Question #350894

Cobalt-60 is used extensively in medicine as source of Y-rays .





What is the half life of Co-60 it's takes 13.0 years to decrease the original activity to 18.0%?

1
Expert's answer
2022-06-16T15:12:04-0400

Nt=N0(12)tt1/2  N_t= N_0 \bigg(\cfrac12\bigg)^{\frac{t}{t_{1/2}}}\\~\\~\\

N(t) = quantity remaining = 0.18

N0 = initial quantity = 1

t = elapsed time = 13

t1/2 = half life of the substance = ?


t1/2= tln(N0Nt)= 13ln(10.18)= 13ln(5.556)= 131.715= 7.58t_{1/2}=~\cfrac {t}{ln(\frac{N_0}{N_t})}=~\cfrac {13}{ln(\frac{1}{0.18})}=~ \cfrac {13}{ln(5.556)}=~\cfrac {13}{1.715}=~ 7.58





Amswer: t1/2 (Co-60) = 7.58 year







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