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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 160 grams of a radioactive isotope, how much will be left after 4 half-lives? Use the calculator provided and round your answer to the nearest gram.

Ask by Rodriquez Deleon. in the United States
Feb 28,2025

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After 4 half-lives, there will be 10 grams left.

Solution

After each half-life, the remaining mass is halved. A quick calculation: After 1 half-life: 160 ÷ 2 = 80 grams After 2 half-lives: 80 ÷ 2 = 40 grams After 3 half-lives: 40 ÷ 2 = 20 grams After 4 half-lives: 20 ÷ 2 = 10 grams So, after 4 half-lives, there will be approximately 10 grams left.

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After one half-life, 160 grams would be reduced to 80 grams. After the second half-life, it would further decrease to 40 grams. Continuing this pattern, after the third half-life, you'd have 20 grams left, and after the fourth half-life, it will dwindle down to just 10 grams. So, after 4 half-lives, you'd have approximately 10 grams of the radioactive isotope remaining. This decay process isn't just theoretical; it's utilized in various fields! For example, carbon dating, used in archaeology, relies on the half-life of carbon-14 to determine the age of ancient organic materials. By measuring how much carbon-14 remains in a sample, scientists can deduce how long ago the organism died, giving us fascinating insights into our past!

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