if a sample of radioactive material of 355g and a half-life of 3.75years. The remaining sample is 22.1875g how many half-lives have the material gone through and how old is the material?

DarkCalculis
Feb 16, 2018

#1**+2 **

Don't know about the big brain part....but.....we have this exponential decay form :

22.1875 = 355 (1/2)^(t / 3.75) we want to find "t"

Divide both sides by 355

22.1875 / 355 = (1/2)^(t/3.75) take the log of both sides

log ( 22.1875 / 355) = log (1/2)^(t / 3.75) and we can write

log ( 22.1875 / 355) = (t / 3.75) * log (1/2) divide both sides by log (1/2)

log ( 22.1875 / 355) / log (1/2) = t / 3.75 multiply both sides by 3.75

3.75 log ( 22.1875 / 355) / log (1/2) = t = 15 years old

Note that since a half-life lasts 3.75 years....it has gone through

15 / 3.75 = 4 half-lives

That worked out kinda' nice and neat .....!!!

CPhill
Feb 16, 2018