posted by Angie on .
A material has 32 atoms in all; 24 decayed and the rest undecayed. If the half-life of the radioactive material is 1000 years, what is the age of the material?
a. 1000 years
b. 2000 years
c. 3000 years
d. 4000 years
The number of radioactive atoms has decayed to 8/32 = 1/4 of the original value. That takes two half lives.
Why two half-lives?
Angie, you can also work the problem as I showed you on the 30 mCi problem you had earlier.
k = 0.693/1000 years = 6.93 x 10^-4
ln(No/N) = kt
[No is the number of atoms we started with; N = number of atoms today]
ln(32/8) = 6.93 x 10^-4*t
ln 4 = 6.93 x 10^-4*t
1.386/6.93 x 10^-4 = t = 2,000 years.