Radioactive Decay PDF

98 4 Radioactive Decay As shown in Fig. 4.7, 222 Rn decays into a series of short-lived daughters, two of which, 218 Po and 214 Po, are alpha emitters.2) When an alpha particle is emitted in the lung, it deposits all of its energy locally within a small thickness of adjacent...

98 4 Radioactive Decay As shown in Fig. 4.7, 222 Rn decays into a series of short-lived daughters, two of which, 218 Po and 214 Po, are alpha emitters.2) When an alpha particle is emitted in the lung, it deposits all of its energy locally within a small thickness of adjacent tissue. An alpha particle from 214 Po, for example, deposits its 7.69 MeV of energy within about 70 µm. A 1-MeV beta particle from 214 Bi, on the other hand, deposits its energy over a much larger distance of about 4000 µm. The dose to the cells of the lung from the beta (and gamma) radiation from radon daughters is very small compared with that from the alpha particles. The “radon problem,” technically, is that of alpha-particle irradiation of sensitive lung tissue by the short-lived daughters of radon and the associated risk of lung cancer. The health hazard from radon is thus closely related to the air concentration of the potential alpha-particle energy of the short-lived daughters. Depending on local conditions, the daughters will be in various degrees of secular equilibrium with one another and with the parent radon in an atmosphere. Rather than using individual concentrations of the various progeny, one can characterize an atmosphere radio- logically by means of a collective quantity: the potential alpha-energy concentration (PAEC). The PAEC is defined as the amount of alpha energy per unit volume of Fig. 4.7 Radon and radon daughters. Alpha emission is represented by an arrow slanting downward toward the right; beta emission, by a vertical arrow. Alpha-particle and average beta-particle energies and half-lives are shown in the boxes. 2 In earlier terminology, the successive short-lived daughters, 218 Po through 210 Pb, were called RaA, RaB, RaC, RaC′ , and RaD, respectively.  4.6 Radon and Radon Daughters 99 undisturbed air that would ultimately be released from the particular mixture of short-lived daughters in their decay to 210 Pb. The PAEC can be expressed in J m–3 or MeV m–3. For a given PAEC, the equilibrium-equivalent decay-product concen- tration (EEDC) is defined as the concentration of each decay product that would be present if secular equilibrium existed. The ratio of the EEDC and the concen- tration of radon is called the equilibrium factor. By definition, this factor is equal to unity if the radon and all of its short-lived daughters are in secular equilibrium. Equilibrium factors for most indoor atmospheres are in the range of 0.2 to 0.6, a factor of 0.5 often being assumed as a rule of thumb. A limitation of the quantities described in this paragraph is that they do not distinguish between the attached and unattached fractions. Until now, we have discussed only 222 Rn, which is a member of the uranium se- ries. Radon is also generated in the other two series of naturally occurring radionu- clides. However, these isotopes of radon are of lesser radiological importance. The thorium series generates 220 Rn, which is also called thoron. The parent nuclide, 232 Th, is somewhat more abundant than 238 U, but has a longer half-life. As a re- sult, the average rate of production of 220 Rn in the ground is about the same as that of 222 Rn. However, the shorter half-life of 220 Rn, 56 s, as compared with 3.82 d for 222 Rn, gives it a much greater chance to decay before becoming airborne. The con- tributions of the daughters of 220 Rn to lung dose are usually negligible compared with 222 Rn. The third (actinium) series produces 219 Rn, also called actinon, after several transformations from the relatively rare original nuclide 235 U. Its half-life is only 4 s, and its contribution to airborne radon is insignificant. Example Measurements of room air show the nuclide activity concentrations given in Table 4.1. Calculate the PAEC for this case. Solution The PAEC (and EEDC) pertain to the short-lived decay products and do not involve the radon itself, which is not retained by the lungs. To obtain the PAEC, we need to calculate the number of daughter atoms of each type per unit volume of air; multiply these numbers by the potential alpha-particle energy associated with each type of Table 4.1 Activity Concentration Nuclide (Bq m–3 ) 222 Rn 120 218 Po 93 214 Pb 90 2l4 Bi 76 214 Po 76 100 4 