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aplinglearning.com/ibiscms/mod/ibis/view.php?id-4941063 hing 15 af Sapling Learning ehis question was with by reported on what may be the world's oldest intact rocks, around 4.10 x 10P years old. Sclentists recently Their estimate is based on the ratio of samarium-146 to neodymium-142. Sm-146 alpha-decays to Nd-142 with a half-life of 7.0 x 10 years. What fraction of the original Sm-146 would be left after 4.10 x10P years? Tools Previous Give Up & View Salution Check Answer Nextxit Hint about us careers privacy policy terms ofuze contact vs e x. Berea College-C- . Netflix-Google c., a Ha 10-Kinetics-phene.. a 1 i-Equilibri DeLL F10 F3 F4 F5 F6 F7 F8 F2 8 7 8 8 3 4 5 6Explanation / Answer
The decay reaction is 1st order, -dC/dt= K[C] (1)
where C= concentration of samarrium-146
when eq.1 is intergrated noting that at t=0, [C]= [C]0 and t= t, [C]=[C]
ln (C/CO)= -Kt (2)
half life (t1/2) is the time required for the concentration to drop to 50% of the initial value, C= CO/2
hence Eq.2 becomes ln(1/2)= -K*t1/2, t1/2= 0.693/K
K= rate constant = 0.693/t1/2= 0.693/(7*107) years-1
at t= 4.10*109 years old, C/CO= fraction of samarrium remaining = exp(-4.10*109*0.693/7*107)=2.35*10-18
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