What is Specific Activity Method for Half Life Determination?

Half life determination: Part 2

Determination of t_1/2 ~10^9 years or more by Specific Activity Method

Specific Activity Method (Independent determination of A and N)

A. Radiometry and Mass Spectrometry

We know the formula, which relates Specific Activity and Mass

A =N. λ

A = N. 0.693/t_1/2
Activity (A, dps) of the radioisotopes can be obtained from nuclear counting techniques like, Gamma Spectrometry, Liquid Scintillation counting with known efficiency.

No. of atoms (N) can be obtained from either mass spectrometry (ICPMS, RIMS with LOD of ng/mL or pg/mL respectively) or by Activation analysis (Neutron or charged particle) technique using relative NAA method using the following equation.

    Specific activity can be obtained by accurate estimation of mass of the radioisotope present in the sample and accurate activity using Ion Chamber, LSC, Proportional counter, Alpha spectrometry. Uncertainty of the analysis can be reduced with enriched radioisotopes as the no. of counts can be increased which shall decrease the counting uncertainty. 

    Weighing can be done by using high precision analytical balance. Necessary correction has to be done for the interfering radioactivities or should be freshly separated before counting e.g. while estimating the activity of 235U, 238U using LSC, its daughters should be removed by chemical separation prior to the LSC counting or necessary corrections should be incorporated. 

    For Jaffey et al (1971) for 238U estimation specific activity of 1519.7±2.4 (dis/min)/(mg natural U) was obtained and t_1/2 was estimated as (4.45± 0.01)10^9 yr 

    Half life of 148Sm was obtained activity from high resolution alpha spectrometer after a continuous counting for 50.2 days and known initial no. of atoms of 148Sm. Gupta et al (1970) reported the half life as (7±3) x 10^15 yr.

    Uncertainties of the half life measurements are addressed in great detail in an article by S Pommé (2015). 

B. Microcalorimetry and Mass Spectrometry

To obtain the specific activity of a radionuclide, activity component can also be obtained by using one of the very old techniques i.e. microcalorimetry. Several authors have obtained half lives of 14C (Jenks G H et al (1952), 226Ra (Holden N E 1990) , 63Ni (Barnes, I. L(1971) et al). etc. 

Advantage
Simple

Disadvantage
Need two techniques (one for A, another for N)

Reference

Barnes, I. L., Garfinkel, S. B., & Mann, W. B. (1971). Nickel-63: standardization, half-life and neutron-capture cross-section. The International Journal of Applied Radiation and Isotopes, 22(12), 777-781.

Gupta, M. C., and R. D. MacFarlane. "The natural alpha radioactivity of samarium." Journal of Inorganic and Nuclear Chemistry 32, no. 11 (1970): 3425-3432. 

Holden, N. E. (1990). Total half-lives for selected nuclides. Pure and Applied Chemistry, 62(5), 941-958.

Jaffey, A. H., K. F. Flynn, L. E. Glendenin, WC T. Bentley, and A. M. Essling. "Precision measurement of half-lives and specific activities of U235 and U238." Physical review C 4, no. 5 (1971): 1889. 

Jenks, G. H., & Sweeton, F. H. (1952). Calorimetric Determination of the Relationship between the Half-Life and Average Beta-Energy of C 14. Physical Review, 86(5), 803.

Kajan, Ivan, Stefaan Pommé, Krzysztof Pelczar, and Stephan Heinitz. "Measurement of the 145Sm half-life." Applied Radiation and Isotopes 178 (2021): 109978..

Pommé, S. "The uncertainty of the half-life." Metrologia 52, no. 3 (2015): S51.