Understanding Carbon Decay: Solving for Decay Rate

[jimmy42]

How can I find the decay rate of carbon? I have found the decay constant and I know the half life and the number of atoms. I think I have the data and I have the answer but I think I am using the wrong equation as my answer does not fit the books.

The decay constant I got as -1.209x10^-4

N = 6.5234X10^10

half life = 5730 years.

I tried this:

R = ln(2) N/half life

That did not work.

 

[planauts]

The formula for finding the decay constant is: k = (ln2)/(half life) = 0.000121 years^-1

Activity = kN
Activity = (0.000121 years^-1)(6.5234*10^10) = 7.89*10^6 particles per year

It might be possible that they expressed their answer in Becquerel, as it is the SI unit for activity. What answer did they give?

 

[jimmy42]

The answer was given in minutes, It should be 15

 

[planauts]

The answer was given in minutes, It should be 15

Then the answer is correct.

7.89*10^6 particles per year

(7.89*10^6)/(365*24*60) particles per minutes = 15.0138 particles per minutes

= 15

 

[jimmy42]

Yes thanks, i didn't think to convert it.