Answer to Question #350894 in General Chemistry for Gwapo

Question

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%?

Answer 1

$N_t= N_0 \bigg(\cfrac12\bigg)^{\frac{t}{t_{1/2}}}\\~\\~\\$

N(t) = quantity remaining = 0.18

N₀ = initial quantity = 1

t = elapsed time = 13

t_1/2 = 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: t_1/2 (Co-60) = 7.58 year