42.7.1 Radiation Dose

Nuclear radiation, which is ionizing radiation, disrupts a cell’s machinery by altering and damaging the biological molecules. The consequences of this disruption vary from genetic mutations to uncontrolled cell multiplication (i.e., tumors) to cell death.

Beta and gamma radiation can penetrate the entire body and damage internal organs. Alpha radiation has less penetrating ability, but it deposits all its energy in a very small, localized volume. Internal organs are usually safe from alpha radiation, but the skin is very susceptible, as are the lungs if radioactive dust is inhaled.

Biological effects of radiation depend on two factors. The first is the physical factor of how much energy is absorbed by the body. The second is the biological factor of how tissue reacts to different forms of radiation.

The absorbed dose of radiation is the energy of ionizing radiation absorbed per kilogram of tissue. The SI unit of absorbed dose is the gray, abbreviated Gy. It is defined as

1 gray = 1 Gy \equiv 1.00 J/kg of absorbed energy

The absorbed dose depends only on the energy absorbed, not at all on the type of radiation or on what the absorbing material is.

Biologists and biophysicists have found that a 1 Gy dose of gamma rays and a 1 Gy dose of alpha particles have different biological consequences. To account for such differences, the relative biological effectiveness (RBE) is defined as the biological effect of a given dose relative to the biological effect of an equal dose of x rays.

TABLE 42.4 shows the relative biological effectiveness of radiation. Larger values correspond to larger biological effects. Neutrons have a range of values because the biological effect varies with the energy of the particle and with the type of cell. Alpha radiation has the largest RBE because the energy is deposited in the smallest volume.

TABLE 42.4 Relative biological effectiveness of radiation

Radiation type	RBE
X rays	1
Gamma rays	1
Beta particles	1
Neutrons	5–20
Protons	10
Alpha particles	20

The product of the absorbed dose with the RBE is called the dose equivalent. Dose equivalent is measured in sieverts, abbreviated Sv. To be precise,

dose equivalent in Sv = absorbed dose in Gy \times RBE

1 Sv of radiation produces the same biological damage regardless of the type of radiation. An older but still widely used unit for dose equivalent is the rem, defined as $1 rem = 0.010 Sv$ . Small radiation doses are measured in millisievert (mSv) or millirem (mrem).

EXAMPLE 42.7 Radiation exposure

A 75 kg laboratory technician working with the radioactive isotope $^{137} Cs$ receives an accidental 1.0 mSv exposure. $^{137} Cs$ produces 0.66 MeV gamma-ray photons. How many gamma-ray photons are absorbed in the technician’s body?

MODEL The radiation dose is a combination of deposited energy and biological effectiveness. The RBE for gamma rays is 1. Gamma rays are penetrating, so this is a whole-body exposure.

SOLVE The absorbed dose is the dose in Sv divided by the RBE. In this case, because $RBE = 1$ , the dose is $0.0010 Gy = 0.0010 J / kg$ . This is a whole-body exposure, so the total energy deposited in the technician’s body is 0.075 J. The energy of each absorbed photon is 0.66 MeV, but this value must be converted into joules. The number of photons in 0.075 J is

\begin{matrix} N & = & \frac{0.075 J}{(6.6 \times 10^{5} eV / photon) (1.60 \times 10^{- 19} J / eV)} \\ = & 7.1 \times 10^{11} photons \end{matrix}

REVIEW The energy deposited, 0.075 J, is very small. Radiation does its damage not by thermal effects, which would require substantially more energy, but by ionization.

TABLE 42.5 gives some basic information about radiation exposure. We are all exposed to a continuous natural background of radiation from cosmic rays and from naturally occurring radioactive atoms (uranium and other atoms in the uranium decay series) in the ground, the atmosphere, and even the food we eat. This background averages about 3 mSv per year, although there are wide regional variations depending on the soil type and the elevation. (Higher elevations have a larger exposure to cosmic rays.)

TABLE 42.5 Radiation exposure

Radiation source	Typical exposure (mSv)
CT abdominal scan	10
Natural background (1 year)	3
Mammogram x ray	0.4
Chest x ray	0.3
Dental x ray	0.01

Medical x rays vary significantly. The average person in the United States receives approximately 0.6 mSv per year from all medical sources. All other sources, such as fallout from atmospheric nuclear tests many decades ago, nuclear power plants, and industrial uses of radioactivity, add up to less than 0.1 mSv per year.

The question inevitably arises: What is a safe dose? This remains a controversial topic and the subject of ongoing research. The effects of large doses of radiation are easily observed. The effects of small doses are hard to distinguish from other natural and environmental causes. Thus there’s no simple or clear definition of a safe dose. A prudent policy is to avoid unnecessary exposure to radiation but not to worry over exposures less than the natural background. It’s worth noting that the $μ Ci$ radioactive sources used in laboratory experiments provide exposures much less than the natural background, even if used on a regular basis.