A stationary 236 U nucleus fissions spontaneously into two...

A stationary 236 $\mathrm{U}$ nucleus fissions spontaneously into two primary fragments, $\frac{87}{37} \mathrm{Br}$ and $\frac{149}{57} \mathrm{La}$ . (a) Calculate the disintegration energy. The required atomic masses are 86.920711 $\mathrm{u}$ for $\frac{87}{35} \mathrm{Br}, 148.934370 \mathrm{u}$ for $\frac{149}{57} \mathrm{La},$ and 236.045562 u for $^{236} \mathrm{U} .$ ( b) How is the disintegration energy split between the two primary fragments? You may use the result of Problem $40 .$ (c) Calculate the speed of each fragment immediately after the fission.

Key Concepts

Calculating Kinetic Energy and Fragment Speeds

Once the kinetic energy of each fragment is known, the speed of each fragment can be calculated using the relationship between kinetic energy, mass, and velocity, given by the equation KE = 0.5mv². This calculation is crucial in understanding the dynamics of the fragments immediately following the fission event.

Kinetic Energy Distribution in Fission

After fission, the disintegration energy is shared between the fission fragments in a way that balances the momentum of the system. Typically, the smaller fragment obtains a greater fraction of the kinetic energy because of its lesser mass, while the larger fragment receives a correspondingly smaller share. This distribution can be deduced using ratios derived from momentum conservation principles.

Nuclear Fission

Nuclear fission is the process in which a heavy nucleus splits into smaller fragments, releasing energy in the process. This energy is primarily due to the conversion of mass to energy as described by Einstein’s mass-energy equivalence principle. Fission can occur either spontaneously or be induced by particle bombardment, and it plays a central role in both nuclear reactors and nuclear weapons.

Mass Defect and Energy Release

The mass defect is the difference in mass between the original nucleus and the sum of the masses of its fission fragments. This lost mass, when multiplied by the square of the speed of light (c^2), gives the energy released during fission according to Einstein’s equation E = mc². The concept is essential for understanding how seemingly small differences in mass translate into large amounts of energy.

Conservation of Energy and Momentum

In nuclear reactions such as fission, both energy and momentum must be conserved. This means that the energy released manifests as kinetic energy of the fragments, and the momentum of the system before and after the reaction remains equal. The conservation laws are fundamental in determining how the energy is split between the fragments and in calculating their subsequent speeds.

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