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

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 4.810×10⁹ nuclei of a particular isotope that has a half-life of 1.56×10³ yr. At this point in time 9.620×10⁸ nuclei of this particular isotope remain. What is the age of the object?

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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 3.820×10¹ Bq due to a particular isotope that has a half-life of 2.73×10³ yr. At this point in time the object has an activity of 4.966 Bq due to this particular isotope. What is the age of the object?

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Expert Solution

Number of radioactive nuclei at time is

Decay constant

Number of nuclei at time is

Initial number of nuclei ,

Age of the object is

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Activity of an isotope at time is

Decay constant

Initial activity of isotope

Activity of isotope at time is

Age of object is

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genius_generous answered 2 years ago

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