A sample of pure radioactive nuclide is allowed to undergodecay for 172.4 months

Question

A sample of pure radioactive nuclide is allowed to undergodecay for 172.4 months. At the end of this time, we discover wehave lost 72.2% of the original radioactive nuclide. What is thehalf-life (months) for this nuclide? THE ANSWER IS 93 BUT I NEED TO UNDERSTAND WHY. ANY HELP WOULDBE GREATLY APPRECIATED. THANK YOU. A sample of pure radioactive nuclide is allowed to undergodecay for 172.4 months. At the end of this time, we discover wehave lost 72.2% of the original radioactive nuclide. What is thehalf-life (months) for this nuclide? THE ANSWER IS 93 BUT I NEED TO UNDERSTAND WHY. ANY HELP WOULDBE GREATLY APPRECIATED. THANK YOU.

Explanation / Answer

Use the formula for first order decay which is[C]=[C]initial*exp(-kt) You want to figure out whats remaining of the sample, which wouldbe 100-72.2=27.8 so then you have 27.8=100exp(-172.4*k)(or .278=exp(-172.4*k) whenyou divide percentage by 100) To figure out k take ln of both sides and you get k=.00742 After you have k solve for time to get the half life---- .5=exp(-.00742*t) ln(.5)/-.00742=93

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