32.1

Biological Effects of Ionizing Radiation

Ionizing radiation consists of photons and/or moving particles that have sufficient energy to knock an electron out of an atom or molecule, thus forming an ion. The photons usually lie in the ultraviolet, X-ray, or -ray regions of the electromagnetic spectrum (see Figure 24-10), whereas the moving particles can be the and particles emitted during radioactive decay. An energy of roughly 1 to 35 eV is needed to ionize an atom or molecule, and the particles and rays emitted during nuclear disintegration often have energies of several million eV. Therefore, a single particle, particle, or ray can ionize thousands of molecules.

The physics of the biological effects of ionizing radiation.

Nuclear radiation is potentially harmful to humans because the ionization it produces can significantly alter the structure of molecules within a living cell. The alterations can lead to the death of the cell and even the organism itself. Despite the potential hazards, however, ionizing radiation is used in medicine for diagnostic and therapeutic purposes, such as locating bone fractures and treating cancer. The hazards can be minimized only if the fundamentals of radiation exposure, including dose units and the biological effects of radiation, are understood.
Exposure is a measure of the ionization produced in air by X-rays or rays, and it is defined in the following manner: A beam of X-rays or rays is sent through a mass m of dry air at standard temperature and pressure (STP: 0 °C, 1 atm pressure). In passing through the air, the beam produces positive ions whose total charge is q. Exposure is defined as the total charge per unit mass of air: exposure = q/m. The SI unit for exposure is coulombs per kilogram (C/kg). However, the first radiation unit to be defined was the roentgen (R), and it is still used today. With q expressed in coulombs (C) and m in kilograms (kg), the exposure in roentgens is given by

| (32.1)

Thus, when X-rays or rays produce an exposure of one roentgen, q = 2.58 × 10−4 C of positive charge are produced in m = 1 kg of dry air:

Since the concept of exposure is defined in terms of the ionizing abilities of X-rays and rays in air, it does not specify the effect of radiation on living tissue. For biological purposes, the absorbed dose is a more suitable quantity because it is the energy absorbed from the radiation per unit mass of absorbing material:

| (32.2)

The SI unit of absorbed dose is the gray (Gy), which is the unit of energy divided by the unit of mass: 1 Gy = 1 J/kg. Equation 32.2 is applicable to all types of radiation and absorbing media. Another unit is often used for absorbed dose—namely, the rad (rd). The word “rad” is an acronym for radiation absorbed dose. The rad and the gray are related by

A N A L Y Z I N G M U L T I P L E - C O N C E P T P R O B L E M S

| Example 1 | | |

Absorbed Dose of Rays Figure 32-1 shows rays being absorbed by water. What is the absorbed dose (in rad) of rays that will heat the water from 20.0 to 50.0 °C?

Figure 32-1 When the water absorbs the rays, its temperature rises.

Reasoning When rays are absorbed by the water, they cause it to heat up. The absorbed dose of rays is the energy (heat) absorbed by the water divided by its mass. According to the discussion in Section 12.7, the heat that must be absorbed by the water in order for its temperature to increase by a given amount depends on the mass and specific heat capacity of the water. We will use the concept of specific heat capacity to evaluate the absorbed dose of rays.
Knowns and Unknowns The following table summarizes the given information:

Description | Symbol | Value
Initial temperature of water | T0 | 20.0 °C
Final temperature of water | T | 50.0 °C
Unknown Variable |  |
Absorbed dose of rays (in rads) | Absorbed dose | ?

Modeling the Problem

| Step 1 Absorbed Dose
| The absorbed dose of rays is the energy (heat) Q absorbed by the water divided by its mass m (see Equation 32.2), as indicated in the right column. Neither Q nor m is known. Both variables will be dealt with in Step 2.

| (32.2)

| Step 2 Heat Needed to Increase the Temperature of the Water
| The heat Q that is needed to increase the temperature of a mass m of water by an amount is (Equation 12.4), where c is the specific heat capacity of water. The change in temperature is equal to the higher temperature T minus the lower temperature T0, or . Thus, the heat can be expressed as

| (12.4)

This expression for the heat absorbed by the water can be substituted into Equation 32.2 for the absorbed dose, as indicated in the right column. Note that the mass m of the water appears in both the numerator and denominator, so it can be eliminated algebraically.

Solution Algebraically combining the results of the two modeling steps gives

Taking the specific heat capacity c of water from Table 12-2, we find that the absorbed dose of rays [expressed in grays (Gy)] is

The problem asks that the absorbed dose be expressed in rads, rather than in grays. To this end, we note that 1 rd = 0.01 Gy, so

Related Homework: Problems 6, 8, 46
The amount of biological damage produced by ionizing radiation is different for different kinds of radiation. For instance, a 1-rad dose of neutrons is far more likely to produce eye cataracts than a 1-rad dose of X-rays. To compare the damage caused by different types of radiation, the relative biological effectiveness (RBE) is used.* The relative biological effectiveness of a particular type of radiation is the ratio of the dose of 200-keV X-rays needed to produce a certain biological effect to the dose of the radiation needed to produce the same biological effect:

| (32.3)

The RBE depends on the nature of the ionizing radiation and its energy, as well as on the type of tissue being irradiated. Table 32-1 lists some typical RBE values for different kinds of radiation, assuming that an “average” biological tissue is being irradiated. A value of RBE = 1 for rays and particles indicates that they produce the same biological damage as do 200-keV X-rays. The larger RBE values for protons, particles, and neutrons indicate that they cause substantially more damage. The RBE is often used in conjunction with the absorbed dose to reflect the damage-producing character of the radiation. The product of the absorbed dose in rads (not in grays) and the RBE is the biologically equivalent dose:

| (32.4)

The unit for the biologically equivalent dose is the rem, short for roentgen equivalent, man. Example 2 illustrates the use of the biologically equivalent dose.

