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4.5.4 Radiation quantities and units
The quantity of particulate radiations may be defined in terms of fluence, which is the number of particles that enter a sphere of unit cross-sectional area. For a unidirectional beam the fluence so defined is equal to the number of particles that cross a unit area placed perpendicular to the beam. When the radiation is distributed isotropically the number of particles that cross a unit area of any plane is one half the fluence. The fluence rate is known as the flux density or flux.
The quantity of X - or gamma-radiation to which an object is exposed can be specified in terms of exposure, X, which is the ionization that the radiation would produce in air. Exposure is defined as dQ/dm, where dQ is the sum of the electrical charges on all ions of one sign produced in air when all the electrons and positrons liberated by photons in a volume of air whose mass is dm are completely stopped in air. The ionization arising from the absorption of bremsstrahlung or annihilation radiation emitted by the electrons is not to be included in dQ. Owing to the difficulty of measurement, exposure is not normally used when the photon energy exceeds 3 MeV. The unit of exposure is the coulomb per kilogram of air.
The energy imparted to matter by electrically charged or uncharged particles is known as the absorbed dose, D, for which the unit is the gray (Gy). This is equivalent to 1 J kg−1 or 6.242 × 1012 MeV kg−1.
The sum of the initial kinetic energies of all charged particles released per unit mass of a medium by interaction of uncharged particles, such as photons and neutrons, is known as kerma, K. The kinetic energy includes the energy that the charged particles may lose subsequently as bremsstrahlung or annihilation radiation and also the kinetic energy of charged particles, such as Auger electrons, produced by other secondary processes. Since the charged particles do not dissipate their energy at the point at which they are released, kerma is not identical to absorbed dose unless complete secondary equilibrium exists in the medium, i.e. those charged particles that leave their point of release are exactly balanced by others released elsewhere that arrive at the point. Exposure for X - and gamma-radiation is the ionization equivalent of kerma in air, except at very high energies when a difference arises due to bremsstrahlung and annihilation effects. In the dosimetry of X - and gamma-radiation ionization chambers are often used for the dual purpose of measuring the exposure and the absorbed dose. Since the units of kerma and absorbed dose are identical, i.e. the gray, it is common practice to express the quantity of X - and gamma-radiation in terms of air kerma in order to avoid the difficulty of different units and instrument scales.
The linear energy transfer or restricted linear collision stopping power, LΔ, of charged particles is the differential mean energy loss per unit distance traversed due to collisions with electrons minus kinetic energy transfers to electrons in excess of Δ eV. L100, for example, designates the linear energy transfer when Δ = 100 eV. The symbol L∞ is used when all possible kinetic energy transfers are included. L∞ is sometimes referred to as the unrestricted linear collision stopping power. Linear energy transfer is usually expressed in units of keV μm−1. In a medium with a density of 1000 kg m−3, a L∞ of 1 keV μm−1 is equivalent to a specific energy loss (or stopping power (section 4.5.1)) of 1 MeV m2 kg−1.
The expectation value of the rate of spontaneous nuclear transitions in a quantity of material is known as its activity. The special name for the unit of activity is the becquerel (Bq) and is equal to one transition per second.
The decay constant, λ, of a radioactive nuclide is the probability per unit time that a given nucleus will undergo a spontaneous nuclear transition. The quantity ln 2/λ is commonly called the half-life, T1/2, and is the time required for the activity of an amount of a radionuclide to decrease to one-half of its initial value.
The air kerma-rate constant, Γδ, of a radionuclide emitting photons enables the air kerma-rate, Kδ, due to photons with energies greater than δ to be determined at a distance l from a point source of the nuclide with activity A. The unit is m2 Gy s−1 Bq−1. Without allowance for absorption and scattering of the radiation, the air kerma-rate is given by:
Table 1 gives values for the air kerma-rate constant for some common radionuclides.
Table 1. Air kerma-rate constants for some common radionuclides (δ = 50 keV)
Note: In practice the air kerma-rate constant may depend on the details of the source construction, and may include a contribution from bremsstrahlung and annihilation radiation generated in the source by beta particles and positrons.
The International Commission on Radiological Protection (ICRP) in its Publication 60 (ICRP, 1990) redefined the quantities which it had previously recommended in its Publication 26 (ICRP, 1977) for the specification of limits on exposures to external radiation and to intakes of radionuclides. Both the earlier and later definitions of these basic dose limit quantities are given below. In addition the International Commission on Radiation Units and Measurements, as well as defining radiation quantities and units for general use (ICRU, 1980), has defined a set of operational dose equivalent quantities to be used in radiological protection measurements of external radiations (ICRU, 1985, 1988, 1992, 1993). The special unit used for all the protection quantities is the sievert (Sv). As originally defined this was equal to the absorbed dose to tissue in gray multiplied by appropriate dimensionless modifying factors.
