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If a radioactive element has a​ half-life of 2 ​hours, then x grams of the element dwindles to x/2 grams after 2 hours. If a nuclear reactor has 800 grams of that radioactive​ element, find the amount of radioactive material after 6 hours.

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Final answer:

After 6 hours, given a half-life of 2 hours, an initial amount of 800 grams of a radioactive element will be reduced to 100 grams through a series of half-life reductions.

Step-by-step explanation:

Calculating the Amount of Radioactive Material After 6 Hours

To calculate the amount of a radioactive element remaining after a certain period of time, we can use its half-life which is a measure of the rate of its radioactive decay. In this case, the radioactive element has a half-life of 2 hours. This means that every 2 hours, the amount of the substance will be reduced by half.

Starting with 800 grams of the radioactive element, after the first 2 hours we will have 400 grams left (first half-life). After another 2 hours (a total of 4 hours), we will have half of 400 grams, which is 200 grams left (second half-life). Finally, after 6 hours, which is another 2 hours later (totaling three half-lives), we will have half of 200 grams, resulting in 100 grams of the radioactive material remaining.

Therefore, after 6 hours, there will be 100 grams of the radioactive element left in the nuclear reactor.

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