Question

The half-life of 131I is 8.10 day.
Calculate how much time it would take for an isolated quantity of 131I to decay by 37%.

I know it's a pretty simple question, I'm just entirely stuck, and if I can get an answer for this one, I can probably figure out the rest of my homework.

Answer 1

\[A=A_0(b)^\frac{t}{p}\]Now A0=amt initially present and A=final amount. Since we are given A=(1-0.37)A0, or A=0.63A0, we can write,\[0.63=b^\frac{t}{P}\]now, b=1/2 because we're dealing with the half-life, P=8.10 days and t is our unknown. \[0.63=(\frac{1}{2})^\frac{t}{8.10}\]Now we solve for t:\[\log_{}0.63=\frac{t}{8.10}\log_{}\frac{1}{2} \]re-arranging:\[t=8.10\frac{\log_{}0.63}{\log_{}0.5} =5.40 \]So, it take about 5.40 days for the sample to decay to 63% of it's original value (or to say it another way, it takes 5.40 days for the sample to decay by 37%).