Question

1. a radioisotope has a half - life of 4 days. how much of a 20 - gram sample of this radioisotope remains at the end of each time period? show your work and box the answer. a. 4 days b. 8 days round your answers to the nearest whole number

Explanation:

Step 1: Recall half - life formula

The formula for radioactive decay is $N = N_0(\frac{1}{2})^{\frac{t}{T_{1/2}}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T_{1/2}$ is the half - life.

Step 2: Identify given values

We are given that $N_0=20$ grams, $T_{1/2} = 4$ days. Let's assume we want to find the amount remaining after different time periods. For example, if $t = 4$ days:
$N = 20\times(\frac{1}{2})^{\frac{4}{4}}$
$N = 20\times\frac{1}{2}=10$ grams. If $t = 8$ days:
$N = 20\times(\frac{1}{2})^{\frac{8}{4}}$
$N = 20\times(\frac{1}{2})^2=20\times\frac{1}{4} = 5$ grams.

Answer:

If the time period $t = 4$ days, the amount remaining is 10 grams. If $t = 8$ days, the amount remaining is 5 grams.