Archeologists can determine the age of an artifact made of wood or bone by measuring the amount of the radioactive isotope. The age of the tool is 15, 396.51 years.
Half-life is the time of the decay of half of the substance.
After its second half-life will have 50% of the 0.5A So, the mass will be 0.25A. So, the percentage of A, is given by:
A = (0.5)n
Where n is quantitative of half-life. So, for 15.5% of C, or 0.155:
0.155 = (0.5)n
Applying log on both sides of the equation:
log 0.155 = log (0.5)n
n log(0.5) = log(0.155)
-0.301n = - 0.809
n = 2.687 half-life
If one half-life is 5,730 yr, than 2.419 will be:
2.687 x 5730 = 15, 396.51 years
Thus, the age of the tool is 15, 396.51 years.
To learn more about the half-life, refer to the link:
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