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Radioactive decay can be used to determine the age of an object. If you know the

ID: 1456599 • Letter: R

Question

Radioactive decay can be used to determine the age of an object. If you know the number of radioactive nuclei with which an object started, the number of radioactive nuclei currently present, and the half-life of the isotope, you can calculate the time since the object was created. Suppose an object was created with 3.830 * 10^9 nuclei of a particular isotope that has a half-life of 1.22 * 10^3 yr. At this point in time 1.455 * 10^9 nuclei of this particular isotope remain. What is the age of the object Since the activity (decay rate) of an isotope is proportional to the number of nuclei, you can use a very similar method to determine the age of an object using the activity. Suppose that at the time of creation an object had an activity of 2.080 * 10^1 Bq due to a particular isotope that has a half-life of 3.38 * 10^3 yr. At this point in time the object has an activity of 3.536 Bq due to this particular isotope remain. What is the age of the object

Explanation / Answer

Here ,

number of nuclei , N0 = 3.5 *10^9

half life , t0.5 = 1.22 *10^3 year

N = 1.455 *10^9

let the age of object is t

as N = N0 * 0.5^(t/t0.5)

1.455 *10^9 = 3.5 *10^9 * 0.5^(t/(1.22 *10^3))

solving for t

t = 1545 year

the age of object is 1545 year
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initial activity , A0 = 2.080 *10^1 Bq

half life , t0.5 = 3.38 *10^3 year

final activity , A = 3.536 Bq

for the age t

A = A0 * 0.5^(t/t0.5)

3.536 = 20.80 * 0.5^(t/(3.38 *10^3))

solving for t

t = 8640.6 year

the age of object is 8640.6 year