E Uranium 92^235 U fissions into two fragments plus three...

E Uranium ${ }_{92}^{235} \mathrm{U}$ fissions into two fragments plus three neutrons: ${ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow(2$ fragments $)+3{ }_{0}^{1} \mathrm{n} .$ The mass of a neutron is $1.008665 \mathrm{u}$ and the mass of ${ }_{92}^{25} \mathrm{U}$ is $235.043924 \mathrm{u}$. If $225.0 \mathrm{MeV}$ of energy is released, what is the total mass of the two fragments?

E Uranium ${ }_{92}^{235} \mathrm{U}$ fissions into two fragments plus three neutrons:
${ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow(2$ fragments $)+3{ }_{0}^{1} \mathrm{n} .$ The mass of a neutron is $1.008665 \mathrm{u}$ and the mass of ${ }_{92}^{25} \mathrm{U}$ is $235.043924 \mathrm{u}$. If $225.0 \mathrm{MeV}$ of energy is released, what is the total mass of the two fragments?

Key Concepts

Nuclear Fission

Nuclear fission is the process by which a heavy nucleus, such as uranium-235, splits into two or more lighter nuclei along with the release of neutrons and a large amount of energy. This process is fundamentally driven by changes in nuclear binding energy and is the basis for both nuclear reactors and nuclear weapons.

Mass Defect

The mass defect refers to the small difference between the mass of a nucleus and the sum of the masses of its individual nucleons. In nuclear reactions, this missing mass is converted into energy according to Einstein’s mass-energy equivalence principle. In a fission reaction, the combined masses of the resulting fragments and emitted neutrons are slightly less than the original mass, and this mass loss accounts for the energy released.

Mass?Energy Equivalence

Mass-energy equivalence, encapsulated by Einstein’s equation E=mc², establishes that mass can be converted into energy and vice versa. In the context of nuclear fission, the mass loss (mass defect) is converted into a quantifiable amount of energy. This principle is used to relate the energy release in reactions to the corresponding decrease in mass.

Atomic Mass Units and Conversion

Atomic mass units (u) are used to express the masses of atomic and subatomic particles. A key conversion factor is that 1 u is equivalent to approximately 931.5 MeV/c². This conversion is crucial when calculating the mass loss in nuclear reactions from the energy released, as it allows one to convert energy in MeV to a corresponding mass in atomic mass units.

Conservation of Mass-Energy

The conservation of mass-energy principle states that the total mass-energy of a closed system must remain constant. In nuclear fission, the sum of the masses (when accounting for the energy liberated) of the fragments and emitted neutrons will be less than the original mass of the reactants by an amount that is exactly equivalent to the energy released, ensuring that the overall mass-energy balance is maintained.

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