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
4 answers
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.
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.
ok thanks
1 answer