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Author Topic: Nuclear Chemistry- question about finding the percent by mass of U-238 in a rock  (Read 1391 times)

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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.
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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 04, 2012, 06:50:49 PM by curiouscat »
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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!
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aafable

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