Radioactive Decay Table 4.2 A λ N E NE Nuclide (Bq m–3 ) (s–1 ) (m–3 ) (MeV) (MeV m–3 ) 2l8 Po 93 3.79 × 10–3 2.45 × 104 13.69 3.35 × 105 214 Pb 90 4.31 × 10–4 2.09 × 105 7.69 1.61 × 106 214 Bi 76 5.83 × 10–4 1.30 × 105 7.69 1.00 × 106 214 Po 76 4.23 × 103 1.80 × 10–2 7.69 1.38 × 10–1 atom; and then sum. The number of atoms N of a radionuclide associated with an activity A is given by Eq. (4.2), N = A/λ, where λ is the decay constant. For the first daughter, 218 Po, for example, we find from the half-life T = 183 s given in Fig. 4.7 (or Appendix D) that λ = 0.693/T = 3.79 × 10–3 s–1. From the activity density A = 93 Bq m–3 given in Table 4.1, it follows that the number density of 218 Po atoms is A 93 Bq m–3 N= = = 2.45 × 104 m–3 , (4.58) λ 3.79 × 10–3 s–1 where the units Bq and s–1 cancel. Each atom of 218 Po will emit a 6.00-MeV alpha par- ticle. Each will also lead to the emission later of a 7.69-MeV alpha particle with the de- cay of its daughter 214 Po into 210 Pb. Thus, the presence of one 218 Po atom represents a potential alpha-particle energy E = 6.00 + 7.69 = 13.69 MeV from the short-lived radon daughters. Using N from Eq. (4.58), we find for the potential alpha-particle en- ergy per unit volume contributed by the atoms of 218 Po, NE = 3.35 × 105 MeV m–3. Similar calculations can be made for the contributions of the other three daughters in Table 4.1 to the PAEC. The only modification for the others is that the potential alpha energy associated with each atom is 7.69 MeV (Fig. 4.7). The complete calculation is summarized in Table 4.2. The individual nuclide contributions in the last column can be added to give the final answer, PAEC = 2.95 × 106 MeV m–3. Note that the half-life of 214 Po, which is in secular equilibrium with 214 Bi (equal activity densities), is so short that very few atoms are present. Its contribution to the PAEC is negligible. Example Calculate the EEDC in the last example. What is the equilibrium factor? Solution By definition, the EEDC is the activity concentration of the short-lived radon daugh- ters that would give a specified value of the PAEC under the condition of secular equilibrium. For the last example, the EEDC is the (equal) concentration that would appear in the second column of Table 4.2 for each nuclide that would result in the given value, PAEC = 2.95 × 106 MeV m–3. The solution can be set up in more than one way. We compute the PAEC for secular equilibrium at unit activity density  4.6 Radon and Radon Daughters 101 Table 4.3 NE/A Nuclide (MeV Bq–1 ) 218 Po 3.60 × 103 214 Pb 1.79 × 104 214 Bi 1.32 × 104 214 Po 1.82 × 10–3 (1 Bq m–3 ), from which the answer follows immediately. The contribution per unit activity from 218 Po, for example, is obtained from Table 4.2: NE 3.35 × 105 MeV m–3 = = 3.60 × 103 MeV Bq–1. (4.59) A 93 Bq m–3 Values for the four nuclides are shown in Table 4.3. Adding the numbers in the sec- ond column gives a total of 3.47 × 104 MeV Bq–1. This is the PAEC (MeV m–3 ) per unit activity concentration (Bq m–3 ) of each daughter in secular equilibrium. There- fore, for the last example we have PAEC EEDC = 3.47 × 104 MeV Bq–1 (4.60) 2.95 × 106 MeV m–3 = 4 –1 = 85.0 Bq m–3. 3.47 × 10 MeV Bq The equilibrium factor is the ratio of this activity concentration and that of the radon (Table 4.1): 85.0/120 = 0.708. This example shows the useful relationship between an equilibrium concentra- tion of 1 Bq m–3 of the short-lived radon daughters and the associated potential alpha-energy concentration: 3.47 × 104 MeV m–3 = 3.47 × 104 MeV Bq–1. (4.61) 1 Bq m–3 Note that the potential alpha energy per unit activity of the daughters in secular equilibrium is independent of the actual concentration of the daughters in air. An older unit for the PAEC is the working level (WL), defined as a potential alpha- particle energy concentration of 1.3 × 105 MeV L–1 of air for the short-lived radon daughters. This value corresponds to the presence of 100 pCi L–1 = 3.7 Bq L–1 of the daughters in secular equilibrium, that is, to an EEDC of 3.7 Bq L–1. The exposure of persons to radon daughters is often expressed in working-level months (WLM), with a working month defined as 170 h. The WLM represents the integrated expo- sure of an individual over a specified time period. Concentrations of radon itself are sometimes reported, rather than PAECs or WLs, which pertain to the daugh- ters. As a rule of thumb, 1 WL of radon daughters is often associated with a radon concentration of 200 pCi L–1 , corresponding to an equilibrium factor of 0.5.