Half life of a nuclear decay via simulation

AI Thread Summary
The discussion focuses on understanding the concept of half-life in nuclear decay and its relationship to probability. It explains that the activity of a radioactive substance is proportional to the number of atoms present, allowing for calculations of the remaining quantity over time. The half-life is defined as the time required for the quantity of atoms to reduce to half its initial value. The conversation also clarifies that half-life is an independent process, unlike the outcomes of rolling dice, which are independent events. Finally, it mentions the application of carbon dating for determining the age of materials, noting its limitations for very old samples.
Kynaston
Messages
3
Reaction score
0
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.
 

Attachments

  • 1.jpg
    1.jpg
    25.3 KB · Views: 479
  • 2.jpg
    2.jpg
    23.3 KB · Views: 452
  • 3.jpg
    3.jpg
    20.2 KB · Views: 464
Physics news on Phys.org
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
 

Similar threads

I Decay constant of Different Elements and Isotopes?
Replies
3
Views
2K
I Half life and radioactivity clarification
Replies
20
Views
2K
I Speeding up the half-life of plutonium
Replies
5
Views
3K
Textbook 'The Physics of Waves': Lifetime of SHM Oscillators
Replies
5
Views
724
Physics question about half life / radioactive decay
Replies
4
Views
2K
Time taken for amount of a nuclear material to remain
Replies
5
Views
2K
What happens if t is greater than half-life?
Replies
3
Views
1K
Radiation Decay: Calculating Half-Life & Nuclei Activity
Replies
1
Views
1K
What is the purpose of the decay time distribution equation?
Replies
3
Views
1K
Solve Half-Life Problem: Find # Atoms Decaying in 12 Days
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top