To tackle the question regarding the deuterium-tritium fusion reaction, let's break down the provided information and analyze each statement carefully. The fusion of deuterium and tritium is a significant process in nuclear physics, particularly in the context of fusion energy. Here’s a detailed look at the statements you've presented:
Understanding the Fusion Reaction
In the deuterium-tritium fusion reaction, two isotopes of hydrogen combine to form helium and release a substantial amount of energy. The reaction can be summarized as:
- 2H + 3H → 4He + n + energy
Analyzing Each Statement
A) Kinetic Energy Needed to Overcome Coulomb Repulsion
The Coulomb repulsion arises because both deuterium and tritium nuclei are positively charged. To initiate fusion, these nuclei must come close enough to overcome this repulsion, which requires a significant amount of kinetic energy. The value given, approximately 8 x 10^-14 J, is indeed a reasonable estimate for the kinetic energy needed to overcome the Coulomb barrier, but it is important to note that this value can vary based on the specific conditions of the reaction.
B) Temperature Required to Initiate Reaction
The temperature required to achieve the necessary kinetic energy for fusion is extremely high. The statement that the gases must be heated to approximately 10^9 K is consistent with the conditions found in stellar environments, such as the core of the sun, where fusion occurs. At these temperatures, the particles have enough energy to overcome the Coulomb barrier and collide with sufficient force to fuse.
C) Energy Liberated in the Reaction
The energy released from the fusion of deuterium and tritium is indeed around 18 MeV. This energy is a result of the mass defect, which is the difference in mass between the reactants and the products of the fusion reaction. This energy is released in the form of kinetic energy of the products and radiation.
D) Mass Defect Involved in the Reaction
The mass defect of approximately 0.0123 amu is a correct representation of the mass lost during the fusion process, which is converted into energy according to Einstein's equation, E=mc². This mass defect is crucial for understanding how much energy is released during the reaction.
Evaluating the Statements
Now, if we consider the possibility that statements B and C are correct while A is not, we need to examine why A might be incorrect. The value of kinetic energy needed to overcome the Coulomb barrier can vary based on several factors, including the specific conditions of the reaction and the precise calculations involved. While 8 x 10^-14 J is a reasonable estimate, it may not be universally applicable under all conditions, particularly in a laboratory setting versus stellar environments.
Conclusion
In summary, statements B and C are indeed accurate reflections of the deuterium-tritium fusion reaction. While statement A provides a useful estimate for kinetic energy, it may not be precise enough for all scenarios, which is why it could be considered incorrect in certain contexts. Understanding these nuances is essential in nuclear physics and fusion research.
