/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 32 It has been suggested that stron... [FREE SOLUTION] | 91影视

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Chapter 21: Problem 32

It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5\() ?\) Discuss.

Short Answer

Expert verified
In conclusion, the suggestion that strontium-90 will decay more rapidly in the desert due to higher temperatures is not reasonable, as radioactive decay is a nuclear process not influenced by external factors like temperature. Furthermore, the concept of activation energy and the Arrhenius behavior do not apply to radioactive decay.

Step by step solution

01

Understand the role of temperature in the decay process

Radioactive decay is a random process that is governed by the laws of quantum mechanics. It's a nuclear process caused by the instability of the nucleus, and is not affected by external factors such as temperature, pressure, or chemical bonds.
02

Determine the reasonableness of the suggestion

Since radioactive decay is not affected by temperature, it is not a reasonable suggestion to say that strontium-90 deposited in the hot desert will undergo radioactive decay more rapidly due to higher temperatures. The decay rate solely depends on the properties of the radioactive nucleus and its half-life.
03

Investigate the activation energy of radioactive decay

Activation energy is a concept from chemistry that describes the minimum energy required to initiate a chemical reaction. Radioactive decay is a nuclear process and not a chemical reaction, so the concept of activation energy does not apply to radioactive decay.
04

Discuss the absence of Arrhenius behavior in radioactive decay

The Arrhenius equation describes the rate of a chemical reaction as a function of temperature. Since radioactive decay is not a chemical reaction and does not depend on external factors such as temperature, the Arrhenius equation does not apply to radioactive decay processes. In conclusion, the suggestion that strontium-90 will decay more rapidly in the desert due to higher temperatures is not reasonable since radioactive decay is a nuclear process that is not influenced by external factors like temperature. Moreover, the concept of activation energy and the Arrhenius behavior do not apply to radioactive decay.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Strontium-90
Strontium-90 is a radioactive isotope that is mainly produced through nuclear fission processes, such as nuclear weapons testing and nuclear reactor operations. Once released into the environment, strontium-90 behaves similarly to calcium, as it can be absorbed by bones and teeth, making it a concern for human health. In terms of health risks:
  • It is a beta emitter, meaning it releases beta particles during decay, which can damage living tissues.
  • Its presence in the body can lead to bone cancer or leukemia.
  • Due to its similar chemical properties to calcium, it can replace calcium in bones.
Understanding strontium-90's behavior and risks is essential, especially in locations affected by nuclear activities. Its potential to bioaccumulate in the food chain further highlights the importance of monitoring and managing its presence in the environment.
Nuclear Chemistry
Nuclear Chemistry is a fascinating branch of chemistry that deals with nuclear reactions and radioactive substances. Unlike typical chemical reactions, which involve electron interactions, nuclear chemistry focuses on changes in the nuclei of atoms. Here are key aspects:
  • Nuclear reactions include processes like fission, fusion, and radioactive decay.
  • These reactions involve changes in an atom鈥檚 nucleus, leading to the formation of different elements or isotopes.
  • Nuclear reactions can release significant amounts of energy, much greater than chemical reactions.
Nuclear chemistry is fundamental to understanding how elements transform and how energy, such as that from nuclear reactors or radioactive isotopes, can be harnessed for various uses. It's also crucial in fields like medicine for treatments and diagnostics, as well as in energy production.
Half-life
The concept of half-life is integral to understanding radioactive decay processes. Half-life is the time required for half the amount of a radioactive substance to decay. Here are some characteristics of half-life:
  • It's a constant property for a given isotope, unaffected by external conditions like temperature or pressure.
  • Helps in calculating how radioactive material will change over time.
  • Can range from seconds to thousands of years, depending on the isotope.
For example, strontium-90 has a half-life of about 29 years, meaning it takes 29 years for half of a given amount of strontium-90 to decay into yttrium-90, a stable isotope. Understanding half-life helps predict the longevity of radioactivity in an environment or material, contributing significantly to areas like waste management and radiometric dating.
Quantum Mechanics
Quantum Mechanics is a branch of physics that deals with phenomena on very small scales, like those of subatomic particles. It plays a crucial role in radioactive decay processes, providing explanations for these phenomena that classical mechanics cannot.
  • Radioactive decay is a quantum phenomenon, inherently probabilistic, meaning the exact time when a particular nucleus will decay is unpredictable.
  • The decay process happens because the atomic nucleus is unstable and quantum tunneling allows particles to escape from the nucleus.
  • Unlike classical physics, quantum mechanics accounts for the wave-particle duality where particles exhibit both particle and wave characteristics.
By using principles of quantum mechanics, scientists can understand and predict the behavior of particles in nuclear processes like radioactive decay, although they cannot pinpoint the exact moment when decay will occur.

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Most popular questions from this chapter

Write balanced nuclear equations for the following processes: (a) rubidium-90 undergoes beta emission; (b) selenium-72 undergoes electron capture; (c) krypton-76 undergoes positron emission; (d) radium-226 emits alpha radiation.

The thermite reaction, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow 2 \mathrm{Fe}(s)+\) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s), \Delta H^{\circ}=-851.5 \mathrm{~kJ} / \mathrm{mol},\) is one of the most exother-mic reactions known. Because the heat released is sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How much heat is released per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) produced? How does this amount of thermal energy compare with the energy released when 2 mol of protons and 2 mol of neutrons combine to form 1 mol of alpha particles?

A laboratory rat is exposed to an alpha-radiation source whose activity is \(14.3 \mathrm{mCi}\). (a) What is the activity of the radiation in disintegrations per second? In becquerels? (b) The rat has a mass of \(385 \mathrm{~g}\) and is exposed to the radiation for \(14.0 \mathrm{~s}\), absorbing \(35 \%\) of the emitted alpha particles, each having an energy of \(9.12 \times 10^{-13} \mathrm{~J} .\) Calculate the absorbed dose in millirads and grays. (c) If the RBE of the radiation is 9.5, calculate the effective absorbed dose in mrem and Sv.

Tests on human subjects in Boston in 1965 and \(1966,\) following the era of atomic bomb testing, revealed average quantities of about \(2 \mathrm{pCi}\) of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{~J}\) of energy and if the average person weighs \(75 \mathrm{~kg}\), calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

A sample of an alpha emitter having an activity of \(0.18 \mathrm{i}\) is stored in a \(25.0-\mathrm{mL}\) sealed container at \(22^{\circ} \mathrm{C}\) for 245 days. (a) How many alpha particles are formed during this time? (b) Assuming that each alpha particle is converted to a helium atom, what is the partial pressure of helium gas in the container after this 245 -day period?
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