Half life of a nuclear decay via simulation

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Homework Help Overview

The discussion revolves around understanding the concept of half-life in nuclear decay, particularly focusing on the probability aspects and real-life applications of half-life, such as in radioactive dating. Participants are exploring the relationship between the number of atoms and their decay over time.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the probability related to half-life and discussing the implications of independent versus dependent half-life. There is also curiosity about the practical applications of half-life in scenarios where the quantity of remaining nuclei is very small.

Discussion Status

The discussion is active with various participants offering insights into the relationship between activity and the number of atoms, as well as raising questions about probability and real-world applications. Some guidance has been provided regarding the proportionality of activity to the number of atoms, but no consensus has been reached on the probability aspects or the concept of dependent half-life.

Contextual Notes

Participants are working under the constraints of homework assignments and are seeking clarification on concepts without being provided with direct solutions. The original poster expresses confusion about the probability of half-life, indicating a need for foundational understanding.

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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