Question

If a sample of C-14 initially contains 1.7 mmol of C-14, how many millimoles will be left after 2260 years?

The half-life for the radioactive decay of C-14C-14 is 5730 years.

Part A Part complete How long will it take for 25% of the C-14C-14 atoms in a sample of C-14C-14 to decay? Express your answer using two significant figures. View Available Hint(s) tt = 2400 yearsyears SubmitPrevious Answers Correct First, the rate (or decay) constant, kk, for the first-order radioactive decay should be determined from the relation between first-order half-life, t1/2t1/2, and the rate constant: k=0.693t1/2=0.6935730years=0.000121years−1k=0.693t1/2=0.6935730years=0.000121years−1 The rate constant can now be used in the first-order integrated rate law to find the time required, tt: ln[A]t[A]0=−ktln⁡[A]t[A]0=−kt where the ratio [A]t/[A]0[A]t/[A]0 can be considered the fraction of C-14C-14 atoms remaining at time tt. Since 25 %% of the C-14C-14 has decayed, 100%−%− 25 %% remains. Rearranging to solve for tt and inserting the values gives t=ln[A]t[A]0−k=ln0.75−1.21×10−4years−1

Answer 1