When calculating the radioactive decay rate of X _ (224 Ra), a quantitative negative exponential relationship is proposed. Its modern expression is:
( 1)
Integral:
(2)
When both sides of formula (2) are multiplied by λ, the corresponding activity relation is obtained:
(3)
Where: decay rate of radionuclide atoms; NO and n are the number of nuclide atoms at initial time (t = 0) and time t; AO and a are the activities at the starting time and t time; λ
Is the decay constant, and its physical meaning is the decay probability of the nucleus per unit time.
Formula (2) shows the statistical law of nuclear decay, that is, the number of radioactive nuclei decreases exponentially with time. Each radionuclide obeys this basic law when it decays alone, but it has its own characteristic decay constant. Such as uranium -238
λ is1.55×10-1, and λ of radium 226 is 4.33× 10-4 years-1. The decay of atomic nuclei is sometimes continuous from generation to generation, and these mixed decays are very complicated.
Law of two successive decays
The parent (nuclide 1) decays into the daughter (nuclide 2), and the daughter decays into a stable nuclide, and the mother and the child are homologous. At this time, formula (1) and formula (2) can calculate nuclides at different times.
Atomic number 1 and solitary nuclide 2. Radionuclide coexisting with radionuclide 1
The change rate of 2 should include two parts, one part is nuclide 1 decay to produce nuclide 2, and the other part is the decay of nuclide 2. So:
(4)
(5)
At first, there were only parent nuclides. In a given sample N 1, 0, the change of N2 with time only depends on λ 1 and λ2. There are three situations:
① The activity (A2) of λ 2λ 1 nuclide 2 first increases with time, then reaches a certain saturation value, which is equal to the activity (A 1) of nuclide 1, and then the activity of nuclide 2 keeps decreasing according to the half-life of nuclide 1, showing a long-term balance (Figure/kloc-0) curve
C is the sum of the activities of nuclide 1 and 2, and curve a is the activity of pure nuclide 1 at the beginning. curve
B comes from pure nuclide
The nuclides gradually accumulate in 1
2, curve b' shows that the activity of isolated nuclide 2 decays with time. Thorium 234 is produced from uranium 238 and radon 222 is produced from radium 226. In addition, when the neutron in the reactor or the ion beam generated by the accelerator is used to produce radionuclides through nuclear reaction, as long as the nuclear reaction rate remains unchanged, the activity change of radionuclides is consistent with the long-term balance.
② The activity of λ 2 > λ1nuclide 2 initially increased with time. After tm reaches a certain maximum, the activity of nuclide 2 is greater than that of nuclide 1, and then gradually tends to decay according to the half-life of nuclide 1, showing a temporary balance (Figure 2). The descriptions of curves A, B, B' and C are the same as those in figure 1. This is the case with bismuth 2 12 produced in lead 2 12 and iodine 132 produced in tellurium 132.
③ λ 2 < λ 1 cannot be balanced in this case. The changes of activity of nuclide 1 and nuclide 2 with time are shown in Figure 3.
Multiple continuous attenuation law
19 10, the British mathematician H. Bateman got the solution of this process. In principle, no matter how many members have radioactive decay series, it is possible to mathematically calculate the atomic number and activity of each generation of members. In fact, intermediate members can often be ignored, and two generations of radionuclides (mother and child) are the most common.
According to the law of radioactive decay, in addition to calculating the atomic number and activity of radionuclides (there are many uses in this field, such as the generation of radionuclides and the calculation of the age of geological samples), the half-life of radionuclides can also be calculated by curve analysis.
Time flies like running water. This semester has passed while you are busy with your work. My friend, as a math teacher, how do you fee