<< Chapter < Page | Chapter >> Page > |
The concept of a radioactive decay chain is important in this determination. In the case of ^{238} U, it decays over many steps to ^{206} Pb. In the process, it goes through ^{234m} Pa, ^{234} Pa, and ^{234} Th. These three isotopes have detectable gamma emissions that are capable of being used quantitatively. As can be seen in [link] , the half-life of these three emitters is much less than the half-life of ^{238} U. As a result, these should exist in secular equilibrium with ^{238} U. Given this, the ratio of activity of ^{238} U to each daughter products should be 1:1. They can thus be used as a surrogate for measuring ^{238} U decay directly via gamma spectroscopy. The total activity of the ^{238} U can be determined by [link] , where A is the total activity of ^{238} U, R is the count rate of the given daughter isotope, and B is the probability of decay via that mode. The count rate may need to be corrected for self-absorption of the sample is particularly thick. It may also need to be corrected for detector efficiency if the instrument does not have some sort of internal calibration.
Isotope | Half-life |
^{238} U | 4.5 x 10 ^{9} years |
^{234} Th | 24.1 days |
^{234m} Pa | 1.17 minutes |
A gamma spectrum of a sample is obtained. The 63.29 keV photopeak associated with ^{234} Th was found to have a count rate of 5.980 kBq. What is the total activity of ^{238} U present in the sample?
^{234} Th ^{} exists in secular equilibrium with ^{238} U. The total activity of ^{234} Th must be equal to the activity of the ^{238} U. First, the observed activity must be converted to the total activity using Equation A=R/B. It is known that the emission probability for the 63.29 kEv gamma-ray for ^{234} Th ^{} is 4.84%. Therefore, the total activity of ^{238} U in the sample is 123.6 kBq.
The count rate of ^{235} U can be observed directly with gamma spectroscopy. This can be converted, as was done in the case of ^{238} U above, to the total activity of ^{235} U present in the sample. Given that the natural abundances of ^{238} U and ^{235} U are known, the ratio of the expected activity of ^{238} U to ^{235} U can be calculated to be 21.72 : 1. If the calculated ratio of disintegration rates varies significantly from this expected value, then the sample can be determined to be depleted or enriched.
As shown above, the activity of ^{238} U in a sample was calculated to be 123.6 kBq. If the gamma spectrum of this sample shows a count rate 23.73 kBq at the 185.72 keV photopeak for ^{235} U, can this sample be considered enriched uranium? The emission probability for this photopeak is 57.2%.
As shown in the example above, the count rate can be converted to a total activity for ^{235} U. This yields a total activity of 41.49 kBq for ^{235} U. The ratio of activities of ^{238} U and ^{235} U can be calculated to be 2.979. This is lower than the expected ratio of 21.72, indicating that the ^{235} U content of the sample greater than the natural abundance of ^{235} U.
This type of calculation is not unique to ^{238} U. It can be used in any circumstance where the ratio of two isotopes needs to be compared so long as the isotope itself or a daughter product it is in secular equilibrium with has a usable gamma-ray photopeak.
Particularly in the investigation of trafficked radioactive materials, particularly fissile materials, it is of interest to determine how long it has been since the sample was enriched. This can help provide an idea of the source of the fissile material—if it was enriched for the purpose of trade or if it was from cold war era enrichment, etc.
When uranium is enriched, ^{235} U is concentrated in the enriched sample by removing it from natural uranium. This process will separate the uranium from its daughter products that it was in secular equilibrium with. In addition, when ^{235} U is concentrated in the sample, ^{234} U is also concentrated due to the particulars of the enrichment process. The ^{234} U that ends up in the enriched sample will decay through several intermediates to ^{214} Bi. By comparing the activities of ^{234} U and ^{214} Bi or ^{226} Ra, the age of the sample can be determined.
In [link] , A _{Bi} is the activity of ^{214} Bi, A _{Ra} ^{} is the activity of ^{226} Ra, A _{U} is the activity of ^{234} U, λ _{Th} is the decay constant for ^{230} Th, λ _{Ra} is the decay constant for ^{226} Ra, and T is the age of the sample. This is a simplified form of a more complicated equation that holds true over all practical sample ages (on the order of years) due to the very long half-lives of the isotopes in question. The results of this can be graphically plotted as they are in [link] .
Exercise : The gamma spectrum for a sample is obtained. The count rate of the 121 keV ^{234} U photopeak is 4500 counts per second and the associated emission probability is 0.0342%. The count rate of the 609.3 keV ^{214} Bi photopeak is 5.83 counts per second and the emission probability is 46.1%. How old is the sample?
Solution : The observed count rates can be converted to the total activities for each radionuclide. Doing so yields a total activity for ^{234} U of 4386 kBq and a total activity for ^{214} Bi of 12.65 Bq. This gives a ratio of 9.614 x 10 ^{-7} . Using [link] , as graphed this indicates that the sample must have been enriched 22.0 years prior to analysis.
Notification Switch
Would you like to follow the 'Physical methods in chemistry and nano science' conversation and receive update notifications?