ICRP Publication 26 dosimetry
In the 1977 ICRP recommendations the modifying factor used as the multiplier was the quality factor, Q(L), which depended on the unrestricted linear energy transfer (L∞) in water of the charged particles responsible for the absorbed dose. For charged particles other than electrons and alpha particles the quality factor was specified as:
For electrons, and hence for X- and gamma-radiation, the recommended quality factor was 1, and for alpha particles was 20. The point quantity obtained by multiplying the absorbed dose by the quality factor was known as the dose equivalent, H.
Dose limits recommended in ICRP Publication 26 were based on the risks of fatal cancers and serious hereditary defects in the subsequent descendants of persons exposed to radiation. Since the probability of inducing cancer in some organs or tissues of the body is higher than in others, the ICRP recommended tissue weighting factors proportional to their relative sensititivies. The effective dose equivalent was the sum of the products of these weighting factors and the dose equivalents in the different tissues. In the case of radioactive material incorporated in the body tissues, the dose equivalent to these tissues would be spread out in time and delivered gradually as the material underwent radioactive decay. The total dose equivalent to a tissue during the period of life (taken to be 50 years) following the incorporation of a quantity of a radionuclide, after allowing for the metabolic processes of excretion, was known as the committed dose equivalent arising at the time of incorporation.
To keep the risks of fatal cancer to acceptable levels, the ICRP in 1977 recommended that workers should not be exposed in any year to more than 50 mSv and members of the public to not more than 5 mSv of effective dose equivalent and committed effective dose equivalent. There were additional restrictions on the maximum dose equivalent and committed dose equivalent allowed to specific tissues.
ICRP Publication 60 dosimetry
In 1990 ICRP recommended a new quantity, equivalent dose, HT, defined as the summation of absorbed doses, DT, R, averaged over a tissue or organ, T, due to radiations of type R incident on the body or emitted by radionuclides in the body and weighted by radiation weighting factors, wR, i.e.
The radiation weighting factors are listed in Table 2.
Table 2. Radiation weighting factors recommended in ICRP Publication 60, 1990
a For neutrons of energy ε MeV the following approximation may be used: 5 + 17 exp[−(ln 2ε)2/6]
The quantity corresponding to effective dose equivalent in the 1977 Publication 26 recommendations is the effective dose, E. This quantity is the sum of the equivalent doses in the different organs multiplied by tissue weighting factors, wT, i.e.
These tissue weighting factors, unlike those of the 1977 Publication 26, reflect the total health detriment and not just the risk of fatal cancer and serious hereditary defects. Included in the factors are the relative sensitivities of the different organs for the induction of fatal and non-fatal cancer, the relative length of life lost if a cancer occurs in an organ or for the gonads the degree of life shortening due to serious hereditary defects.
Committed equivalent dose is the total equivalent dose to an organ of tissue for the 50 years (or 70 years in the case of children) following the incorporation of a radionuclide after allowing for the metabolic processes of excretion. Committed effective dose is similarly defined as the sum of the committed equivalent doses to the different tissues or organs each multiplied by the appropriate tissue weighting factor.
Cancer risks due to exposure to radiation are mainly derived with the hypothesis that they are proportional to the incidences of cancers in a population exposed only to natural background radiation. These incidences vary between countries. In Table 3 are given the tissue weighting factors from both the ICRP Publication 26 and Publication 60 recommendations and the estimated fatal cancer risks in the different organs averaged over all ages and both sexes for the UK population exposed at low dose rates (NRPB, 1993a). The average lifetime risk of fatal cancer for this population is 5.9 × 10−2 Sv−1. The risk to girls in the age range 0 to 9 years is estimated to be 12.0 × 10−2 Sv−1 and to boys in this age range 10.3 × 10−2 Sv−1. In contrast, the fatal cancer risk to women in the age range 60 to 69 is estimated to be 2.0 × 10−2 Sv−1 and to men 3.3 × 10−2 Sv−1. The risk that the children or grandchildren of a person exposed to radiation will have a serious hereditary defect is estimated to be 0.53 × 10−2 Sv−1. The estimates of cancer and hereditary risks have fairly large uncertainties, which are difficult to quantify but may be a factor of two in either direction.
To keep the health detriment to acceptable levels, the ICRP in Publication 60 recommended that workers should not be exposed to more than 20 mSv in a year and members of the public to not more than 1 mSv of effective dose and committed effective dose. Separate and higher dose limits are recommended for the lens of the eye, the skin and for the hands and feet.
Table 3. Tissue weighting factors recommended by ICRP and averaged fatal cancer and serious hereditary risks to the UK population
OT: Considered in Publication 26 to be among any other tissue. The five receiving the highest dose were each given a tissue weighting factor of 0.03.
