A radioactive substance decays by 30% each year. If the initial mass is 500 grams, what is the remaining mass after 2 years?
["Understanding Radioactive Decay: How Much Remains After 2 Years?", "Radioactive decay is a natural process in which unstable atomic nuclei lose energy by emitting radiation over time. One key concept in nuclear physics is the rate at which a radioactive substance decays—often measured as a percentage decrease per year. In this article, we explore a specific case: a radioactive substance that decays by 30% annually. Starting with an initial mass of 500 grams, we calculate how much remains after 2 years.", "---", "### What Does a 30% Annual Decay Mean?", "A decay rate of 30% per year means that, each year, 70% of the radioactive material remains. This is because 100% − 30% = 70%. To model decay mathematically, we use exponential decay:", "[\n\ ext{Remaining mass} = \ ext{Initial mass} \ imes (1 - \ ext{decay rate})^t\n]", "Here, the decay rate is 0.30 (30%), and ( t = 2 ) years.", "---", "### Step-by-Step Calculation", "1. Initial mass (m₀):\n 500 grams", "2. Decay factor per year:\n ( 1 - 0.30 = 0.70 )", "3. Mass after 1 year:\n ( 500 \ imes 0.70 = 350 ) grams", "4. Mass after 2 years:\n ( 350 \ imes 0.70 = 245 ) grams", "Alternatively, using the formula directly:\n[\n\ ext{Remaining mass} = 500 \ imes (0.70)^2 = 500 \ imes 0.49 = 245 \ ext{ grams}\n]", "---", "### Summary", "After 2 years, only 245 grams of the initial 500-gram radioactive sample remain, having decayed by 30% each year. This demonstrates how quickly radioactive substances diminish over time, highlighting the importance of radiation safety and decay timelines in fields like medicine, archaeology, and nuclear energy.", "---", "### Why This Matters", "Understanding radioactive decay rates enables scientists to:", "- Estimate the half-life—the time it takes for half the substance to decay—critical for radiometric dating.\n- Predict safe handling and disposal intervals for radioactive materials.\n- Develop accurate diagnostic and therapeutic tools in nuclear medicine.", "---", "In summary:\nStarting with 500 grams of a radioactive substance decaying by 30% per year, 245 grams remain after 2 years—a clear example of exponential decay in action.", "---", "Keywords: radioactive decay, radioactivity, half-life calculation, 30% annual decay, exponential decay formula, 500 grams decay, radiation safety, nuclear physics."]
