Question

The half-life for the radioactive decay of iridium-192 is 74.2 days. Calculate the amount in grams of Ir-192 that will be left from a 13.65g sample after a) 199.2 days b) 350 days

Answer 1

Answer: There are

a) 2.12 g of Ir-192 after 199.2 days

b) 0.52 g of Ir-192 after 350 days

Explanation:

Radioactive decay follows a first-order kinetics since the half life does not depend on the initial amount, then the equation which describes this process is:

$N(t)=N_{o}*e^{-\frac{-0.693*t}{t_{1/2} } }$

Where $N(t)$ is the amount given a certain t time, and $N_{o}$ is the initial amount. $t_{1/2}$ is the half life.

Then, the radioactive decay equation for this problem is:

$N(t)=13.65 g*e^{-\frac{-0.693*t}{74.2 days} }$

Note that the half life and the given time t must be on the same units, in this case days. Finally you calculate the amount for a) 199.2 days and b) 350 days:

$a) N(t)=13.65 g*e^{-\frac{-0.693*199.2 days}{74.2 days} }=2.12 g$

$b) N(t)=13.65 g*e^{-\frac{-0.693*350 days}{74.2 days} }=0.52 g$

Hope it helps!