[TinkerBell2175]

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=kN_t, so I tried to use it.  I am finding N_t with having the Rate and k.  This is when I ran started running into difficulty. 

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

[curiouscat]

(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

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.

[TinkerBell2175]

(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

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!

[aafable]

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