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Determination of Bulk Radon Emanation Rates by High Resolution Gamma-Ray Spectroscopy
Published in Barbara Graves, Radon, Radium, and Other Radioactivity in Ground Water, 2020
Nancy M. Davis, Rudolph Hon, Peter Dillon
Bulk radon loss from the various particle sizes of the selected granites has been determined. The analytical method involves first determining the absolute activities of radon precursors (Th-234 and Ra-226) and of radon progeny (Pb-214 and Bi-214) in each of the samples. The theory behind this analytical technique involves two principal considerations or assumptions: 1) secular equilibrium among the uranium-238 series nuclides in the solid has been established; and 2) a fraction of the radon atoms which form in the solid is able to and in fact does escape from the solid. A condition of secular equilibrium for the uranium-238 nuclides requires that the decay (production) rate of any daughter in the chain is equal to that of its parent. In a decay series consisting of a very long lived parent and a series of short-lived intermediate daughters (e.g. U-238), the condition of secular equilibrium is propagated through the entire series in such a manner that all intermediate nuclides have equal decay rates: () λ1N1=λ2N2=λ3N3=…=λnNn
Fundamental Concepts and Quantities
Published in Shaheen A. Dewji, Nolan E. Hertel, Advanced Radiation Protection Dosimetry, 2019
If the daughter’s half-life is less than the parent’s, but not in the extreme, as in secular equilibrium, the daughter will eventually establish transient equilibrium and decay at the same rate as it is produced by the parent. The decay equation for transient equilibrium is found from Equation (2.83) under the assumption that for times sufficiently large e−λ2t is negligible compared to e−λ1t and becomes N2(t)≅N1(0)λ1λ2−λ1e−λ1t
Radioactive Materials and Radioactive Decay
Published in Robert E. Masterson, Nuclear Engineering Fundamentals, 2017
which were first introduced to the reader in Section 6.21. However, if the parent isotope in the decay chain (N1) is very stable and does not decay appreciably over time, then the daughter elements can decay away no faster than they are produced by the decay of the parent. This implies that eventually all of the daughter elements will be produced and will decay at a constant rate, which can be correlated to the overall activity of the sample. Then, one can set dN1/dt ≈ 0, dN2/dt ≈ 0, and dN3/dt ≈ 0, and a condition of pseudo equilibrium is reached for each successive daughter isotope in the decay chain. This condition of equilibrium is often referred to as secular equilibrium. In this case,
A Feasibility Study on the Transmutation of 100Mo to 99mTc with Laser-Compton Scattering Photons
Published in Nuclear Technology, 2018
Jiyoung Lee, Haseeb ur Rehman, Yonghee Kim
After about five half-lives of a radioactive isotope, its activity reaches the secular equilibrium state. For 99Mo, the time needed to reach the secular equilibrium state is 13.75 days (330 h). Irradiation for 13.75 days with a gamma-ray intensity of 1015 γ/s gives an activity of 24.8 six-day curies for 99Mo. For 1 week of production with the equivalent gamma-ray intensity, the produced activity is 21.2 six-day curies, which is 85% of the activity at the secular equilibrium state.