Answer to Question #88395 in Atomic and Nuclear Physics for Sydnee

Question

The half-life of Yttrium-91 is 59 days. How much of a 90.3 g sample of Yttrium-91 will remain after 324 days?

(answer is in grams, no units required)

Answer 1

Let’s use the formula for radioactive decay:

$$N = N_0e^{- \lambda t},$$

here, $N_0 = 90.3 g$ is the initial amount of Yttrium-91, $N$ is the amount of Yttrium-91 that will remain after 324 days, $\lambda = 0.693/T_{1/2}$ is the decay rate, $T_{1/2} = 59 days$ is the half-life of Yttrium-91 and $t = 324 days$ is the time elapsed.

Then, we get:

$$N = N_0e^{- \lambda t} = 90.3 g \cdot e^{- \dfrac{0.693 \cdot 324 days}{59 days} } = 2.0 g.$$

Answer:

$N = 2.0 g.$