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

Explanation:

Step1: Calculate the number of half - lives

The half - life of the radioisotope is 4 days. The time period considered is not given in the problem statement, but if we assume we want to know the amount remaining after some time, let's first find the number of half - lives $n$. If we assume a time $t$, $n=\frac{t}{T_{1/2}}$. Since we are not given $t$, let's assume we want to know the general formula for the amount remaining. The initial amount of the sample $N_0 = 20$ g. The formula for the amount of a radioactive substance remaining after $n$ half - lives is $N = N_0\times(\frac{1}{2})^n$.

Step2: Analyze the decay process for different time periods

If we consider 4 days (1 half - life), $n = 1$. Then $N=20\times\frac{1}{2}=10$ g. If we consider 8 days ($n = 2$), $N = 20\times(\frac{1}{2})^2=20\times\frac{1}{4} = 5$ g.

Step3: Calculate the remaining amount for a general case

Let's assume we want to know the amount remaining after $t$ days. $n=\frac{t}{4}$. So $N = 20\times(\frac{1}{2})^{\frac{t}{4}}$.

If we assume we want to know the amount remaining after 4 days:

Answer:

10 g