Answer to Question #350894 in General Chemistry for Gwapo

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

"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 = ?


"t_{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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