Step 1: Understanding the Question:
The question asks for the major product when a tertiary alkyl halide, specifically tert-butyl bromide, reacts with silver fluoride ($\mathrm{AgF}$) under heating conditions.
Step 2: Key Formula or Approach:
The reaction of an alkyl halide with metal fluorides like $\mathrm{AgF}$, $\mathrm{Hg}_2\mathrm{F}_2$, $\mathrm{CoF}_2$, or $\mathrm{SbF}_3$ to prepare alkyl fluorides is known as the Swarts reaction. It is a nucleophilic substitution reaction where the halide ion (bromide) is replaced by a fluoride ion.
Step 3: Detailed Explanation:
Tert-butyl bromide has the structural formula $(\mathrm{CH}_3)_3\mathrm{C-Br}$.
When treated with silver fluoride ($\mathrm{AgF}$), a halogen exchange takes place via a Swarts reaction framework. The silver ion precipitates out with bromide as insoluble $\mathrm{AgBr}$, driving the equilibrium forward.
The nucleophilic fluoride ion attacks the tertiary carbocation intermediate or reaction center, replacing 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 name 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, which corresponds to option (B).