An isotope of postassium K^(40) undergoes two parallel type of decay, one by electron capture and other by beta decay with half lives as 1.3 xx 10^(9) year and (1.3)/(9) xx 10^(9) yearrespectively. If in a sample of a mineral mass ratio of K : Ar: Cais 5,1.5 & 16 then calculate age of the mineral if it known that all Ca^(40) in the mineral is not from the radioactive decay of potassium. [ Express youranswer in terms of 10^(7) year for eg. if you answer is 2 xx 10 ^(9) years fill 0200 in OMR sheet]

An isotope of postassium K^(40) undergoes two parallel type of decay,

1.	An isotope of postassium K^(40) undergoes two parallel type of decay, one by electron capture and other by beta decay with half lives as 1.3 xx 10^(9) year and (1.3)/(9) xx 10^(9) yearrespectively. If in a sample of a mineral mass ratio of K : Ar: Cais 5,1.5 & 16 then calculate age of the mineral if it known that all Ca^(40) in the mineral is not from the radioactive decay of potassium. [ Express youranswer in terms of 10^(7) year for eg. if you answer is 2 xx 10 ^(9) years fill 0200 in OMR sheet]
Answer» Solution : Assumed that all AR PRODUCED from K. `{:("K","Ar","Ca",,),("t=0","a",0,0,),("t=t","a-x-y","x","y prpduced",):}` `(x)/(y)=(lambda_(1))/(lambda_(2))=((t_(1//2))_(2))/((t_(1//2))_(1))=(1)/(9)` `y=9x` `x=(1.5)/(40) " " y=(9 xx1.5)/(40)` `a-x-y=(5)/(40)` `a=(5)/(40)+(1.5)/(40)+(9xx1.5)/(40)=(20)/(40)` `lambda t=ln (a)/(a-x-y)` `((LN2)/(1.3xx10^(9))+(ln2)/((1.3)/(9)xx10^(9)))t=ln.(20//40)/(5//40)` `t=26xx10^(7)`