Half life of a nuclear decay via simulation

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SUMMARY

The discussion centers on understanding the concept of half-life in nuclear decay and its probabilistic nature. Participants clarify that the activity, represented as dN/dt, is directly proportional to the number of atoms, N, with λ as the constant of proportionality. The half-life is defined as the time required for the quantity of atoms to reduce to half its initial amount, N0/2. Additionally, the conversation highlights that half-life is an independent process, contrasting it with dependent events, using the example of rolling dice to illustrate independent probabilities.

PREREQUISITES
  • Understanding of nuclear decay and half-life concepts
  • Familiarity with probability theory, particularly independent events
  • Basic knowledge of radioactive-carbon dating techniques
  • Experience with mathematical modeling in simulations
NEXT STEPS
  • Research the mathematical formulation of half-life in nuclear decay
  • Study the principles of probability, focusing on independent and dependent events
  • Explore radioactive-carbon dating methods and their applications
  • Learn about simulations in physics, particularly in modeling decay processes
USEFUL FOR

Students in physics or chemistry, educators teaching nuclear decay concepts, and researchers interested in radioactive dating techniques will benefit from this discussion.

Kynaston
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I don't know how to solve the questions that my lecturer gave me. I not understand about probability of half life. Can anyone explain to me and help me solve the questions as well? My lecturer ask us to prove the probability as shown in the picture.
 

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For the first part, you should know that the activity, dN/dt is directly proportional to the number of atoms N. So you can solve for N there since λ is the constant of proportionality.

EDIT: For the half-life, this is the time at which the number of atoms present is N0/2.
 
How about the probability? The 1/6? And what is the difference between dependent and independent half-life?
 
Kynaston said:
How about the probability? The 1/6?


Well consider a cube or a die (which has six sides) and you mark one face. Well let's just consider the die, with faces marked as 1,2,3,4,5,6.

If you throw a die, P(any number) = 1/6 (one number per face in six faces)

So P(Getting 1) = 1/6. Now consider when we throw two dice.

1st die: P(Getting 1) = 1/6

2nd; die: P(Getting 1) = 1/6

Now they are the same. If the first die gets a '1', it does not affect the second die as it has its own six faces and a '1' on a face. So what does this mean?


Kynaston said:
And what is the difference between dependent and independent half-life?

Well half-life is independent, so I don't think there is such thing as dependent half-life.
 
Last question,
For real life application (eg: age of a rock), if the quantity of remaining nuclei, N is very small, will this nuclei still be useful?
 
Well if it is still decaying and the radiation can be detected, you can probably use some sort of radioactive-carbon dating type technique.
 
rock.freak667 said:
Well if it is still decaying and the radiation can be detected, you can probably use some sort of radioactive-carbon dating type technique.

Carbon Dating is generally used to find ages from ~6000 yrs

you'll get large error for ages like 600yrs for 15000Yrs
 

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