A^238 U nucleus emits a 4.196 MeV alpha particle. Calculate the disintegration energy Q for this

step 1 For the given problem, we use a law of conservation of energy and momentum. Let K -alpha be the

A^238 U nucleus emits a 4.196 MeV alpha particle. Calculate...

$\mathrm{A}^{238} \mathrm{U}$ nucleus emits a $4.196 \mathrm{MeV}$ alpha particle. Calculate the disintegration energy $Q$ for this process, taking the recoil energy of the residual ${ }^{234} \mathrm{Th}$ nucleus into account.

Key Concepts

Recoil Energy Calculation

Recoil energy calculation involves using conservation of momentum to determine the kinetic energy imparted to the daughter nucleus during particle emission. Although this energy is typically much smaller than that carried by the emitted particle, its inclusion is essential for accurately assessing the total energy released in the decay.

Conservation of Energy in Nuclear Reactions

In nuclear processes such as decay, energy conservation demands that the total energy, including rest mass and kinetic energy, remains constant before and after the reaction. This principle ensures that the energy released in the decay (the Q-value) is distributed among all the decay products.

Conservation of Momentum in Nuclear Decay

Momentum conservation is crucial in nuclear decay, where the momentum carried away by an emitted particle, like an alpha particle, must be balanced by the recoil momentum of the daughter nucleus. This balance explains why even a heavy residual nucleus gains a small amount of kinetic energy despite its larger mass.

Alpha Decay

Alpha decay is a fundamental type of radioactive decay in which an unstable nucleus emits an alpha particle (a helium nucleus) to transform into a more stable nucleus with a lower mass and atomic number. This process is central to nuclear physics and underlies the natural decay chains of heavy elements.

Q-value

The Q-value of a nuclear reaction is the net energy released during the process, calculated as the mass difference between the reactants and the products converted into energy (using E=mc²). It serves as a key indicator of the reaction’s energetics and stability.

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