The half life can be used to calculate the amount of the radioactive element remaining. From the calculations carried out, the age of the mineral is 2 * 10^7 years.
The half life of a radioactive element refers to the time taken for only about half of the number of radioactive atoms to remain.
Let us recall that there was no loss of atoms hence;
Number of Ut-189 atoms initially present = 150 + 50 = 200 atoms
Number of Ut-189 remaining after time t = 50 atoms
Half life of the mineral = 10 million years
Using;
N/No = (1/2)^t/t1/2
50/200 = (1/2)^t/1 * 10^7
1/4 = (1/2)^t/1 * 10^7
(1/2)^2 = (1/2)^t/1 * 10^7
2 = t/1 * 10^7
t = 2 * 1 * 10^7
t = 2 * 10^7 years
The age of the mineral is 2 * 10^7 years.
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