Archeologists can determine the age of artifacts made of wood and bone by measur

Question

Archeologists can determine the age of artifacts made of wood and bone by measuring the concentration of the radioactive 14_C present in the object The amount of isotope decays via a first order process If 15.5% of the original amount of 14_C is present in a wooden tool at the time of analysis, what is the age of the tool' The half-life of 14_C is 5730 years What is the half-life in see for a second order reaction in reactant A with the rate constant k = 4.57 times 10^-1 M^-1 S^-1 if the initial concentration is 0.0200 M?

Explanation / Answer

Q5.

Apply Half life equation

recall that:

A = A0*(1/2)^(t/HL)

where

A = final concentration

A0 = initial concentration

1/2 = due to half life

t = time elapsed

HL = half life

so

substitute all data

A = A0*(1/2)^(t/HL)

15.5% = 100% * ( 1/2) ^(t / 5730)

solve for t

ln(15.5/100) = ln(1/2) * (t / 5730)

t =5730 * ln(15.5/100) / ln(1/2)

t = 15411.751 years old

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