Question

The activity of a certain isotope dropped from 3200 ci to 800 ci in 24.0 years. what is the half-life of this isotope (in years)? show your work.

Answer 1

Ln(800/3200) = - kt
t = 24 years.
ln(0.25) = -k*24
(- 1.3863) = -k*24
1.3863  / 24 = k
0.05776 = k

ln(0.5) = -k*t
-0.6931 = - 0.05776 t
12 = t

I don't know if you can just look at the question and know the answer. If 24 years is a quarter life then is it obvious that the 1/2 life is 12 years? It might be, but the method I've used works for sure.