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The radioactive isotope of Carcon (^14C)has a half life of 5730. What is the decay constant of ^14C? If we start with a sample of 1000 carcon nuclei, how many will be left in 22920 years time?

  • Pre-Cal - ,

    22920 years is exactly 4 half-lives, so the number of nuclei is 2^4 = 16 times less. That will leave 1000/16 = 67 C14 atoms.

    The relationship of the decay constant (k) and the half-life (T1/2) is:

    k = 0.693/(T1/2)

    so k = 1.21*10^-4 years-1

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