How Accurate is the Law of Nuclear Decay in Describing Radioactive Processes?

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Discussion Overview

The discussion centers on the accuracy of the law of nuclear decay, which states that the rate of decay is linearly proportional to the number of nuclides available. Participants explore whether this law is sufficient to describe radioactive processes or if alternative models exist.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states that radioactive decay is characterized by the equation dN/dt=-aN, questioning the law's accuracy and the existence of better models.
  • Another participant argues that the basic law is quite accurate, noting that the probability of an atom decaying is independent of another atom decaying.
  • A different participant compares the law of nuclear decay to the inverse square laws of gravity and electrostatics, suggesting that while the laws are simple and accurate, they may break down at very precise measurements.
  • Another participant acknowledges that while the law works well in practice, it may not hold under all conditions, particularly due to the quadratic nature of quantum mechanics versus the linear relation of radioactive decay. They suggest that the exponential decay law is valid only for certain time scales.
  • This participant provides links to external resources and literature that discuss the limitations and nuances of the decay law, including references to "Zeno" and "non-exponential decay."

Areas of Agreement / Disagreement

Participants express differing views on the accuracy and applicability of the law of nuclear decay, with some asserting its reliability while others highlight its limitations and the potential for alternative models. The discussion remains unresolved regarding the completeness of the law in various contexts.

Contextual Notes

Participants note that the law may not be accurate under all conditions, particularly in short or long time frames, and that its validity may depend on specific assumptions about quantum mechanics.

pivoxa15
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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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The basic law is quite accurate. The physical assumption is that the probability of an atom decaying is independent of another atom decaying.
 
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?
 
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


Here are some references:
http://arxiv.org/abs/quant-ph/0202105
http://www.aip.org/pnu/1997/split/pnu327-2.htm
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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