A radioactive substance has a half-life of 5 years. If you start with 80 grams, how much remains after 15 years?
["Understanding Radioactive Decay: How Half-Life Affects Substance Quantity", "When exploring radioactive materials, one key concept is half-life—the time it takes for half of a radioactive substance to decay. Understanding how half-life works helps explain why and how substances decay over time, applicable in nuclear physics, medicine, and environmental science.", "In our example, we focus on a substance with a half-life of 5 years. Starting with an initial amount of 80 grams, let’s calculate how much remains after 15 years—a duration that spans three half-lives.", "### What Is Half-Life?", "A half-life is the time required for half of the radioactive atoms present to undergo decay. This exponential decay process means the amount of substance decreases by half each half-life period.", "### Calculating Remaining Mass After 15 Years", "Since 15 years equals three half-lives (15 ÷ 5 = 3), we repeatedly halve the initial mass:", "- After 1st half-life (5 years):\n ( 80\ \ ext{g} ÷ 2 = 40\ \ ext{g} )\n- After 2nd half-life (10 years):\n ( 40\ \ ext{g} ÷ 2 = 20\ \ ext{g} )\n- After 3rd half-life (15 years):\n ( 20\ \ ext{g} ÷ 2 = 10\ \ ext{g} )", "### Final Answer", "After 15 years, 10 grams of the original 80 grams of radioactive substance remain.", "This straightforward decay pattern illustrates the predictable nature of radioactive materials—making half-life a powerful tool in fields ranging from carbon dating to medical diagnostics.", "---", "Key Words for SEO:\nradioactive decay, half-life calculator, radioactive half-life, half-life formula, how much remains after 15 years, 5-year half-life, nuclear physics, common radioactive substances with half-life, decay over time, half-life problems.", "---", "In summary, using the half-life concept, we find that 15 years after starting with 80 grams of a substance with a 5-year half-life, only 10 grams remain—demonstrating the reliable, exponential reduction in radioactive material over time."]
