Difference between revisions of "Solutions 2"
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− | + | #The shale contains all of the daughter products from <sup>238</sup>U and <sup>235</sup>U in equilibrium. In 10 g natural Uranium there is 125 kBq <sup>238</sup>U and 5.75 kBq <sup>235</sup>U this gives: <math>D(^{226}Ra)=D(^{238}U)=125\,kBq \rightarrow N=\frac{D}{\lambda}=9.1 \cdot 10^{15} = 3.4\cdot10^{-5}\, g</math><math>D(^{226}Ra)=D(^{238}U)=5.75\,kBq \rightarrow N=\frac{D}{\lambda}=8.2 \cdot 10^{9} = 3.0\cdot10^{-5}\, g</math><br> | |
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Revision as of 11:04, 19 June 2012
1:
- 1000g Th(NO3)4 = 2.083 mol arrow N(Th)= 1.25 1024 atoms. This is natural thorium, where the equilibrium in Th-series will lead to equal aktivity of 232Th and 228Th. Since 232Th has a incredibly long half-life and 228Th is short compared to this and we can approximate N(Th) N(232Th)=1.25 10^24 The disintegration for both is 1.96 106Bq.
- 6.43 10-8g
- 10000 Bq 228Ra = 2.62 1012 atoms = 90% arrow 100% 2.92 1012 atoms. If 232Th is N1 and 228Ra is N2 we can use the formulas for mother/daughter realations: Alternatively it can be solved by using D(228Ra) = 11 111Bq:
- 224Ra is created from 228Th immeasurable amounts of 228Th is created in three days, creation of new 224Ra can therefore be ignored. D0(224Ra)=D0(228Th)=1.36
106 Bg, and we get a normal decay: - 228Ac, 220Rn,216Po, 212Pb, 212Bi, 212Po.
2:
- When T= 0 it's only the natural isotopes of uranium: 238U, 235U and 234U.
- D(238U)=D(234U) 12.5 kBq, D(235U) = 575 Bq.
- When t = 23.5 h there is created some 234Th and some 234Pa, but creation of other daugthers from 238U is negligible. From the 235U there is created231Th
- D(238U) = D(234U) =D0,
D(234Th) = D(234Pa) = 376 Bq,
D(235U) = D0,
D(231Th) = 287.5 Bq.
- When t = 23 days the same radionuclides are present.
- D(238U) = D(234U) =D0,
D(234Th) = D(234Pa) = 6250 Bq,
D(235U) = D0,
D(231Th) = D(235U) =575 Bq.
- When t = 1.0 y the same radionuclides are present.
- D(238U) = D(234U) =D0,
D(234Th) = D(234Pa) = D(238U) = 12,5 kBq,
D(235U) = D0,
D(231Th) = D(235U) =575 Bq.
- When t = 10.0 y the same radionuclides are present.
- same as 8.
3:
- The shale contains all of the daughter products from 238U and 235U in equilibrium. In 10 g natural Uranium there is 125 kBq 238U and 5.75 kBq 235U this gives: