Question

The total kinetic energy carried by the products of the spontaneous fission of plutonium- 240 is typically about \(180 \mathrm{MeV}\). Use this to argue that reduction in Coulomb repulsion is the main impetus behind the process. Assume for simplicity that the two fragment nuclei are of equal \(Z\).

Short answer

The high kinetic energy observed in the fission products of plutonium-240 indicates that the energy initially released is significantly greater than the Coulomb repulsion energy. This suggests that reducing the Coulomb repulsion is the primary factor contributing to the overall fission process.

Step-by-step solution

Defining Key Concepts

The concept of Kinetic Energy (KE) in this context relates to the energy carried by the particles emitted during the spontaneous fission of Plutonium-240. This energy is 180 MeV. This must be compared to the energy due to Coulomb repulsion, which is the energy required for repelling the two identical charged fragments produced during the fission process. The greater the Coulomb repulsion, the more energy will be taken up in overcoming this, leaving less as kinetic energy to the fragments.

Comparing Energies

Since kinetic energy of the fragments is high, this indicates that large energy must have been released during the fission. Now, the nuclear binding energy does not significantly change in the fission process, so much of this energy must have been used to overcome the Coulomb repulsion between the large, similarly charged fragment nuclei.

Arguing the Result

Considering that Coulomb repulsion influences the energy distribution in this process, if the energy released did not significantly exceed these Coulomb forces, the remaining kinetic energy would not be as high. This high kinetic energy, therefore, points to a significant enough decrease in Coulomb repulsion. Thus, the reduction in Coulomb repulsion is indeed the main driving force in the spontaneous fission of plutonium-240.

Key concepts

Kinetic Energy

In the context of spontaneous fission, kinetic energy refers to the energy carried by the fragments produced when an atomic nucleus, like Plutonium-240, splits into smaller parts. This energy is typically around 180 MeV. What this number tells us is that once fission occurs, a substantial amount of energy is imparted as motion to these fragmented pieces. When we talk about 180 MeV, it highlights how energetic these products can be, influencing their speed and trajectory after the fission event.

Understanding kinetic energy helps us recognize the powerful forces at play during fission. It also provides insights into how the energy from the nucleus is transformed and transferred to the fragments involved. Considering the high amount of kinetic energy observed, it suggests that a substantial portion of the initial energy goes into moving these particles apart after the nucleus splits.

Coulomb Repulsion

Coulomb repulsion refers to the force that pushes two like charges away from each other. Imagine each fragment from the fission process like a small positively charged sphere. When the fission of Plutonium-240 happens, these positively charged fragments naturally repel each other due to their like charges.

The energy associated with overcoming this repulsion is significant. The more the fragments push away from each other, the more it influences the overall energy dynamics. In the case of spontaneous fission, overcoming Coulomb repulsion takes a substantial amount of energy that originally exists within the nucleus.

• This energy needs to be reduced for fission to occur smoothly.
• The nuclear process rearranges this energy, allowing the repulsion to decrease, resulting in the high kinetic energy seen in the products.

The ability to overcome Coulomb repulsion efficiently means that more of that internal energy gets converted into the kinetic energy of the fragments.

Plutonium-240

Plutonium-240 (\(\text{Pu-240}\), as it's often abbreviated) is a specific isotope of the element plutonium. It is well-known for its tendency to undergo spontaneous fission. What makes Pu-240 interesting is its ability to split without any added external energy, unlike other isotopes that need a neutron bombardment to fission.

This isotope's behavior is especially significant in nuclear science because it contributes to the overall activity of plutonium. Its fission products, combined with their considerable kinetic energy, play a crucial role in both the generation of power in nuclear reactors and nuclear weaponry. It's a vital aspect of understanding how energy is released in these processes.

• Pu-240’s propensity for spontaneous fission can result in increased neutron background, which affects how nuclear reactors operate.
• Its unique characteristics make it a central subject in safety evaluations for nuclear technologies.

Learning about Pu-240 offers insight into the complexities of nuclear energy and safety protocols related to handling fissile materials.