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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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Most popular questions from this chapter

There is much more uranium- 235 in a typical nuclear power plant than there was in the bomb that destroyed the city of Hiroshima. Why can't the reactor explode like an atomic bomb?

A mixture of two common isotopes of oxygen, oxygen-16 and oxygen-18, is put in a chamber that is then spun around at a very high speed. It is found that one isotope is more concentrated near the axis of rotation of the chamber and the other is more concentrated near the outer part of the chamber. Why is that, and which isotope is where?

One cause of uncertainty in carbon- 14 dating is that the relative abundance of carbon- 14 in atmospheric carbon dioxide is not always constant. If it is discovered that during some era in the past carbon-14 was more abundant than it is now, what effect would this have on the estimated ages of artifacts dated from that period?

During the normal operation of nuclear power plants and nuclear processing facilities, machinery, building materials, and other things can become radioactive even if they never come into physical contact with radioactive material. What causes this?

One-half of the nuclei of a given radioisotope decays during one half-life. Why doesn't the remaining half decay during the next half-life?
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