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The previous part could be done without using the decay equation, because the ratio of original 14C14C to present 14C14C was an integer power of 1/2. Most problems are not so simple. To solve more general carbon-dating problems, you must first find the value of the decay constant for 14C14C, so that you can easily use the decay equation. Using the given half-life, 5730 yearsyears, find the value of the decay constant for 14C14C. Express your answer in inverse years to three significant figures. View Available Hint(s)

Answer :

Answer: The decay constant for C14 is [tex]0.000121years^{-1}[/tex]

Explanation:

Expression for rate law for first order kinetics is given by:

[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]

[tex]k=\frac{0.693}{5730years}=0.000121years^{-1}[/tex]

The decay constant for C14 is [tex]0.000121years^{-1}[/tex]

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