Given:
Initial amount of
A1=40gInitial amount of
A2=160gHalf-life of
A1,TA1=20sHalf-life of
A2,TA2=10sTo determine when the amounts of
A1 and
A2 will be equal, we use the decay formula:
N=N0(‌)t∕TFor
A1, the remaining amount is:
NA1=40(‌)t∕20For
A2, the remaining amount is:
NA2=160(‌)t∕10To find the time when these amounts are equal, set
NA1=NA2 :
40(‌)t∕20‌=160(‌)t∕102t∕10‌=4⋅2t∕20⇒2‌−‌=42t∕20‌=22⇒‌=2t‌=40sTherefore, the amounts of
A1 and
A2 in the mixture will become equal after 40 seconds.