(a) The following fission reaction is typical of those...

(a) The following fission reaction is typical of those occurring in a nuclear electric generating station: $_{0}^{1} \mathrm{n}+_{92}^{255} \mathrm{U} \rightarrow$ $\frac{141}{56} \mathrm{Ba}+_{36}^{92} \mathrm{Kr}+3\left(\begin{array}{c}{1} \\ {0}\end{array}\right)$ Find the energy released. The masses of the products are $$ M\left(\begin{array}{c}{141} \\ {56}\end{array}\right)=140.9144 \mathrm{u} \quad M\left(\begin{array}{c}{92} \\ {36}\end{array}\right)=91.9262 \mathrm{u} $$ (b) What fraction of the initial mass of the system is transformed?

(a) The following fission reaction is typical of those occurring in a nuclear electric generating station:
$_{0}^{1} \mathrm{n}+_{92}^{255} \mathrm{U} \rightarrow$ $\frac{141}{56} \mathrm{Ba}+_{36}^{92} \mathrm{Kr}+3\left(\begin{array}{c}{1} \\ {0}\end{array}\right)$
Find the energy released. The masses of the products are
$$
M\left(\begin{array}{c}{141} \\ {56}\end{array}\right)=140.9144 \mathrm{u} \quad M\left(\begin{array}{c}{92} \\ {36}\end{array}\right)=91.9262 \mathrm{u}
$$
(b) What fraction of the initial mass of the system is transformed?

Key Concepts

Energy Conversion Factors

In nuclear physics, conversion factors such as 1 atomic mass unit (amu) being equivalent to approximately 931.494 MeV are used. This factor provides a bridge between the mass defect measured in atomic mass units and the energy released in mega electron volts, making it possible to quantify the energy production in nuclear processes.

Nuclear Fission Reaction

This concept involves the splitting of a heavy nucleus into two or more lighter nuclei, typically accompanied by the release of energy and additional neutrons. In the context of nuclear power generation, fission reactions are controlled to provide a steady energy output, and they form the foundation for designing reactors and understanding the overall reaction dynamics.

Mass Defect

The mass defect is the difference between the mass of the reactants and the mass of the products in a nuclear reaction. This 'missing' mass has been converted into energy according to the mass-energy equivalence principle, and its calculation is crucial for determining the energy released during fission.

Einstein's Mass-Energy Equivalence

Represented by the equation E=mc², this principle explains how a small amount of lost mass (mass defect) is converted into a large amount of energy. It is the fundamental concept that allows us to calculate the energy yield from nuclear reactions, using the established conversion factor between mass units and energy.

Fraction of Mass Transformed

This concept refers to the portion of the initial mass of a system that is converted to energy during a nuclear reaction. It is typically expressed as a percentage and highlights the efficiency of nuclear reactions, illustrating that even very small mass conversions can result in significant energy outputs.

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