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Radioactivity

Problem 6.227

A certain preparation includes two beta-active components with different half-lifes. The measurements resulted in the following dependence of the natural logarithm of preparation activity on time tt expressed in hours:

∈A\in A ( t 3.60 23571014203.102.602.061.821.601.320.90\begin{array}{ccccccc}2 & 3 & 5 & 7 & 10 & 14 & 20 \\ 3.10 & 2.60 & 2.06 & 1.82 & 1.60 & 1.32 & 0.90\end{array} 4.10 Find the half-lifes of both components and the ratio of radioactive nuclei of these components at the moment t=0t=0.

Find the half-lifes of both components and the ratio of radioactive nuclei of these components at the moment t=0t=0.

Reveal Answer
 6.227. T1=1.6 hours, T2=9.8 hours; N2/N1=(T2/T1)××exp⁡(ln⁡A2−ln⁡A1)=10\begin{aligned} &\text { 6.227. } T_{1}=1.6 \text { hours, } T_{2}=9.8 \text { hours; } N_{2} / N_{1}=\left(T_{2} / T_{1}\right) \times\\ &\times \exp \left(\ln A_{2}-\ln A_{1}\right)=10 \end{aligned}
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