Radioactive Decay - Gaussian or Poisson

In summary, the conversation discussed the use of Poisson and Gaussian distributions to model radioactive decay probability. It was concluded that the Poisson distribution will always be the better fit, as the Gaussian distribution is derived from the Poisson and may not accurately represent very few events.
  • #1
binbagsss
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Radioactive Decay Probability?

Say you are counting the number of decays and the time of observation is varied. I know that as time increases, the Gaussian Distribution becomes a closer fit to the observed probability than when the time interval takes smaller values because the mean count rate increases, but which is the better fit - Poisson or Gaussian?

I expect Poisson disttribution to remain the better fit throughout, as in this situation the Gaussian distribution can be derived from the Poisson?

Thanks
 
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  • #2
Yes, the Poisson will always be the exact fit for this. The Gaussian will never give the right shape for very few events.
 

FAQ: Radioactive Decay - Gaussian or Poisson

1. What is radioactive decay?

Radioactive decay is the process by which an unstable atom loses energy and transforms into a more stable atom. This is often accompanied by the release of radiation.

2. What is the difference between Gaussian and Poisson distribution in relation to radioactive decay?

Gaussian and Poisson distributions are two mathematical models used to describe the probability of observing a certain number of radioactive decays within a given time period. The main difference is that Gaussian distribution assumes a continuous and symmetrical distribution of decay events, while Poisson distribution assumes a discrete and random distribution.

3. Which distribution is more commonly used to model radioactive decay?

Poisson distribution is more commonly used to model radioactive decay because it is better suited for discrete events like radioactive decay and it does not assume a fixed time interval.

4. Can radioactive decay ever follow a Gaussian distribution?

In some cases, radioactive decay may follow a Gaussian distribution if the number of observed decays is large and the time interval is small. However, this is rare and Poisson distribution is still the preferred model for radioactive decay.

5. How is the decay constant related to the shape of the decay curve?

The decay constant, also known as the half-life, is a measure of how quickly an unstable atom decays. In a Poisson distribution, a smaller decay constant will result in a steeper decay curve, while a larger decay constant will result in a more gradual decay curve.

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