Answer:
T_{1/2} = 5,776 10³ years
We see this life time as it is very close to the life time of carbon 14, so it could be used for dating ancient objects
Explanation:
The radioactive decay of described by an equation of the form
N = N₀
where N is the number of atoms present, N₀ is the number of initial atoms λ is the activity of the material.
The average life time is defined as the time for which the number of remainng atoms is N = N₀ / 2
= ln 2 /λ
With these expressions, the best method to determine the average life time is to find the activity of the first equation.
For this we look for a point on the graph as accurate as possible,
N₀ = 100, N = 30 and t = 10,000 years
we substitute in the equation
30 = 100 e^{-\lambda 10000}
ln 0.3 = - λ 10000
λ = - (ln 0.3) / 10000
λ = 1.2 10-4
now we can find the average life time
= ln 2 / 1,2 10-4
T_{1/2} = 5,776 10³ years
We see this life time as it is very close to the life time of carbon 14, so it could be used for dating ancient objects