# Radiation Decay: Calculating Half-Life & Nuclei Activity

• Michael1974
In summary, the conversation discusses the concept of half-life and its calculation through a function expression. The graph provided shows the result of throwing sixty different dice, representing atomic nuclei, and disintegrating those that roll a 3 before the next roll. The function expression is 15.19 * e ^ -0.25x, indicating an exponential decay. The relationship between nuclei activity and half-life is mentioned and the calculation of half-life is discussed using the maximum likelihood approach. Lastly, there is confusion about the model and the representation of 60 dice compared to one atomic nucleus.
Michael1974
1. If I throw sixty different dice (compared to an atomic nucleus) and each dice that gets a 3 is disintegrated and disappear before the next roll. Altogether I make ten roll, where each roll corresponds to one day. The result is illustrated in a graph: http://imgur.com/TbXF4mf click on the picture to see. X = time in days, Y = decays under a day These questions must be answered: a) How can I read and calculate the half-life through my function expression? b) What is the function expression? c) the relationship between nuclei activity d) The difference between a nucleus and dice?2. No equations given.3. The half-life must surely be somewhere between the third and fourth day (throw). But how can I calculate it exactly by reading? Functional expression is well in my graph: 15.19 * e ^ -0,25x. This is indeed a exponentiellfunktion, if I understand correctly? How can I get out activity between nuclei I have not decay constant? The last question I do not understand at all ..

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Michael1974 said:
how can I calculate it exactly by reading?
I believe the usual approach is maximum likelihood. I.e., what value of the parameter makes the observations most likely?
See e.g. https://en.wikipedia.org/wiki/Exponential_distribution.

Not sure that I understand the model, though.
Michael1974 said:
sixty different dice (compared to an atomic nucleus)
Are you saying 60 dice represent (the neutrons in?) one nucleus? If so, once one has decayed everything changes. So I would have thought 60 dice represented 60 nuclei. Presumably, as they decay, you roll fewer dice each day.

## Related to Radiation Decay: Calculating Half-Life & Nuclei Activity

Radiation decay is the spontaneous process by which an unstable atomic nucleus loses energy in the form of radiation, in order to become more stable. This process can occur in different ways, such as alpha, beta, and gamma decay.

## What is half-life?

Half-life is the amount of time it takes for half of the radioactive nuclei in a sample to decay. This is a characteristic property of a specific radioactive element and is not affected by external factors.

## How is half-life calculated?

The formula for calculating half-life is t1/2 = (ln2 / λ), where t1/2 is the half-life, ln2 is the natural log of 2, and λ is the decay constant of the radioactive element. This formula can be used to determine the amount of time it will take for a specific amount of a radioactive element to decay by half.

## What is nuclei activity?

Nuclei activity, also known as radioactive activity, is a measure of the number of nuclear decays that occur in a sample of a radioactive element per unit of time. It is measured in becquerels (Bq) or curies (Ci).

## How does radiation decay and half-life affect the safety of nuclear power?

Radiation decay and half-life are important factors to consider in nuclear power safety. The longer the half-life of a radioactive element, the longer it will take for it to decay and become less harmful. However, some radioactive elements have very long half-lives, which can pose a potential risk for nuclear power accidents. Proper handling and disposal of radioactive waste is crucial in ensuring the safety of nuclear power.

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