Let's walk through the problem step-by-step to identify the correct equation illustrating the fusion process of two deuterium nuclei forming helium-3 and emitting a neutron.
1. Understanding Deuterium:
- Deuterium, also known as hydrogen-2, is an isotope of hydrogen.
- A deuterium nucleus contains one proton and one neutron.
2. Fusion Process:
- When two deuterium nuclei fuse, they form helium-3 (which has 2 protons and 1 neutron) and emit a neutron.
3. Possible Equations:
- Let's evaluate each given equation to identify the correct one.
4. Equation 1:
[tex]\[
2 H_2 + O_2 \rightarrow 2 H_2O
\][/tex]
- This equation represents the chemical reaction for the formation of water from hydrogen and oxygen, not relevant to the fusion process of deuterium.
5. Equation 2:
[tex]\[
2{ }_1^2 H \rightarrow{ }_1^3 H +{ }_1^1 H
\][/tex]
- In this equation, two deuterium nuclei (each with 1 proton and 1 neutron) would theoretically form tritium ([tex]\( { }_1^3 H \)[/tex], having 1 proton and 2 neutrons) and a normal hydrogen atom ([tex]\( { }_1^1 H \)[/tex], with 1 proton).
- This does not match the problem description as it involves helium-3 and a neutron, not tritium and hydrogen.
6. Equation 3:
[tex]\[
2{ }_1^1 H \rightarrow{ }_1^2 H +{ }_1^0 e
\][/tex]
- This equation shows the fusion of regular hydrogen nuclei ([tex]\( { }_1^1 H \)[/tex]) resulting in deuterium ([tex]\( { }_1^2 H \)[/tex]) and an undisclosed particle.
- This also does not match the process described in the problem.
7. Equation 4:
[tex]\[
2{ }_1^2 H \rightarrow{ }_2^3 He +{ }_0^1 n
\][/tex]
- Here, two deuterium nuclei ([tex]\( { }_1^2 H \)[/tex]) fuse to form helium-3 ([tex]\( { }_2^3 He \)[/tex], with 2 protons and 1 neutron) and a neutron ([tex]\( { }_0^1 n \)[/tex]).
- This equation matches the problem's description exactly.
Thus, the correct equation illustrating the fusion process of two deuterium nuclei forming helium-3 and emitting a neutron is:
[tex]\[
2{ }_1^2 H \rightarrow{ }_2^3 He +{ }_0^1 n
\][/tex]
As a result, the correct option is number 4.
