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Topic: Nuclear Chemistry- question about finding the percent by mass of U-238 in a rock  (Read 7676 times)

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Offline TinkerBell2175

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Hello, I have been working on this problem going on a week today.  I was wondering if anyone can give me some pointer or hints.

Problem is:
The half-life of U-238 is 4.5*109 yrs.  A sample of rock of mass 1.6g is found to produce 29 disintegration per second (dis/s).  Assuming that all the radioactivity is due to U-238, find the percent by mass of U-238 in the rock.

This is what I have so far, I am not sure if I am doing this right, I am going on the few hints my prof gave me.

I found k constant doing 0.693/half-life which is 1.54*10-10yrs-1 

I then changed that into s-1. I did my conversion:

(1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)
=1.23544644*10-16s-1

my prof suggested that I used Rate=kNt, so I tried to use it.  I am finding Nt with having the Rate and k.  This is when I ran started running into difficulty. 

Nt=Rate/k
I am not sure whether do plug it in:
Nt=(4.5*109)/(1/(1.24*10-16s))= 3.596*10-15
                             -or-
Nt=(4.5*109)/(1.24*10-16s-1)=2.338709677*1017

I then changed nuclei remaining into grams using avagando's number and 238g for 1 mole of U-238.
(3.596*10-15)(6.002*1023 moles U-238)(238g U-238)=5.136799696*1011grams

(2.338709677*1017)(6.002*1023 moles U-238)(238g U-238)=3.340790645*1043grams

These large answers I got above make no sense to me and seemed way too big.

I don't know where to go from here or if the way I did it up till now is correct.  If someone can give me hints and steps to follow for this problem I would much appreciate...I can't learn by having someone just tell me the answer.

Thank you for looking at my post and if you have any idea, please let me know.

Offline curiouscat

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(1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)
=1.23544644*10-16s-1

Bug #1:

 (1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)

Bug #2:

(1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)
=1.23544644*10-16s-1

Quote
I don't know where to go from here or if the way I did it up till now is correct.  If someone can give me hints and steps to follow for this problem I would much appreciate...I can't learn by having someone just tell me the answer.

Your steps seem right to me. Trouble's in the arithmetic.

I get 0.1424%. Sounds reasonable; might yet be wrong. Check it.
« Last Edit: December 05, 2012, 12:50:49 AM by curiouscat »

Offline TinkerBell2175

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(1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)
=1.23544644*10-16s-1

Bug #1:

 (1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)

Bug #2:

(1/1.54*10-10yr-1)(1 year/365 days)(1 day/24 hours)(1 hour/60 seconds)
=1.23544644*10-16s-1

Quote
I don't know where to go from here or if the way I did it up till now is correct.  If someone can give me hints and steps to follow for this problem I would much appreciate...I can't learn by having someone just tell me the answer.

Your steps seem right to me. Trouble's in the arithmetic.

I get 0.1424%. Sounds reasonable; might yet be wrong. Check it.

Thank you so much for your *delete me*  I thought it might be arithmetic issues, but when you work on it for a week and still get crazy answers, it takes new eyes to help out.  :) I appreciate it!

Offline aafable

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Thanks! I've been having trouble with this as well. Glad I found it here!

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