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*10^{9} 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^{-10}yrs^{-1}

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

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

=1.23544644*10^{-16}s^{-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*10^{9})/(1/(1.24*10^{-16}s))= 3.596*10^{-15}

-or-

N_{t}=(4.5*10^{9})/(1.24*10^{-16}s^{-1})=2.338709677*10^{17}

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*10^{23} moles U-238)(238g U-238)=5.136799696*10^{11}grams

(2.338709677*10^{17})(6.002*10^{23} moles U-238)(238g U-238)=3.340790645*10^{43}grams

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.