To determine which half-reaction correctly describes an oxidation process, we need to understand that oxidation is the loss of electrons. This means we need to look for the half-reaction where an element is losing electrons.
Let's analyze each given half-reaction:
1. [tex]\( Ca(s) + 2e^- \longrightarrow Ca^{2+}(aq) \)[/tex]
In this equation, calcium metal is gaining 2 electrons to form [tex]\( Ca^{2+} \)[/tex] ions. Since gaining electrons is a reduction process, this is not an oxidation reaction.
2. [tex]\( Br_2 + 2e^- \longrightarrow 2 Br^- \)[/tex]
Here, molecular bromine is gaining 2 electrons to form bromide ions. Since gaining electrons is a reduction process, this is not an oxidation reaction either.
3. [tex]\( Na^+(aq) \longrightarrow Na(s) + e^- \)[/tex]
In this equation, sodium ions are losing an electron to form sodium metal. While this does involve a loss of electrons, it is important to check the context for all reactions to be accurate.
4. [tex]\( Cr(s) \longrightarrow Cr^{3+}(aq) + 3e^- \)[/tex]
Here, chromium metal is losing 3 electrons to form [tex]\( Cr^{3+} \)[/tex] ions. Since losing electrons is the definition of oxidation, this reaction correctly describes an oxidation process.
Considering all the reactions, the half-reaction that correctly describes an oxidation process is:
[tex]\[ Cr(s) \longrightarrow Cr^{3+}(aq) + 3e^- \][/tex]
Thus, this corresponds to the fourth reaction in the list. The numerical index for this reaction is:
[tex]\[ 3 \][/tex]
Therefore, the half-reaction that correctly describes an oxidation process is the fourth one, corresponding to the numerical result 3.
