if the half - life of substance a is 1.5 years, how long would it take an 8.0 gram sample of substance a to…

if the half - life of substance a is 1.5 years, how long would it take an 8.0 gram sample of substance a to decay such that only 1.0 gram remained?\n____ years\ndo not include units in your answer.

if the half - life of substance a is 1.5 years, how long would it take an 8.0 gram sample of substance a to decay such that only 1.0 gram remained?\n____ years\ndo not include units in your answer.

Answer

Explanation:

Step1: Determine the number of half - lives

The formula for radioactive decay is $N = N_0(\frac{1}{2})^n$, where $N$ is the final amount, $N_0$ is the initial amount, and $n$ is the number of half - lives. Given $N_0 = 8.0$ g, $N = 1.0$ g. We substitute these values into the formula: $1.0=8.0\times(\frac{1}{2})^n$. Then $\frac{1.0}{8.0}=(\frac{1}{2})^n$, and $\frac{1}{8}=(\frac{1}{2})^n$. Since $\frac{1}{8}=(\frac{1}{2})^3$, $n = 3$.

Step2: Calculate the total time

The half - life $t_{1/2}=1.5$ years. The total time $t$ is given by $t=n\times t_{1/2}$. Substituting $n = 3$ and $t_{1/2}=1.5$ years, we get $t=3\times1.5$.

Answer:

4.5