Ch.11 Nuclear Chemistry

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187Not the one you use?Change textbook

McMurry 8th Edition

Ch.11 Nuclear Chemistry

Problem 54

Chapter 11, Problem 54

What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?

Verified step by step guidance

Understand the concept of half-life: The half-life of a radioactive isotope is the time it takes for half of the radioactive nuclei in a sample to decay into a more stable form.

Relate the half-life to strontium-90: When we say that strontium-90 has a half-life of 28.8 years, it means that after 28.8 years, half of the original amount of strontium-90 will have decayed into its daughter isotopes.

Express this mathematically: The decay of a radioactive isotope can be modeled using the equation \( N_t = N_0 \cdot e^{-kt} \), where \( N_t \) is the amount remaining at time \( t \), \( N_0 \) is the initial amount, \( k \) is the decay constant, and \( t \) is time.

Relate the decay constant to the half-life: The decay constant \( k \) is related to the half-life \( t_{1/2} \) by the formula \( k = \frac{\ln(2)}{t_{1/2}} \). For strontium-90, \( t_{1/2} = 28.8 \) years.

Interpret the significance: This means that if you start with a certain amount of strontium-90, after 28.8 years, only half of it will remain. After another 28.8 years (a total of 57.6 years), only one-quarter of the original amount will remain, and so on.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Half-Life

Half-life is the time required for half of the radioactive atoms in a sample to decay. For strontium-90, a half-life of 28.8 years means that after this period, only half of the original amount of strontium-90 will remain, while the other half has transformed into a different element or isotope through radioactive decay.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha, beta, or gamma decay. Strontium-90 undergoes beta decay, where it transforms into a more stable isotope, releasing beta particles in the process.

Nuclear Waste Management

Nuclear waste management involves the processes of handling, storing, and disposing of radioactive waste produced by nuclear power plants. Understanding the half-life of isotopes like strontium-90 is crucial for determining safe storage durations and methods, as the waste remains hazardous for many years due to its long half-life.

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Related Practice

Textbook Question

A selenium-75 source is producing 300 rem at a distance of 2.0 m?

b. What is its intensity at 25 m?

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How does nuclear fission differ from normal radioactive decay?

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Why are rems the preferred units for measuring the health effects of radiation?

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Textbook Question

If a radiation source has an intensity of 650 rem at 1.0 m, what distance is needed to decrease the intensity of exposure to below 25 rem, the level at which no effects are detectable?

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Textbook Question

Bismuth-212 attaches readily to monoclonal antibodies and is used in the treatment of various cancers. This bismuth-212 is formed after the parent isotope undergoes a decay series consisting of four α decays and one β decay (the decays could be in any order). What is the parent isotope for this decay series?

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Textbook Question

Identify the starting radioisotopes needed to balance each of these nuclear reactions:

a. ? + ⁴₂He → ¹¹³₄₉In

b. ? + ⁴₂He → ¹³₇N + ¹₀n

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