Measuring Radiation in a Closed System

[confyoused]

Suppose we have a closed system in which molecules cannot escape. Into this system we enter some radioactive molecules with $\beta^+$ decay. We know that the resulting daughter nuclide is also radioactive. We have some equations to describe the amount of parent nuclides and daughter nuclides, involving some constants which are correct. The equations are given by:
$$\frac{dN_1}{dt} = -\lambda_1 N_1$$
$$\frac{dN_2}{dt} = -\lambda_2 N_2 + \lambda_1 N_1$$

with $\lambda_1, \lambda_2$ the decay rates. Suppose we want to measure the amount of radiation in this system.

Could there be any reason why the predicted amount of radiation differs greatly from the measured amount of radiation. We know that molecules cannot leave the system so that cannot be a reason. We could say that faulty measuring equipment could be a reason but besides that is there any other reason? Maybe absorption of the molecules could be a factor?

 

[ZapperZ]

Suppose we have a closed system in which molecules cannot escape. Into this system we enter some radioactive molecules with $\beta^+$ decay. We know that the resulting daughter nuclide is also radioactive. We have some equations to describe the amount of parent nuclides and daughter nuclides, involving some constants which are correct. The equations are given by:
$$\frac{dN_1}{dt} = -\lambda_1 N_1$$
$$\frac{dN_2}{dt} = -\lambda_2 N_2 + \lambda_1 N_1$$

with $\lambda_1, \lambda_2$ the decay rates. Suppose we want to measure the amount of radiation in this system.

Could there be any reason why the predicted amount of radiation differs greatly from the measured amount of radiation. We know that molecules cannot leave the system so that cannot be a reason. We could say that faulty measuring equipment could be a reason but besides that is there any other reason? Maybe absorption of the molecules could be a factor?

This is frustratingly vague! It appears as if you are trying to find an explanation for something that you have in mind, but won't describe it fully here. Consequently, what you have written here is full of holes.

For example, what is this "closed system"? You never offered an explanation. Is it a physical vessel of some kind? Beta radiation are energetic electrons that will move away very quickly. So what are you containing them with? And what is this "equipment" that you are using? Radiation detection equipment are not sensitive to ALL types of radiation.

My answer is as vague or as accurate as the question itself.

Zz.