Age Dating Fundamentals

发布网友发布时间：2022-05-01 00:05

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热心网友时间：2022-06-21 01:38

Before w e delve into practical aspects of age-dating isotopes，it is w orth mentioning a common misconception. The term “age ”sometimes creates the impression that the number represents a simple piston flow transit time of a small w ater parcel. Despite the prevalent use of this term， isotope hydrologists understand that the w ater sample measured represents the integrated travel time information; “age”and“mean residence time”are used interchangeably.

Unstable isotopes periodically but predictably emit a particle or break into two smaller nuclei. The time period between emissions is known as the half-life for radioactive decay，and forms the basis for most age-dating methods. An ideal age-dating isotope should behave conservatively by not experiencing any losses or additions ring the transit time of the water. This is rarely the case，but the ideal case will be discussed to illustrate the straightforward age-dating technique.

The time since groundw ater recharged ( left the atmosphere) can be calculated if w e know the original recharge concentration of a radioacctive isotope ( N₀) ，its associated half-life ( T_{1 /2}) ，and measure the number of atoms remaining in our groundwater sample at the time of collection ( N_t) . T_{1 /2}is related to the decay constant ( λ) by

Assuming a single flow path w ithout mixing，losses，or additions of the isotope，w e can calculate the approximate time since recharge as

For practical reasons，w e might have to make assumptions regarding the initial parent atom concentration，w hich creates larger uncertainties. Therefore，it is more direct to measure the parent atom remaining ( N_t) and daughter proced ( D_t) at the sample collection time. This approach is appropriate if the radioactive parent isotope decays to a stable daughter proct that remains w ith the w ater parcel containing the parent isotope. In this case the age calculation is

Another method to determine residence time is to compare measured concentrations w ith the time-varying concentrations know n as input source functions. Careful historical measurements or reconstructions of the time-varying global fluxes of anthropogenic isotopes can be exploited to derive fairly informative age determinations over the past several decades. Precipitation measurements betw een 1950 and present day record peak-shaped curves ( such as for³H，¹⁴C and³⁶Cl) w hile others related to nuclear pow er facilities or fuel rod reprocessing have either increased steadily ( such as⁸⁵Kr) or remain elevated ( such as¹²⁹I) . If only one anthropogenic isotope is measured，then the interpretation may be limited to the determination that the w ater w as recharged w ithin the last 50 years.

Due to their varying concentrations through time，if more than one anthropogenic isotope is measured，then more precise age determinations may be possible. Often the ratios of two isotopes ( such⁸⁵Kr /³H and³⁶Cl /¹²⁹I) can be combined with each separate isotope concentration to create a unique time when all three factors match the historical signals. Tritium (³H) ，an anthropogenic isotope，has an advantage because it decays to a stable daughter proct (³He) ，and both can be measured in the water sample collected in the field. In this case，one can use the age equation［Equation ( 17. 8) ］as long as enough tritium and³He remains in the sample to be measured in the lab. Also since³H is part of the H₂O molecule it directly tracks the movement of the water.