Half life of a nuclear decay via simulation

1. Jul 25, 2011

Kynaston

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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2. Jul 25, 2011

rock.freak667

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.

3. Jul 25, 2011

Kynaston

How about the probability? The 1/6? And what is the difference between dependent and independent half-life?

4. Jul 25, 2011

rock.freak667

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?

Well half-life is independent, so I don't think there is such thing as dependent half-life.

5. Jul 25, 2011

Kynaston

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?

6. Jul 25, 2011

rock.freak667

Well if it is still decaying and the radiation can be detected, you can probably use some sort of radioactive-carbon dating type technique.

7. Jul 26, 2011

cupid.callin

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

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