Comparing Decay Rates from Two Methods: Is α = β?

[lisab]

I’m going to post this here even though this question straddles Chemistry and Physics. I think I know the answer but I’d like confirmation.

Let's say I am measuring a property P that is decaying exponentially, but I am measuring it using two different test methods. Let’s call them method A and method B.

The data from method A fit the curve:

P(t) = A₀e^-αt

The data from method B fit the curve:

P(t) = B₀e^-βt

In this case, I know the methods well enough that I know that A₀ and B₀ will be different numbers. But isn’t it true that α = β?

 

[Borek]

If you are measuring the same property, but getting different results, something is wrong. And if something is wrong, everything can go wrong (that is, if A₀≠B₀, I don't see why to expect α=β).

Is it just an experimental error, or is there more to the difference between both methods?

 

[I like Serena]

If α = β, but A0<B0, then the first curve is less then the second curve everywhere.
In other words, they cannot fit the same data regardless of systematic or experimental errors.

Therefore, if A0≠B0 then that implies α≠β.

 

[lisab]

OK, mystery (sort of) solved.

Turns out there are two typos. One, the author accidentally used the same variable for the exponent. Two, in a graph showing results from both tests, there are supposed to be two sets of axes but only one got into the report.

I didn't notice the first typo but it was the graph that made my head spin. The units weren't right -- method A and method B give results in different units, so I was confused !

Thanks, Borek and ILS.

 

[LudusRex]

I understand your curiosity about whether α = β in this scenario. However, it is important to note that comparing decay rates from two different methods is not a straightforward process. There are several factors that can influence the decay rate, such as experimental conditions, sample preparation, and measurement techniques. Therefore, it is not safe to assume that α = β without further investigation and confirmation.

To determine if α = β, you would need to carefully analyze the data from both methods and assess the potential sources of error. This could include conducting control experiments, repeating the measurements multiple times, and comparing the results to known values. Additionally, you may also need to consider the underlying assumptions and equations used in each method to calculate the decay rate.

In some cases, it is possible that α and β may not be exactly equal, but they could still be within a reasonable margin of error. This could be due to the inherent variability of the measurement methods or the natural variability of the property being measured.

Therefore, as a scientist, it is important to exercise caution when comparing decay rates from different methods. It is always best to thoroughly analyze the data and consider all potential sources of error before drawing any conclusions.