Half-Life Worksheet With Answers For Easy Learning
Table of Contents :
Half-Life is a fundamental concept in chemistry and physics that refers to the time it takes for a substance to reduce to half of its original quantity. Understanding half-life is crucial for various fields, including nuclear physics, pharmacology, and radiometric dating. In this article, we’ll explore the concept of half-life, provide a worksheet with answers for easy learning, and highlight some important notes to reinforce your understanding.
What is Half-Life? 📚
Half-life is defined as the time required for the quantity of a substance to decrease to half its initial value. This concept is commonly applied to radioactive decay, where unstable isotopes decay over time.
For example, if you start with 100 grams of a radioactive substance with a half-life of 3 years, after 3 years, only 50 grams will remain. After another 3 years (6 years total), 25 grams will be left, and so on.
The Half-Life Formula
The formula used to calculate the remaining quantity of a substance after a certain number of half-lives is:
[ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} ]
Where:
- ( N(t) ) = Remaining quantity after time ( t )
- ( N_0 ) = Initial quantity
- ( t_{1/2} ) = Half-life of the substance
- ( t ) = Total time elapsed
Importance of Half-Life 🧪
Understanding half-life has many practical applications:
- Nuclear Medicine: Determining dosages and understanding the duration of a drug's effectiveness in the body.
- Geology: Dating ancient rocks and fossils using radiometric dating methods.
- Environmental Science: Assessing the longevity and impact of pollutants in ecosystems.
Half-Life Worksheet 📝
Below is a worksheet designed to test your understanding of the half-life concept. Try to solve the questions before checking the answers at the end!
Questions:
- A sample of Carbon-14 has an initial quantity of 80 grams. The half-life of Carbon-14 is 5730 years. How much of the sample remains after 11460 years?
- If you start with 10 mg of a substance that has a half-life of 4 hours, how much will be left after 12 hours?
- A radioactive isotope has a half-life of 10 days. If you start with 160 grams, how much remains after 30 days?
- How many half-lives have passed if only 12.5% of the original quantity of a substance remains?
- A patient receives a dose of medication that has a half-life of 6 hours. If the initial dose was 200 mg, how much will remain after 18 hours?
Answer Key 📌
<table> <tr> <th>Question</th> <th>Answer</th> </tr> <tr> <td>1</td> <td>20 grams</td> </tr> <tr> <td>2</td> <td>1.25 mg</td> </tr> <tr> <td>3</td> <td>20 grams</td> </tr> <tr> <td>4</td> <td>3 half-lives</td> </tr> <tr> <td>5</td> <td>25 mg</td> </tr> </table>
Important Notes 🔍
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Radioactive Decay is Random: The process of decay is probabilistic, meaning it cannot be predicted when a single atom will decay, but large quantities will decay at a predictable rate.
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Multiple Half-Lives: After multiple half-lives, the remaining quantity will continue to decrease exponentially. It’s important to recognize the pattern of decrease as it helps in understanding the longevity of materials in different applications.
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Applications: The concept of half-life is not only limited to radioactive substances; it also applies to any process that follows a similar exponential decay pattern, such as the concentration of drugs in the bloodstream.
Conclusion
The half-life concept is essential for students and professionals in various scientific fields. By utilizing worksheets and engaging in problem-solving exercises, learners can solidify their grasp of this critical topic. Whether in nuclear physics, chemistry, or medicine, a clear understanding of half-life enables informed decisions based on the timing and quantity of substances. Keep practicing, and you’ll master this concept in no time! 🌟