Plutonium-239 has been used as a power source for heart...

Plutonium-239 has been used as a power source for heart pacemakers. What is the energy obtained from the following decay of $215 \mathrm{mg}$ of plutonium- 239 ? $$ { }_{94}^{239} \mathrm{Pu} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{92}^{235} \mathrm{U} $$ Suppose the electric energy produced from this amount of plutonium-239 is $25.0 \%$ of this value. What is the minimum grams of zinc that would be needed for the standard voltaic cell $\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ to obtain the same electric energy?

Plutonium-239 has been used as a power source for heart pacemakers. What is the energy obtained from the following decay of $215 \mathrm{mg}$ of plutonium- 239 ?
$$
{ }_{94}^{239} \mathrm{Pu} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{92}^{235} \mathrm{U}
$$
Suppose the electric energy produced from this amount of plutonium-239 is $25.0 \%$ of this value. What is the minimum grams of zinc that would be needed for the standard voltaic cell $\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ to obtain the same electric energy?

Key Concepts

Electrochemical Energy Conversion

This idea involves the conversion of chemical energy into electrical energy using electrochemical cells (voltaic cells). It includes understanding how the reactions at the electrodes produce electrical energy and how to calculate the mass of reactants required to generate a specific amount of electric energy, thus bridging the gap between chemical and electrical energy sources.

Nuclear Decay Energy Calculation

This concept involves determining the amount of energy released in a nuclear reaction by using the decay's Q-value, which is the difference in mass between reactants and products converted to energy via Einstein’s mass–energy equivalence. It requires converting the mass of the radioactive material into moles to find the total number of decays and then multiplying by the energy released per decay event.

Stoichiometry and Molar Mass

This refers to the use of molar mass and mole concept to relate a given mass of a substance to the number of particles or reactions occurring. In the context of energy calculations, it enables the conversion from a sample’s mass to the total energy release by accounting for molecular or atomic quantities involved in the decay or reaction.

Energy Conversion Efficiency

This concept addresses the fact that not all the energy released in a process can be harnessed as useful work. Efficiency factors, such as the 25.0% electric energy yield mentioned, are used to adjust the theoretical energy available to the practical, usable energy obtained in applications.

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