The highly radioactive plutonium in nuclear waste undergoes first-order decay with a half-life of approximatel

Question

The highly radioactive plutonium in nuclear waste undergoes first-order decay with a half-life of approximately 24,000 years. How many years must pass before the level of radioactivity due to the plutonium falls to 1/128th (about 1%) of its original potency?

Answer 1

Actually, 128 is 2 to the seventh power, not the eighth, so it's seven times 24,000, or 168,000, years.

Edit:

Ok, 1st 24,000 years - 1/2
2nd - 1/4
3rd - 1/8
4th - 1/16
5th - 1/32
6th - 1/64
7th - 1/128

7 * 24,000 = 168,000, NOT 192,000. It's just simple arithmetic.

Answer 2

It takes 24,000 yrs to decay by one-half (50% or 0.5) leaving half the sample, in another 24,000 yrs the remaining sample will have decayed by one-half leaving you with 1/4th the original or 0.25. In another 24,000 yrs that sample will have half of itself decay leaving 1/8th of the original, or 0.125 and so on. Keep going until you reach a value close to 0.01 (1%) and then add up the years it took. BTW, the original fuel for nuclear reactors isn't very radioactive, but the waste certainly is. That's why it is kept under 28 feet of water or stored in casks underground (Yucca Mountain for example). Maybe in Russia they carry it around in barrels on trucks, but not here in the US. FWIW, I lived near a nuclear waste reclamation project and have some experience with reactors.

Answer 3

EVery 24,000 years, it loses half its potency. So after 48,000 (24K * 2) years, it's at 1/2 potency. After 72,000 (24K * 3) years, it's at 1/4 (1/2^2), and after 24K*4 years, it's at 1/2^3, etc. So to get to 1/128 (which is 1/2^7), it'd take 24,000*8 = 192,000 years.

I hope you don't just copy that down but actually learn from the explanation.

Edit: Response to the post below..... if you read carefully you'll see it DOES say 2^7.... When you have 2^i, you multiply 24,000 by i+1. It's all explained above.

Answer 4

I question your statement about highly radioactive. Anything with that long of a half-life has a very low activity.

Now then, rules of thumb about decay:

7 half-lives gets you just under 1%
10 half-lives gets you to 0.1%

7X24,000 yr = 168,000 years until it is at 1%
10X 24, 000 yr = 240,000 years until 0.1%

BTW, the plutonium you are writing about is Pu-239, excellent source of power. In fact, a light-water reactor winds up using a great deal of Pu-239 and Pu-240 at the end of its year and a half run. It is made and burned in the fuel.