Question

Carbon-11, used in medical imaging, has a half- life of 20.4 min. The carbon-11 nuclides are formed, and the carbon atoms are then incorporated into an appropriate compound. The result ing sample is injected into the patient, and the medical image is obtained. If the entire process takes five half-lives, what percentage of the original carbon-11 remains at this time?

Answer 1

$5 half-lives\\ \% decayed \space is \space 100 \% -> 50 \% -> 25 \% -> 12.5 \%-> 6.125\% -> 3.0625 \%\\ So \space amount \space left \space is \space 3.0625 \%\\ We \space can\space use \space also\space 1st \space order \space kinetics t = (\frac{1}{k}) \ln(\frac{a}{a-x})\\ t = 5 *20.4 , k = \frac{0.693}{20.4}, a= 100 , we \space get \space a-x = 3.0625\\$