In this nuclear fusion process, we are looking at the fusion of two deuterium nuclei to form helium-3 and release a neutron.
Let's break down the key components described in the problem:
1. Deuterium ( [tex]\(_1^2 \text{H} \)[/tex]):
- Each deuterium nucleus contains one proton and one neutron.
2. Fusion Reaction Outcome:
- When two deuterium nuclei fuse, a helium-3 ([tex]\(_2^3 \text{He} \)[/tex]) nucleus and a neutron ([tex]\(_0^1 \text{n} \)[/tex]) are produced.
- Helium-3 nucleus contains 2 protons and 1 neutron.
3. Equation Representation:
- The equation to represent the process should show two deuterium nuclei on the reactant side transforming into a helium-3 nucleus and a free neutron on the product side.
Now, evaluate the options given:
1. [tex]\(2 H _2 + O _2 \rightarrow 2 H _2 O\)[/tex]
- This is a chemical reaction representing the formation of water and not a nuclear fusion reaction.
2. [tex]\(_2^2 H \rightarrow{ }_1^3 H +{ }_1^1 H\)[/tex]
- This suggests a transformation into tritium ([tex]\(_1^3 \text{H} \)[/tex]) and a proton ([tex]\(_1^1 \text{H} \)[/tex]), which is not the process described.
3. [tex]\(2{ }_1^1 H \rightarrow{ }_1^2 H +{ }_1^0 e\)[/tex]
- This equation is incorrect because deuterium is [tex]\(_1^2 \text{H}\)[/tex] not [tex]\(_1^1 \text{H}\)[/tex], and it does not form helium-3.
4. [tex]\(_1^2 H +{ }_1^2 H \rightarrow{ }_2^3 He +{ }_0^1 n\)[/tex]
- This correctly illustrates the fusion reaction where two deuterium nuclei collide to form a helium-3 nucleus and a neutron.
Thus, the equation that illustrates the described fusion process is:
[tex]\[2_1^2 H \rightarrow{ }_2^3 He +{ }_0^1 n\][/tex]
This option correctly represents the nuclear reaction where two deuterium nuclei fuse to form a helium-3 nucleus and a neutron.
