If a radioactive substance decays to half its mass every 4 days, how much of a 160-gram sample remains after 12 days?
["Title: Understanding Radioactive Decay: How Much of a 160-gram Sample Remains After 12 Days?", "When dealing with radioactive materials, one key concept to grasp is half-life—the time it takes for half of a radioactive substance to decay. In this article, we explore a practical example: a radioactive sample with an initial mass of 160 grams, decaying to half its mass every 4 days. We’ll discover precisely how much remains after 12 days.", "---", "### What Is Half-Life and Why Does It Matter?", "Radioactive decay follows an exponential pattern, governed by its half-life—the time required for half of the material to transform into a different element or isotope. Here, the substance decays to half its mass every 4 days, meaning the half-life is 4 days.", "Understanding this principle is essential not only in nuclear physics but also in fields like medicine, archaeology (radiocarbon dating), and environmental science.", "---", "### The Decay Process Over Time", "Let’s calculate how much remains after 12 days, using the rule that every 4 days the sample halves:", "- Initial mass: 160 grams\n- Half-life: 4 days\n- Total time elapsed: 12 days", "Number of half-lives in 12 days:\n[\n\frac{12\ \ ext{days}}{4\ \ ext{days/half-life}} = 3\ \ ext{half-lives}\n]", "Each half-life reduces the mass by half:", "- After 1st half-life (4 days):\n[\n160\ \ ext{g} \div 2 = 80\ \ ext{g}\n]\n- After 2nd half-life (8 days):\n[\n80\ \ ext{g} \div 2 = 40\ \ ext{g}\n]\n- After 3rd half-life (12 days):\n[\n40\ \ ext{g} \div 2 = 20\ \ ext{g}\n]", "---", "### Final Calculation: How Much Remains After 12 Days?", "After 12 days (3 half-lives), the remaining mass of the 160-gram radioactive sample is:", "[\n\boxed{20\ \ ext{grams}}\n]", "---", "### Conclusion", "Radioactive decay follows precise mathematical rules, enabling accurate predictions. If a 160-gram sample decays by half every 4 days, only 20 grams remain after 12 days. This predictable decay process is not just theoretical—it plays a vital role in nuclear safety, medical imaging, isotopic dating, and environmental monitoring.", "Understanding how much remains helps in managing radioactive materials responsibly and highlights the power of exponential decay in science.", "---", "Keywords: radioactive decay, half-life calculation, 160 gram sample, 12 days decay, exponential decay, nuclear physics, radioactive materials, decay process, half-life example", "Meta Description: Learn how much of a 160-gram radioactive sample remains after 12 days when it decays by half every 4 days using clear step-by-step calculations and scientific reasoning."]
