Question

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Alpha particles produced by radioactive decay eventually pick up electrons from their surroundings to form helium atoms. Calculate the volume (in mL) of He collected at STP when 3.60 g of pure ²²⁶Ra is stored in a closed container for 136 years. (Assume that there are five alpha particles generated per ²²⁶Ra as it decays to ²⁰⁶Pb.)

Answer 1

One mole at STP corresponds to 22400ml

Assuming the half-life to be t yrs then we can say it has passed 136/t=k half-lives and we know matter left after n half lives is (0.5)ⁿ*initial

Hence after k half lives it is (0.5)^k*(3.6/226) moles

Hence decayed =(1-(0.5)^k)*(3.6/226)

Moles of He produced =(3.6/226)*5*((1-(0.5)^k))

Volume at STP= Moles of He *22400ml

Volume=1792*((1-(0.5)^k) Just put the value of k=136/t where t is half life of Ra and you are done

Assuming t=1600

Volume=1792*0.05721=102.53 ml