The half-life for the radioactive decay of c-14 is 5730 years and is independent of the initial concentration. how long does it take for 25% of the c-14 atoms in a sample of c-14 to decay? if a sample of c-14 initially contains 1.5 mmol of c-14, how many millimoles are left after 2255 years?

1. If 25% of the c-14 atoms in the sample decay, that means the final weight would be 100-25%= 75% of the initial weight. Then, the amount of time elapsed would be:

final weight= initial weight * 1/2^ (t/t1/2)
0.75* of the initial weight= initial weight * 2^-t/5730     >1/2 = 2^-1
0.75 = 2^-t/5730  
log2 0.75 = log2 (2^-t/5730)
-0.415= -t/5730       >2^-0.415= 0.75
t=0.415*5730
t=2378 years

2. if a sample of c-14 initially contains 1.5 mmol of c-14, how many millimoles are left after 2255 years?


final weight= initial weight * 1/2^ (t/t1/2)
final weight= 1.5mol * 1/2^ (2255/5730)
final weight= 1.5mol* 1/2^0.39354
final weight= 1.5mol*  0.761= 1.14 mol