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Author Topic: Half life decay problem. Please Help  (Read 856 times)

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anneheather98

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Half life decay problem. Please Help
« on: December 15, 2018, 07:58:48 AM »

A rock sample from Western Greenland contains 0.603 mg of 206-Pb for every mg of 238-U. The half-life decay for
uranium to turn into lead is 4.5*10^9 years. How old is the rock?

The answer is 3.4*10^9 years old.

I've spent so long trying to figure out how to get this answer, nothing online has been found to help me. I'm sure it's really simple and straightforward. I've been using the formulas:

ln(N/N-initial)=-kt

and

k=ln2/halflife

If you could please use these when explaining I'd appreciate it alot I've been going nuts over this problem.
Thank you
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Borek

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Re: Half life decay problem. Please Help
« Reply #1 on: December 15, 2018, 12:19:08 PM »

You have 1 mg of U-238 and 0.603 mg of Pb-206. Can you calculate initial mass of U-238?
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anneheather98

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Re: Half life decay problem. Please Help
« Reply #2 on: December 15, 2018, 02:40:43 PM »

You have 1 mg of U-238 and 0.603 mg of Pb-206. Can you calculate initial mass of U-238?

1.603? I've tried using that and about 40 different calculations moving the numbers around. I'm missing where the figures should be applied to the formulas.
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Borek

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Re: Half life decay problem. Please Help
« Reply #3 on: December 15, 2018, 09:37:53 PM »

You have 1 mg of U-238 and 0.603 mg of Pb-206. Can you calculate initial mass of U-238?

1.603?

No. That's mass of U-238 and Pb-206, not initial mass of the U-238. Initial mass was higher, as Pb-206 is not the only product of decay.
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anneheather98

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Re: Half life decay problem. Please Help
« Reply #4 on: December 16, 2018, 04:44:18 PM »

You have 1 mg of U-238 and 0.603 mg of Pb-206. Can you calculate initial mass of U-238?

1.603?

No. That's mass of U-238 and Pb-206, not initial mass of the U-238. Initial mass was higher, as Pb-206 is not the only product of decay.

Can you just tell me please how you find the initial mass number. I get you want to walk me through it but its really not doing me any favors. I'm studying for a final which I now have tomorrow and I can actually understand it if you tell me. This is the only thing I cannot figure out.
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Borek

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Re: Half life decay problem. Please Help
« Reply #5 on: December 16, 2018, 09:43:19 PM »

For every atom of Pb-206 present now there was an atom of U-238, you know (at least approximately) masses of both atoms, so you can easily calculate initial mass of U-238 that decayed (beware: that's not total, but you know how much was left). This is not different from a simple stoichiometry.
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Enthalpy

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Re: Half life decay problem. Please Help
« Reply #6 on: December 17, 2018, 02:29:46 AM »

I wondered why one should assume that the rock contained no 206Pb when it formed. Wiki has the answer:
https://en.wikipedia.org/wiki/Uranium%E2%80%93lead_dating
"A rock sample" doesn't suffice. Instead,
"The dating method is usually performed on the mineral zircon. The mineral incorporates uranium and thorium atoms into its crystal structure, but strongly rejects lead. Therefore, one can assume that the entire lead content of the zircon is radiogenic".
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