Law of Nuclear Decay: Exploring Models and Accuracy

In summary, radioactive decay is typically described by the law that states the rate of decay is linearly proportional to the number of nuclides available, with the constant of proportionality being a positive value. This law is generally accurate, but there are situations where it may not hold true due to the quadratic nature of quantum mechanics. This can result in deviations from the exponential decay law for both short and long periods of time. There are numerous articles and studies exploring this topic, with some suggesting alternative models such as the "Zeno" or "non-exponential" decay. Overall, while the basic law is accurate in most cases, there are still ongoing discussions and research on better models for describing nuclear decay.
  • #1
pivoxa15
2,255
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Radioactive decay is normally characterised by 'the rate of decay is linearly proportional to the number of nuclides avaliable'. i.e dN/dt=-aN (a>0)

How correct is this law? Are there better models of describing nuclear decay? If so what are they?
 
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  • #2
The basic law is quite accurate. The physical assumption is that the probability of an atom decaying is independent of another atom decaying.
 
  • #3
So this law is like the inverse square gravitational and electrostatic laws in that they are very simple but extremely accurate and only when one goes down to several decimal points does it break down?
 
  • #4
pivoxa15 said:
How correct is this law?

In practice, in most situations, it works very well. However, not always. The problem is that quantum mechanics is a quadratic theory, while radioactive decay follows a linear relation. Consequently, things only decay following the exponential law for times that are not too short and not too long.

Here's some slides showing the issue:
http://www.drake.edu/artsci/physics/petridis_other_files/dnp_talk_10_19_01.ppt [Broken]


Here are some references:
http://arxiv.org/abs/quant-ph/0202105
http://www.aip.org/pnu/1997/split/pnu327-2.htm [Broken]
http://arxiv.org/abs/physics/0505042
http://arxiv.org/abs/quant-ph/0411145
http://arxiv.org/abs/quant-ph/9806079

From the peer-reviewed literature:
http://prola.aps.org/abstract/PRA/v63/i6/e062110

There are tons of articles on this. Search for "Zeno" or "non exponential decay".

Carl
 
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1. What is the Law of Nuclear Decay?

The Law of Nuclear Decay is a fundamental principle in nuclear physics that describes the rate at which radioactive nuclei decay over time. It states that the number of radioactive nuclei in a sample will decrease exponentially over time, with a constant decay rate known as the half-life.

2. How is the Law of Nuclear Decay applied in scientific research?

The Law of Nuclear Decay is used in a variety of scientific fields, including nuclear medicine, radiocarbon dating, and nuclear energy. It allows scientists to accurately determine the age of ancient artifacts, track the spread of pollutants, and design safe and efficient nuclear reactors.

3. What are some common models used to study nuclear decay?

One common model used to study nuclear decay is the exponential decay model, which describes the rate of decay as a function of time. Another model is the Bateman equation, which takes into account multiple decay pathways and allows for the calculation of the activity of each decay product.

4. How accurate is the Law of Nuclear Decay?

The Law of Nuclear Decay is a highly accurate model for predicting the rate of radioactive decay. However, it is based on statistical probability and cannot predict the exact time of decay of an individual nucleus. Additionally, factors such as external influences and experimental error can affect the accuracy of results.

5. Can the Law of Nuclear Decay be applied to all types of radioactive decay?

While the Law of Nuclear Decay applies to most types of radioactive decay, there are some exceptions. For example, it does not apply to spontaneous fission, a form of nuclear decay that occurs in very large and unstable nuclei. Additionally, it may not accurately predict the decay of some short-lived and highly energetic particles.

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