Question

The half-life of a radioactive Isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 210 grams of aradioactive Isotope, how much will be left after 3 half-lives?Use the calculator provided and round your answer to the nearest gram.

Answer 1

the answer is 26 grams

Step-by-step explanation

We can determine the amount of a radioactive isotope remaining after a given number half-lives by using the following expression:

`\text{amount remaining= Initial amoutn (}(1)/(2))^n`

where n is the time

Step 1

Let

`\begin{gathered} \text{ Initial amount= 210 grams} \\ n=\text{ 3} \end{gathered}`

replace

`\begin{gathered} \text{amount remaining= Initial amoutn (}(1)/(2))^n \\ \text{amount remaining= 210 (}(1)/(2))^3 \\ \text{amount remaining= 210 (}(1)/(8))^{} \\ \text{amount remaining= }26.25 \\ \text{rounded} \\ \text{amount remaining=}26 \end{gathered}`

so, the answer is 26 grams

i hope this helps you