A wooden artifact from a Chinese temple has a 14C

aspifsGak5u 2021-12-15 Answered
A wooden artifact from a Chinese temple has a 14C activity of 38.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. From the half-life for 14C decay, 5715 yr, determine the age of the artifact.
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Expert Answer

Debbie Moore
Answered 2021-12-16 Author has 43 answers
Half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t12
All radioactive decay processes follow first order reaction.
The equation for the half-life for first order reaction follows:
t12=0.693k
where,
k = rate constant of first order reaction
Given value:
t12=5715 years
Plugging value in equation 1, we get:
k=0.6935715
k=1.21×104yr1
The integrated rate law expression for first order reaction follows:
t=2.303kloga(ax)
where,
t = time period
a = initial concentration of the reactant = 58.2 counts per minute
(a-x) = Concentration of reactant left after time t = 38.0 counts per minute
k = rate constant of first order reaction =1.21×104yr1
Plugging value in equation, we get:
t=2.3031.21×104yr1log58.238.0
t=3523.77yr

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