RADIOACTIVITY METHODS 993 



radioactive isotope (Lu^'^^) is only 2.5 per cent. The element itself is very 

 rare and usually is associated w^ith yttrium in nature. The recently reported 

 /? activity of rhenium probably comes from jsRe'^^'^ which has an isotopic 

 abundance of 61.8 per cent. The reported half -life is immense, and the 

 radiation very weak (approximately 3 • 10^^ years, 0.04 Mev). Small 

 amounts of rhenium are found in columbite, tantalite, and wolframite. 

 It is clear that rubidium, samarium, lutecium, and rhenium, although 

 interesting in themselves, are not commonly encountered in radioactivity 

 exploration, and are therefore of little importance within the scope of this 

 book. 



Equilibrium 



If we take a fixed amount of uranium that has just been purified, some 

 of it will immediately start decaying into its first daughter element (see 

 Figure 605) which in turn decays into its own daughter and so on down 

 the line until the last stage is reached — a stable isotope of lead. The rate 

 at which a radioactive element decays is frequently expressed in terms of 

 the half -life T, which is the length of time required for the decay of half 

 the atoms in a given amount. The half -life is inversely proportional to the 

 decay constant A, which is defined as the number of atoms which decay in 

 one unit of time divided by the total number of atoms in the sample of the 

 decaying element. 



The relation between T and X is 



_ loge2 _ .693 

 ~ A A 



As the decay cascade proceeds, the isotopes with a small A will tend to 

 accumulate, and those with a very large A will decay a very short time after 

 their birth. We can visualize the process if we imagine water running 

 through a series of vats connected in cascade by pipes of different sizes. 

 The water accumulates and builds up pressure in the vats with small outlet 

 pipes, but runs right through the vats with large drains. 



The concept of equilibrium becomes very important when we try to 

 measure the amount of any particular radioactive element in a rock by 

 measuring the rate of overall radiation. We must remember that radioactive 

 parent and daughter are always chemically different and can therefore be 

 separated in nature by normal geological processes. The result is the same 

 as if one or more of our vats had sprung a leak and we could no longer be 

 sure that the amount of flow from any particular vat to the next lower one 

 was the same as the flow from the top vat. 



Such a case arises when we measure the radiation from some of the 

 supergene uranium minerals (carnotite, tyuyamunite, and others). One 

 of the daughter elements of uranium is radon, a noble gas, and these min- 

 erals are sufficiently porous to permit the escape of some of the gas with 

 the consequent loss of radiation from radon and its numerous daughter 



