An organic reaction used to convert an aryl diazonium salt into an aryl halide using a copper(I) halide catalyst is called:

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Step-by-step explanation:

- The reaction that converts an aryl diazonium salt into an aryl halide using a copper(I) halide catalyst is the Sandmeyer reaction.

- General transformation: $\mathrm{ArN_2^+\ X^- + CuX \longrightarrow ArX + N_2 + 	ext{(copper species)}}$. The key steps involve single-electron transfer (SET) from Cu(I) to the diazonium, loss of $\mathrm{N_2}$ to give an aryl radical, and capture of that radical by halide to form $\mathrm{ArX}$.

- Why the other options are incorrect:
  - Finkelstein reaction: halide exchange (typically alkyl halides, e.g. $\mathrm{RCl \leftrightarrow RI}$ using NaI in acetone), not via diazonium/Cu(I).
  - Balz–Schiemann reaction: converts diazonium salts to aryl fluorides by thermal decomposition of diazonium tetrafluoroborates (no Cu(I) halide catalyst).
  - Gattermann reaction: refers to other transformations (e.g., Gattermann–Koch formylation) and is not the standard name for the Cu(I)-mediated diazonium → aryl halide conversion.

Therefore the correct choice is option (3), Sandmeyer reaction.

FINAL_ANSWER: c

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