) of tissue and that the \(\mathrm{RBE}\) of the electrons is 1.5 .
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