I got k=2.13 x 10^-6 yrs^-1 i dont know what to do next?

Question

Chlorine-36 is a beta emitter, with a half-life of 3.0 x 10^5 years. how many beta particles are emitted in one minute from a 5.0mg sample of 36Cl? How many Curies of radiations does the 5.0mg sample it represents?

Answer 1

My calculator had a real hard time dealing with this when I first tried this, but let me take you through what I did.  

I first took the number of half-lives that occurred over 15000 years (15000/3x10^5), which gives you 0.5.  You then use this as your exponent of 1/2 to give you the proportion of the original sample remaining (0.5^0.5=0.707...).  Keep that number somewhere, either written or stored in your calculator's memory.  Using such a large amount of time will keep the exponent high and will thus give you a number that the calculator can work with.

You should then calculate the number of atoms of 36-Cl you start with.  Take 0.005g / (35.453 g/mol) * 6.0221x10^23 atoms/mol and you should get 8.493x10^19 atoms.  Multiply this number by the number you saved above (0.707...) to get 6.0055x10^19 atoms, which represents the number of atoms of 36-Cl you have left undecayed after 15000 years.  

I then took the difference between the starting atoms and the ending atoms to get 2.4876x10^19 atoms.  This represents the number of chlorine atoms that decayed over 15000 years.  You can then take this number and do the divisions to get the number of decays that occurred over 1 minute.  

(2.4876x10^19)/15000/365/24/60 = 3.1552x10^9 particles emitted for that minute.

To get the curies, you must first divide the above answer by 60 to get the decays per second = 5.2587 x 10^7.  You must then divide this number by 3.7 x 10^10 since 1 Ci is equal to 3.7x10^10 decays per second.  Your number should be 1.4212 x 10^-3 Ci or 1.4212 mCi.