How many half-lives occurred if 5.2 x 10^24 atoms of Pb-212 decay into 0.54 miles of Bi-212? Round to nearest whole number.

Answer 1

There are a few ways to approach this. You can use the integrate rate equation for a first order reaction, but an easier way (in my opinion) is to use the formula F = 0.5n where F= fraction remaining and n = number of half lives that have elapsed. In this particular question, we will be solving for n.

First we will find the fraction remaining.

initial moles = 5.2x1024 atoms x 1 mol/6.02x1023 atoms = 8.64 moles

moles remaining = 0.54 moles

Fraction remaining = F = 0.54/8.64 = 0.0625

F = 0.5n

0.0625 = 0.5n

log 0.0625 = n log 0.5

-1.20 = -0.301n

n = 4.00 = number of half lives that have elapsed.