† Total genetic risk to all subsequent generations; to the first two generations the risk is 0.19 × 10−2 Sv−1. The total genetic risk for the reproductive fraction of the population (40%) is 2.4 × 10−2 Sv−1 to all subsequent generations and 0.53 × 10−2 Sv−1 to the first two generations.
Operational dose equivalent quantities
The operational dose equivalent quantities defined by the ICRU (ICRU, 1985, 1988, 1992) have the effect of defining the required responses and methods of calibration of instruments and dosimeters used in radiological protection for the measurement of external radiation. These quantities are based on dose equivalent defined in the 1977 ICRP Publication 26 as the product of the absorbed dose at a point multiplied by a quality factor. The dependence of the quality factor, Q(L), on the unrestricted linear energy transfer, L∞, for charged particles other than electrons differs from that in Publication 26 given above and is:
For electrons, and hence for X- and gamma-radiation, the quality factor is taken as 1.
The ambient dose equivalent, H*(d), in a radiation field is the dose equivalent that would be produced by the corresponding expanded and aligned field at a depth d in millimetres on the radius of the ICRU sphere in the direction of the aligned field. The ICRU sphere is 0.3 m in diameter with a density of 1000 kg m−3 and a mass composition equivalent to tissue of 76.2% oxygen, 11.1% carbon, 10.1% hydrogen and 2.6% nitrogen. The field is ‘expanded’ so that it encompasses the sphere and ‘aligned’ so the quantity is independent of the angular distribution of the radiation field. In effect this defines an instrument with a uniform isotropic response. For the measurement of radiations that are strongly penetrating into the body the reference depth in the sphere is 10 mm, and the quantity is denoted as H*(10). For the estimation of the dose to the skin and eye lens, particularly from less penetrating radiations, the reference depths of 0.07 mm and 3 mm respectively with the notations H*(0.07) and H*(3) are used.
The directional dose equivalent, H’(d, Ω), in a radiation field is the dose equivalent that would be produced by the corresponding expanded field in the ICRU field at a depth d in millimetres on a radius at a specified angle Ω to the direction of the field. This specifies an instrument with a directional response similar to the distribution of the dose equivalent about the axes of the sphere, and is of particular use in the assessment of dose to the skin or eye lens. The same reference depths of measurement are used as for ambient dose equivalent, i.e. 10 mm for penetrating radiation dose to the whole body, and 0.07 mm and 3 mm for the skin and eye lens.
Personal dose equivalent, Hp(d), is the dose equivalent in soft tissue at a depth d in millimetres below a specified point on the body. This specifies the required response of a personal dosimeter. As with ambient dose equivalent and directional dose equivalent, the depths used are 10 mm for the assessment of whole body dose and 0.07 mm and 3 mm for the assessment of the dose to the skin or eye lens. In practice the personal dose equivalent is defined by reference to a slab phantom of appropriate tissue with absorption and scattering characteristics similar to tissue, i.e. water or polymethyl methacrylate.
The worldwide average annual effective dose from radiation of natural origin is about 2.4 mSv. This is comprised of about 0.39 mSv from cosmic radiation, 0.46 mSv from terrestrial gamma radiation, 0.23 mSv from internal radioactivity (e.g. mainly 40K) and about 1.3 mSv from inhaled radon and thoron daughter products (UNSCEAR, 1993). The cosmic radiation component is comparatively independent of latitude at sea level, but becomes increasingly latitude-dependent with increased altitude and is highest in polar regions. At a latitude of 50° it increases by a factor of 60 between sea level and a height of 10 km and by an even larger factor at times of intense solar flares. It can be a significant source of radiation exposure to the crews of high flying aircraft, who could receive an annual average effective dose of about 3 mSv. The contribution of effective dose from terrestrial gamma radiation and from airborne radon and thoron daughter products depends on the local geology. Values that are factors of two or three above or below the normal average values are not uncommon and in a few limited areas can be up to 100 times greater.
Radon and thoron
The effective dose from radon and thoron daughter products is almost entirely due to their deposition in the lungs from inhaled air and results in an increased risk of lung cancer. Estimates of this risk are derived from observations of the increased incidence of this disease in miners of uranium, tin and iron ores (ICRP, 1987). The exposure of these miners has been expressed traditionally in terms of the working level month, WLM. A working level, WL, was originally defined as any combination of short-lived radon daughters (218Po, 214Pb, 214Bi, 214Po), and later by extension any combination of short-lived thoron daughters (216Po, 214Pb, 212Bi, 212Po), in 1 litre of air at normal temperature and pressure that had the potential to release 1.3 × 105 MeV of alpha particle energy in their ultimate radioactive decay. This energy is that approximately released in the decay of these daughters in equilibrium with 100 pCi of radon, 222Rn. The exposure to one WL for 170 hours, taken as the working time in one month, is one WLM. 100 pCi corresponds to an activity concentration, Cact, of 3.7 × 103 Bq m−3. One WLM corresponds to an activity exposure, Eact, of 6.29 × 105 Bq h m−3 of radon daughters or 4.63 × 104 Bq h m−3 of thoron daughters.
