Radioactive dating ?

Question

It has been shown that the half-life for this radioactive isotope is 20 years. In the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery. It is shown that 95% of the nuclei have decayed.

How long ago was the pottery made?

Answer 1

8644 years. in the year 2000.

Answer 2

the relevant equations (first order kinetics) are

ln(Nt/N0) = -kt

and

t1/2 = 0.693/k

now if t1/2 is 20 yr

k = 0.693/20 = 0.03465

95% decay means that 5% nuclei have not decayed. So Nt/N0 = 0.05 (Nt is the number of nuclei left at time t)

therefore

ln 0.05 = -0.03465t

solve for t in years. It gives t = 86.5 years ago