Question

help!!
How long does it take for 78% of the Iodine-131 atoms (half-life = 8.04 days) in a sample of Iodine-131 to decay?

Answer 1

100% - 0 days
50% - 8.04 days

We know that at 78%, it between day 0-8.04.

Answer 2

Radioactive decay can be modelled as a first-order process:

\(\sf \large [A]_t=[A]_o*e^{-kt}\)

Find k, the decay constant:

\(\sf \large k=\dfrac{ln(2)}{t_{1/2}}=\dfrac{ln(2)}{8.04~days}\)


we're asked to find t, when: \(\sf \large [A]_t=[A]_o*0.78\)

\(\sf \large [A]_o*0.78=[A]_o*e^{-(\dfrac{ln(2)}{8.04~days})t}\)

\(\sf \large 0.78=e^{-(\dfrac{ln(2)}{8.04~days})t}\)


\(\sf \large ln(0.78)=\dfrac{-t*ln(2)}{8.04~days}\rightarrow t=2.88196~days\)