Decay constant is one of the most fundamental parameters to describe radioactive

Question

Decay constant is one of the most fundamental parameters to describe radioactive decay. However, it is sometimes very hard to measure. In this exercise we will try three different methods to determine decay constant for 87Rb decay to 87Sr: 1) Direct measurement: assuming we have 1 kg of 87Rb (this will cost a fortune, typical price for pure 87Rb is a few hundred dollars per milligram from Oak Ridge National lab), we use a scintillation counter and measured - particles in a year is 1.65x1013 (it has been calibrated that the counting efficiency of this scintillation counter is 60%, counting low-energy - particles is not a trivial task). What is the decay constant? 2) Radiogenic isotope produced: assuming after 1 year, we found the concentration of 87Sr is 14.2 ppt (parts per trillion, this is very hard to measure as well, but can actually be done by isotope dilution method), what is the decay constant; 3) Empirical calibration by rocks with known ages: most frequently used geological samples are meteorites which are not disturbed by thermal event. Minister, Birck and Allegre (1982) have obtained a Rb-Sr whole rock isochron for 38 ‘undistrubed ’ H, LL and E type chondrites. This isochron has an intercept of 0.69885 and a slope of 0.0659. Using U-Pb method, it was determined these chondrites have an age of 4.56 billion years (bys), calculate the decay constant for 87Rb decay to 87Sr. Which one of these three results is most reliable?

Explanation / Answer

From these three results, Direct measurement produces the most reliable result as the process of scintillation is used( production of smaller particles) and the measurement of decay constant will produce accurate result by incorporating the dimensions of smaller particles and their life time.

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