The problem presented involves the fusion of nuclear isotopes, specifically the fusion of Deuterium (\(^2_1H\)) and Tritium (\(^3_1H\)) to form Helium (\(^4_2He\)).
Fusion Reaction:
[tex]\[ {}_1^2 H + {}_1^3 H \rightarrow {}_2^4 He \][/tex]
The process described is one in which two isotopes of hydrogen combine to form a helium nucleus. Here's a detailed breakdown:
1. Identify the Isotopes:
- Deuterium (\(^2_1H\)) has one proton and one neutron.
- Tritium (\(^3_1H\)) has one proton and two neutrons.
2. Fusion Process:
- When these isotopes fuse, they combine their protons and neutrons.
- Total protons involved: \(1 (\text{from Deuterium}) + 1 (\text{from Tritium}) = 2\)
- Total neutrons involved: \(1 (\text{from Deuterium}) + 2 (\text{from Tritium}) = 3\)
3. Helium Formation:
- The resulting Helium nucleus (\(^4_2He\)) will have 2 protons and 2 neutrons.
- This creation also releases a neutron:
[tex]\[
{}_1^2 H + {}_1^3 H \rightarrow {}_2^4 He + {}_0^1 n
\][/tex]
- Note: For completeness, \(^4_2He\) is often referred to in basic fusion equations, but the actual fusion reaction also involves the release of excess energy in the form of a neutron.
4. Energy Release:
- This nuclear process releases a significant amount of energy, typically in the form of kinetic energy of the products and electromagnetic radiation, due to the conversion of a small portion of mass into energy (according to Einstein's \(E = mc^2\)).
Given the complexity and the requirement for a detailed understanding of nuclear physics, solving or modeling this process accurately goes beyond simple arithmetic or basic algebraic manipulations.
In conclusion:
- The fusion reaction you described, involving Deuterium and Tritium to form Helium, is a fundamental process in nuclear fusion.
- The correct and detailed answer to the query involves understanding the underlying nuclear physics principles and not merely a numerical calculation.
