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 3.270×10⁹ nuclei of a particular isotope that has a half-life of 1.66×10³ yr. At this point in time 1.079×10⁹ nuclei of this particular isotope remain. What is the age of the object?

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 2.740×10¹ Bq due to a particular isotope that has a half-life of 4.52×10³ yr. At this point in time the object has an activity of 3.562 Bq due to this particular isotope. What is the age of the object?

Answer 1

a)

let,

No=3.27*10^9

N=1.079*10^9

and

t1/2=1.66*10^3 year

use,

N=No*e^-lambda*t

here,

lambda=0.693/t1/2

lambda=0.693/(1.66*10^3)

=0.417*10^-3 decay/year

now,

N=No*e^-lambda*t

1.079*10^9=3.27*10^9*e^(-0.417*10^-3*t)

==> t=2.659*10^3 years

age of the object is, t=2.659*10^3 years

b)

let,

Ao=27.4 Bq

A=3.562 Bq

and

t1/2=4.52*10^3 year

use,

A=Ao*e^-lambda*t

here,

lambda=0.693/t1/2

lambda=0.693/(4.52*10^3)

=0.1533*10^-3 decay/year

now,

A=Ao*e^-lambda*t

3.562=27.4*e^(-0.1533*10^-3*t)

==> t=13.31*10^3 years

age of the object is, t=13.31*10^3 years