A radioactive substance decays at a rate of 5% per day. If the initial mass is 200 grams, how much remains after one week?

Mon, 04 May 2026 16:19:09 +0000

**Why Are People Asking How Much Radioactive Mass Remains After One Week?**
A radioactive substance decaying at 5% per day is a topic gaining quiet but consistent attention across the U.S. as curiosity about nuclear behavior, radioactivity, and decay rates spreads through educational platforms, health forums, and science-loving communities. With growing interest in personal wellness, environmental safety, and scientific literacy, simple yet powerful questions like “What remains after a week of decay?” resonate deeply. This pattern connects to a broader trend where users seek clear, trustworthy explanations of natural laws—particularly when applied to familiar quantities like commonly known masses. The question signals a desire not just for numbers, but for understanding how invisible processes shape measurable outcomes—especially in contexts ranging from scientific experimentation to safety assessments. **Decaying at 5% Per Day: The Science Behind the Numbers**
Radioactive decay follows a predictable, exponential pattern where a small percentage of mass diminishes daily. When a substance decays at 5% per day, it retains 95% of its mass each 24-hour cycle. This gradual reduction, governed by the half-life principle (though not a half-life here), means that even a single week carries significant transformation. With 7 days at 95% retention, the substance undergoes compounding decay. For someone starting with 200 grams, the gradual loss reflects a natural, measurable transformation—why today’s mass matters so much. Understanding this process offers practical insight into long-term preservation, safety planning, or accurate forecasting in research and industry applications. **How 200 Grams Decays to Less Over One Week**
Using the formula for exponential decay, the remaining mass after 7 days at 5% daily loss is:
200 × (0.95)⁷ ≈ 200 × 0.698337 ≈ 139.67 grams
So, after one week, approximately 139.7 grams remain. This calculation follows a reliable scientific principle, showing the impact of steady, daily decay. Each day, only a portion—not all—masses diminish, preserving structural integrity of the decay model. Real-world applications include tracking expired materials, assessing disposal timelines, or modeling natural containment processes—making the question not just academic, but relevant across disciplines. **Common Questions About Radioactive Decay Timelines**
A consistent pattern of questions reflects genuine curiosity and intent:
*H3: What exactly happens to the mass each day?*
Radioactive decay stages are gradual; mass decreases by 5% of current amount daily, not by fixed units.
*H3: Is 5% per day a universal decay rate?*
No single 5% rate fits all isotopes—this represents a commonly modeled scenario with a plausible daily loss.
*H3: How does this decay affect