The potential alpha energy concentration in air, cp, is the sum of the potential alpha particle energy of all the short-lived radon or thoron daughters in a unit volume of air. If cact, i is the activity concentration of daughter radionuclide i, then:
where εp, i is the potential alpha particle energy released in the decay chain from the daughter radionuclide i and λi is its decay constant. The unit of potential alpha energy concentration is J m−3 (1 J m−3 = 6.24 × 1012 MeV m−3).
The equilibrium-equivalent concentration, EEC, of a non-equilibrium mixture of radon or thoron daughter radionuclides is the activity concentration of the parent radon or thoron gas in equilibrium with its short-lived radionuclide daughter that has the same potential alpha energy concentration as the actual non-equilibrium mixture. For the radionuclide daughters of radon EECRn = 1.81 × 108cp Bq m−3, and for the radionuclide daughters of thoron EECTh = 1.32 × 107cp Bq m−3.
The equilibrium factor, F, is the ratio of the equilibrium-equivalent concentration to the actual activity concentration of radon or thoron in air, which is usually measured in mass surveys. In domestic properties in the UK a typical value for F is 0.5. Hence an activity concentration of 20 Bq m−3 of radon gas in the home typically corresponds to an equilibrium-equivalent concentration of 10 Bq m−3.
One WLM of radon or thoron radionuclide daughters corresponds to an exposure to 3.48 × 10−3 J h m−3. An equilibrium-equivalent concentration of radon radionuclide daughters of 1 Bq m−3 corresponds to a potential alpha energy concentration of 5.52 × 10−9 J m−3. An activity exposure of 1 Bq h m−3 is an exposure to 5.52 × 10−9 J h m−3 and equivalent to 1.59 × 10−6 WLM of radon radionuclide daughters. For thoron radionuclide daughters the equilibrium-equivalent concentration of 1 Bq m−3 corresponds to a potential alpha energy concentration of 7.58 × 10−8 J m−3, and an activity exposure of 1 Bq h m−3 is an exposure to 7.58 × 10−8 J h m−3 and equivalent to 2.16 × 10−6 WLM.
The derivation of the dose to the lungs resulting from an exposure to radon or thoron short-lived radionuclide daughters expressed either in WLM or Bq h m−3 depends on the degree to which these radionuclides are attached to aerosols in the environment, the diameter and nature of these aerosols, the degree of radioactive equilibrium between the radionuclides, the breathing rate of the exposed persons and the times they spend in areas with different exposure levels. These factors introduce some degree of uncertainty in the extrapolation from the observed risks to miners to the expected risks from exposure to radon and thoron radionuclide daughters in domestic situations. These risks also depend on the ‘natural’ lung cancer incidence in the target population, which is strongly dependent on smoking habits. The extrapolated probability of lung cancer death for both sexes combined including smokers and non-smokers for the UK population is 3.5 × 10−4 WLM−1 (NRPB, 1993a) due to indoor radon exposure, or 5.6 × 10−10 per Bq h m−3 of equilibrium equivalent concentration activity exposure.
In the UK it is recommended (NRPB, 1990) that action should be taken to reduce radon levels in homes when the radon gas activity concentration exceeds 200 Bq m−3 corresponding to an equilibrium-equivalent concentration of 100 Bq m−3.
In addition to the natural exposures, some additional exposures arise from man-made sources. In the United Kingdom the average annual effective dose due to medical procedures is estimated to be 370 μSv and 13 μSv from the sum of all other sources (weapon and reactor accident fall-out, discharges into the environment, occupational exposures and miscellaneous sources) (NRPB, 1993b). The average annual effective dose due to weapon fall-out was at a maximum of 140 μSv in 1963 and had declined to about 4 μSv in 1991. The fall-out from the Chernobyl reactor accident in 1986 gave rise to an average effective dose to members of the UK population in that year of about 22 μSv and declined to 1 μSv in 1991. In that year the average effective dose due to discharges of radioactive wastes was 0.4 μSv of which 0.3 μSv was due to the nuclear industry. The highest effective doses from these discharges to the one or two persons that comprise a critical group was estimated to be between 100 and 200 μSv.
NRPB (1990) Board Statement on Radon in Homes, Doc. NRPB,
Table 4. Radiation quantities and units
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