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Chapter 11: Problem 11

Explain the concept of half-life.

Short Answer

Expert verified
Answer: Half-life is the time it takes for half of a radioactive substance to undergo decay, or the time required for 50% of the unstable nuclei or atoms in a sample to transform into a more stable state. It is important for various fields, such as nuclear physics, chemistry, geology, and archaeology, as it helps determine the age of rocks, fossils, and artifacts, and understand the behavior of radioactive substances.

Step by step solution

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1. Definition of Half-Life

Half-life is a term used in physics and chemistry to describe the time it takes for half of a quantity of a radioactive substance to undergo decay. In other words, it is the time required for 50% of the unstable nuclei or atoms in a sample to transform into a more stable state.
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2. Importance of Half-Life

Understanding half-life is crucial in various fields, such as nuclear physics, chemistry, geology, and archaeology, as it helps determine the age of rocks, fossils, and artifacts, as well as the behavior of radioactive substances. It also helps in controlling the release of radioactive materials in medical treatments, industrial applications, and nuclear power generation.
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3. Mathematical Representation

The half-life of a substance can be mathematically represented using the formula: \[ N(t) = N_0 \times (1/2)^{\frac{t}{t_{1/2}}}\] where: - \(N(t)\) is the remaining amount of the substance at time t, - \(N_0\) is the initial amount of the substance, - \(t_{1/2}\) is the half-life of the substance, - \(t\) is the time elapsed.
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4. Real-life Example

Carbon-14 is a radioactive isotope used to date organic materials, such as fossils and archaeological artifacts. The half-life of Carbon-14 is approximately 5,730 years. This means that after 5,730 years, half of the Carbon-14 atoms in a sample would have decayed into Nitrogen-14 atoms. This is used to estimate the age of the fossil or the artifact.

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