Match Nuclear Processes with Corresponding Physical Properties and Phenomena

To match the nuclear processes in Column I with the appropriate properties/phenomena in Column II, we analyze each process individually:

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(A) Nuclear fusion

1. Energy production in stars (R): The primary source of energy in stars (like the Sun) is nuclear fusion, where hydrogen nuclei fuse to form helium via the proton-proton ($p\text{-}p$) chain or the CNO cycle.
2. Neutrino emission (T): During the initial steps of the $p\text{-}p$ chain fusion reaction ($p + p \rightarrow d + e^+ + \nu_e$), electron neutrinos ($\nu_e$) are produced and emitted.

$\text{Hence, } \mathbf{A \rightarrow R \text{ (or } R, T)}.$

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(B) Fission in a nuclear reactor

1. Absorption of thermal neutrons by $^{235}_{92}\text{U}$ (P): Nuclear reactors commonly use $^{235}_{92}\text{U}$ as fuel, which absorbs thermal (slow) neutrons to undergo nuclear fission: $^{235}_{92}\text{U} + \,^1_0n \rightarrow \,^{236}_{92}\text{U}^* \rightarrow \text{Fission Products} + \text{neutrons} + \text{Energy}$
2. Heavy water (S): Heavy water ($\text{D}_2\text{O}$) is widely used in nuclear reactors (e.g., Pressurized Heavy Water Reactors) as a moderator to slow down fast neutrons to thermal energies, enabling efficient fission.

$\text{Hence, } \mathbf{B \rightarrow P, S}.$

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(C) $\beta$-decay

1. $^{60}_{27}\text{Co}$ nucleus (Q): Cobalt-60 ($^{60}_{27}\text{Co}$) is a well-known radioisotope that undergoes $\beta^-$-decay to form an excited state of Nickel-60 ($^{60}_{28}\text{Ni}$): $^{60}_{27}\text{Co} \rightarrow \,^{60}_{28}\text{Ni}^* + e^- + \bar{\nu}_e$
2. Neutrino emission (T): By Pauli's neutrino hypothesis, $\beta$-decay involves the emission of a neutrino ($\nu_e$) in $\beta^+$-decay or an antineutrino ($\bar{\nu}_e$) in $\beta^-$-decay to conserve energy, angular momentum, and lepton number.

$\text{Hence, } \mathbf{C \rightarrow Q, T}.$

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(D) $\gamma$-ray emission

1. Energy production in stars via hydrogen conversion to helium (R): During the fusion reactions in stars, significant energy is released directly in the form of high-energy gamma-ray ($\gamma$-ray) photons, such as in the reaction: $p + d \rightarrow \,^3\text{He} + \gamma \quad (Q = 5.49\text{ MeV})$ These $\gamma$-ray photons carry a major portion of the energy produced in the stellar core.

$\text{Hence, } \mathbf{D \rightarrow R}.$

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Final Correct Matching:

• (A) $\rightarrow$ R or R, T
• (B) $\rightarrow$ P, S
• (C) $\rightarrow$ Q, T
• (D) $\rightarrow$ R