Step 1: Understanding the Question:
The query seeks the principal product when a tertiary alkyl bromide, namely tert-butyl bromide, interacts with silver fluoride ($\mathrm{AgF}$) under thermal conditions.
Step 2: Key Formula or Approach:
The transformation of an alkyl halide using metallic fluorides such as $\mathrm{AgF}$, $\mathrm{Hg}_2\mathrm{F}_2$, $\mathrm{CoF}_2$, or $\mathrm{SbF}_3$ to synthesize alkyl fluorides is termed the Swarts reaction. This represents a nucleophilic substitution where the bromide ion gets displaced by a fluoride ion.
Step 3: Detailed Explanation:
Tert-butyl bromide possesses the structural arrangement $(\mathrm{CH}_3)_3\mathrm{C-Br}$.
Upon treatment with silver fluoride ($\mathrm{AgF}$), halogen interchange occurs following a Swarts reaction pathway. The silver cation precipitates with bromide as insoluble $\mathrm{AgBr}$, which pushes the equilibrium forward.
The fluoride nucleophile attacks the tertiary carbocation center, substituting the bromine atom.
$$\mathrm{(CH}_3)_3\mathrm{C-Br} + \mathrm{AgF} \xrightarrow{\Delta} \mathrm{(CH}_3)_3\mathrm{C-F} + \mathrm{AgBr}\downarrow$$ The IUPAC designation of the product $(\mathrm{CH}_3)_3\mathrm{C-F}$ is 2-Fluoro-2-methylpropane.
Step 4: Final Answer:
The major product obtained is 2-Fluoro-2-methylpropane, corresponding to option (B).