Posted by **Angie** on Wednesday, April 15, 2009 at 11:47pm.

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

- Science -
**drwls**, Thursday, April 16, 2009 at 1:00am
The number of radioactive atoms has decayed to 8/32 = 1/4 of the original value. That takes two half lives.

- Science -
**Angie**, Thursday, April 16, 2009 at 1:27pm
Why two half-lives?

- Science -
**DrBob222**, Thursday, April 16, 2009 at 3:15pm
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.

- Science -
**Angie**, Thursday, April 16, 2009 at 3:41pm
ok thanks

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