Radioactive decay can be used to determine the age of an object. If you know the
ID: 1456580 • 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 3.500×109 nuclei of a particular isotope that has a half-life of 1.58×103 yr. At this point in time 7.350×108 nuclei of this particular isotope remain. What is the age of the object? Submit Answer Tries 0/10 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 2.000×101 Bq due to a particular isotope that has a half-life of 4.09×103 yr. At this point in time the object has an activity of 2.800 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 = 1.58 *10^3 year
N = 7.35 *10^8
let the age of object is t
as N = N0 * 0.5^(t/t0.5)
7.35 *10^8 = 3.5 *10^9 * 0.5^(t/(1.58 *10^3))
solving for t
t = 3557.43 year
the age of object is 3557.43 year
-------------------------------
initial activity , A0 = 2 *10^1 Bq
half life , t0.5 = 4.09 *10^3 year
final activity , A = 2.8 Bq
for the age t
A = A0 * 0.5^(t/t0.5)
2.8 = 20 * 0.5^(t/(4.09 *10^3))
solving for t
t = 11601 year
the age of object is 11601 year
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