Question

which of these is a fusion reaction (A) ${ }^{3}{ }_{1} \mathrm{H}+{ }_{1}^{2} \mathrm{H}={ }_{2}^{4} \mathrm{He}+{ }_{0} \mathrm{n}^{1}$ (B) ${ }^{12}{ }_{7} \mathrm{C} \rightarrow{ }_{6} \mathrm{C}^{12}+\beta^{+}+\mathrm{g}$ (C) ${ }_{92} \mathrm{U}^{238} \rightarrow{ }^{206}{ }_{82} \mathrm{~Pb}+8\left({ }_{2}^{4} \mathrm{He}\right)+6\left(_{1-} \mathrm{e}\right)$ (D) None of these

Short answer

The correct answer is (A) \({ }^{3}{ }_{1} \mathrm{H}+{ }_{1}^{2} \mathrm{H}={ }_{2}^{4}\mathrm{He}+{ }_{0} \mathrm{n}^{1}\) as this is a fusion reaction involving the combination of tritium and deuterium nuclei to form a heavier helium-4 nucleus and a neutron.

Step-by-step solution

Analyze each reaction type

Let's analyze each given reaction to determine if it is a fusion reaction. (A) \({ }^{3}{ }_{1} \mathrm{H}+{ }_{1}^{2} \mathrm{H}={ }_{2}^{4}\mathrm{He}+{ }_{0} \mathrm{n}^{1}\) Here, we have two atomic nuclei, tritium (\({ }^{3}{ }_{1} \mathrm{H}\)) and deuterium (\({ }_{1}^{2} \mathrm{H}\)), combining to form a single heavier nucleus, helium-4 (\({ }_{2}^{4}\mathrm{He}\)), and a neutron. This seems like a fusion reaction. (B) \({ }^{12}{ }_{7} \mathrm{C} \rightarrow{ }_{6}\mathrm{C}^{12}+\beta^{+}+\mathrm{g}\) In this reaction, one nucleus, carbon with a mass number of 12 and an atomic number of 7 (\({ }^{12}{ }_{7} \mathrm{C}\)), is decaying into another nucleus, carbon with a mass number of 12 and an atomic number of 6 (\({ }_{6}\mathrm{C}^{12}\)), while also emitting a positron (\(\beta^{+}\)) and a photon (g). This type of reaction is not fusion, as there's no combining of atomic nuclei. (C) \({ }_{92} \mathrm{U}^{238} \rightarrow{ }^{206}{ }_{82}\mathrm{~Pb}+8\left({ }_{2}^{4} \mathrm{He}\right)+6\left(_{1-}\mathrm{e}\right)\) In this reaction, a uranium-238 nucleus (\({ }_{92} \mathrm{U}^{238}\)) is breaking apart into a lead-206 nucleus (\({ }^{206}{ }_{82}\mathrm{~Pb}\)), eight helium-4 nuclei, and six electrons. This is a fission reaction, not fusion, as the initial nucleus is splitting into smaller ones.

Determine the correct answer

Now that we analyzed each reaction, we can confidently say that the correct answer is: (A) \({ }^{3}{ }_{1} \mathrm{H}+{ }_{1}^{2} \mathrm{H}={ }_{2}^{4}\mathrm{He}+{ }_{0} \mathrm{n}^{1}\) This is a fusion reaction because two atomic nuclei, tritium and deuterium, combine to form a single heavier nucleus, helium-4, and a neutron.