Textbook Question
Complete and balance the following nuclear equations by supplying the missing particle: (e) 23592U + 10n¡13554Xe + 2 10n + ?
Ch.21 - Nuclear Chemistry
Chapter 21, Problem 34
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? (Section 14.5) (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5)?
Verified step by step guidance1
Step 1: Understand the nature of radioactive decay. Radioactive decay is a nuclear process where an unstable atomic nucleus loses energy by emitting radiation. This process is not influenced by external factors such as temperature, pressure, or chemical state.
Step 2: Consider the suggestion that higher temperatures might affect the rate of radioactive decay. In chemical reactions, higher temperatures can increase reaction rates due to increased molecular motion and collision frequency. However, radioactive decay is a nuclear process, not a chemical one.
Step 3: Evaluate the concept of activation energy in the context of radioactive decay. Activation energy is a term used in chemical kinetics to describe the minimum energy required for a reaction to occur. Radioactive decay does not require activation energy because it is a spontaneous process governed by the stability of the nucleus.
Step 4: Compare radioactive decay to chemical reactions. Chemical reactions often follow the Arrhenius equation, which shows that reaction rates increase with temperature due to activation energy. Radioactive decay, however, is not affected by temperature changes because it does not involve breaking or forming chemical bonds.
Step 5: Conclude whether the suggestion is reasonable. Given that radioactive decay is a nuclear process unaffected by temperature, the suggestion that strontium-90 will decay more rapidly in a hot desert due to higher temperatures is not reasonable. The decay rate is determined by the isotope's half-life, which is constant regardless of environmental conditions.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radioactive Decay
Radioactive decay is a spontaneous process by which unstable atomic nuclei lose energy by emitting radiation. This process occurs at a characteristic rate for each isotope, defined by its half-life, which is the time required for half of the radioactive atoms in a sample to decay. Temperature does not significantly affect the rate of decay, making the suggestion that higher temperatures would increase decay rates unreasonable.
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Rate of Radioactive Decay
Half-Life
The half-life of a radioactive isotope is the time it takes for half of the original amount of the substance to decay into its daughter products. This concept is crucial for understanding the stability and longevity of radioactive materials. For strontium-90, the half-life is approximately 28.8 years, indicating that its decay is a time-dependent process rather than one influenced by external temperature conditions.
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Activation Energy in Radioactive Decay
Activation energy is the minimum energy required for a chemical reaction to occur, often associated with the Arrhenius equation in chemical kinetics. However, radioactive decay does not have an activation energy in the same sense as chemical reactions; it is a nuclear process that occurs independently of temperature and does not require energy input to proceed. Thus, the decay rate remains constant regardless of environmental conditions.
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Related Practice
Textbook Question
Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?
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Textbook Question
It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. What is the half-life of radium-230?
Textbook Question
Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to 75% of the original sample. If an original sample was purchased in June 2021, when will it be necessary to replace the cobalt-60?