Question

An archaeologist in Turkey discovers a spear head that contains 32% of it's original amount of C-14.
Find the age of the spear head to the nearest year

Answer 1

for a first order reaction, you can use the exponential growth/decay equation:

\(A_{t}=A_0*e^{-kt}\)

where \(A_{t}\) is the amount after t time elapsed, \(A_0\) is the initial amount. t is time, and k is the decay constant (see below).

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Alternatively, you can use the first-order integrated rate law:

\(\large ln[A]_t=-kt+ln[A]_o\)

where \(ln[A]_o\) is the initial concentration of the substance
\(k\) is the decay constant
\(t\) is time
\(ln[A]_t\) is the concentration of substance at time \(t\)
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\(\large t_{1/2}=\dfrac{ln(2)}{k}\).

\(t_{1/2}\) is the half-life

Answer 2

great, so you have all the variables. plug them into the equation and solve it

Answer 3

Or you can rearrange them first, then plug your values in. Either works

Answer 4

\[0.32=e^{-.0001t}\] solve for \(t\)

Answer 5

0.0001 * t = in(1/32) ?

Answer 6

yep it's ln not in

Answer 7

so t = (1/32)/0.0001 ?

Answer 8

dont forget the ln

\(t = \dfrac{ln(1/32)}{0.0001}\)

Answer 9

oh ps, it's 0.32 not 32

\(t = \dfrac{ln(1/.32)}{0.0001}\)

Answer 10

i got it now :D

Answer 11

dope