Chapter 8: Problem 2
Calculate the mass of \({ }^{210}\) Po required to generate \(10 \mathrm{~W}\) of electric power using a thermoelectric converter that operates with an efficiency of \(15 \% .{ }^{210} \mathrm{Po}\) has a halflife of 138 days and emits an \(\alpha\) particle with decay energy \(Q_{\alpha}=5.4 \mathrm{MeV}\).
Short Answer
Step by step solution
Convert Energy from MeV to Joules
Calculate Energy Output Per Second
Determine Number of Decays Per Second
Use Radioactive Decay Law to Find Initial Mass
Conclusion
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Thermoelectric Conversion
The efficiency of thermoelectric devices is usually modest. In the example given, the efficiency is 15%. This means that only 15% of the thermal energy is successfully converted into electrical energy. Understanding these efficiency limits is crucial when designing systems that rely on thermoelectric conversion for power generation. Therefore, always account for the efficiency when calculating the desired output.
Nuclear Physics
Radioactive decay occurs when an unstable atomic nucleus loses energy by emitting particles. This is a natural process and can happen in several ways, including alpha, beta, and gamma decay. Understanding these types of decay leads to insights into how elements transform and where energy in nuclear reactions comes from.
Alpha Decay Energy
The energy released during alpha decay, known as alpha decay energy, is significant. In the given example, it is stated as 5.4 MeV. This energy is a measure of the energy carried away by the alpha particle when it is emitted from the nucleus. To make it understandable in practical terms, we often convert it to Joules, especially when calculating energy outputs in physics.
Decay Constant
In our given problem, knowing the decay constant helps us determine the rate at which a radioactive material like \( ^{210} \)Po will decay. This information is crucial for calculating how much material is initially needed to achieve a particular energy output, considering the decay rate.