How can radioactive half-life be used to date fossils?

1 Answer
1s2s2p
Mar 16, 2018

#A=A_0e^(-lambdat)#, where:
#A# = current activity (#s^-1#)
#A_0# = original activity (#s^-1#)
#lambda# = decay constant #(ln(2)/t_(1/2))# (#s^-1#)
#t# = time (#s#, though sometimes uses different units like #year^-1# when #lambda# is given in terms of years)

#A/A_0=e^(-lambdat)#

#ln(A/A_0)=-lambdat#

#t=-ln(A/A_0)/lambda#

#t=-(t_(1/2)ln(A/A_0))/ln(2)#

#t# #(text(years))=-(5730ln(A/A_0))/ln(2)#

If we know the current activity of the decay of #""^14"C"# and use living material for a rough estimate for the original activity of #""^14"C"#, then we can put them into this equation to find its age in years.

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