Table 32-1 Relative Biological Effectiveness (RBE) for Various Types of Radiation

Type of Radiation | RBE
200-keV X-rays | 1
rays | 1
particles (electrons) | 1
Protons | 10
particles | 10–20
Neutrons |
Slow | 2
Fast | 10

| Example 2 | | |

Comparing Absorbed Doses of Rays and Neutrons A biological tissue is irradiated with rays that have an RBE of 0.70. The absorbed dose of rays is 850 rd. The tissue is then exposed to neutrons whose RBE is 3.5. The biologically equivalent dose of the neutrons is the same as that of the rays. What is the absorbed dose of neutrons?
Reasoning The biologically equivalent doses of the neutrons and the rays are the same. Therefore, the tissue damage produced in each case is the same. However, the RBE of the neutrons is larger than the RBE of the rays by a factor of 3.5/0.70 = 5.0. Consequently, we will find that the absorbed dose of the neutrons is only one-fifth as great as that of the rays.
Solution According to Equation 32.4, the biologically equivalent dose is the product of the absorbed dose (in rads) and the RBE; it is the same for the rays and the neutrons. Therefore, we have

Solving for the absorbed dose of the neutrons gives

Everyone is continually exposed to background radiation from natural sources, such as cosmic rays (high-energy particles that come from outside the solar system), radioactive materials in the environment, radioactive nuclei (primarily carbon and potassium ) within our own bodies, and radon. Table 32-2 lists the average biologically equivalent doses received from these sources by a person in the United States. According to this table, radon is a major contributor to the natural background radiation. Radon is an odorless radioactive gas and poses a health hazard because, when inhaled, it can damage the lungs and cause cancer. Radon is found in soil and rocks and enters houses via a mechanism that is not well understood. One possibility for indoor radon entry is through cracks and crevices in the foundation. The amount of radon in the soil varies greatly throughout the country, with some localities having significant amounts and others having virtually none. Accordingly, the dose that any individual receives can vary widely from the average value of 200 mrem/yr given in Table 32-2 (1 mrem = 10−3 rem). In many houses, the entry of radon can be reduced significantly by sealing the foundation against entry of the gas and providing good ventilation so it does not accumulate.

Table 32-2 Average Biologically Equivalent Doses of Radiation Received by a U. S. Resident*

Source of Radiation | Biologically Equivalent Dose (mrem/yr)*
Natural background radiation |
Cosmic rays | 28
Radioactive earth and air | 28
Internal radioactive nuclei | 39
Inhaled radon | ≈200
Man-made radiation |
Consumer products | 10
Medical/dental diagnostics | 39
Nuclear medicine | 14
Rounded total: | 360

a) |  | National Council on Radiation Protection and Measurements, Report No. 93, “Ionizing Radiation Exposure of the Population of the United States,” 1987.

b) |  | 1 mrem = 10−3 rem.

To the natural background of radiation, a significant amount of man-made radiation has been added, mostly from medical/dental diagnostic X-rays. Table 32-2 indicates an average total dose of 360 mrem/yr from all sources.
The effects of radiation on humans can be grouped into two categories, according to the time span between initial exposure and the appearance of physiological symptoms: (1) short-term or acute effects that appear within a matter of minutes, days, or weeks, and (2) long-term or latent effects that appear years, decades, or even generations later.
Radiation sickness is the general term applied to the acute effects of radiation. Depending on the severity of the dose, a person with radiation sickness can exhibit nausea, vomiting, fever, diarrhea, and loss of hair. Ultimately, death can occur. The severity of radiation sickness is related to the dose received, and in the following discussion the biologically equivalent doses quoted are whole-body, single doses. A dose less than 50 rem causes no short-term ill effects. A dose between 50 and 300 rem brings on radiation sickness, the severity increasing with increasing dosage. A whole-body dose in the range of 400–500 rem is classified as an LD50 dose, meaning that it is a lethal dose (LD) for about 50% of the people so exposed; death occurs within a few months. Whole-body doses greater than 600 rem result in death for almost all individuals.
Long-term or latent effects of radiation may appear as a result of high-level brief exposure or low-level exposure over a long period of time. Some long-term effects are hair loss, eye cataracts, and various kinds of cancer. In addition, genetic defects caused by mutated genes may be passed on from one generation to the next.
Because of the hazards of radiation, the federal government has established dose limits. The permissible dose for an individual is defined as the dose, accumulated over a long period of time or resulting from a single exposure, that carries negligible probability of a severe health hazard. Federal standards (1991) state that an individual in the general population should not receive more than 500 mrem of man-made radiation each year, exclusive of medical sources. A person exposed to radiation in the workplace (e.g., a radiation therapist) should not receive more than 5 rem per year from work-related sources.

Check Your Understanding 1

A person faces the possibility of the following absorbed doses of ionizing radiation: 20 rad of rays (RBE = 1), 5 rad of neutrons (RBE = 10), and 2 rad of particles (RBE = 20). Rank the amount of biological damage that these possibilities will cause in decreasing order (greatest damage first). (The answer is given at the end of the book.)
Background: The biological damage caused by ionizing radiation is related to the amount of the absorbed dose and the relative biological effectiveness of the radiation.
For similar questions (including calculational counterparts), consult Self-Assessment Test 32.1, which is described at the end of Section 32.7.

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