Step 1: Understanding the stability of free radicals.
The stability of free radicals increases with the number of alkyl groups attached to the carbon center. The more alkyl groups, the greater the electron donation, stabilizing the radical.
Step 2: Analyzing the options.
(A) R-CH\(_2\): This is a primary radical and is less stable due to fewer electron-donating groups.
(B) R\(_3\)-C•: This is a tertiary radical, which is the most stable due to the three electron-donating alkyl groups.
(C) CH\(_3\)•: This is a methyl radical, which is a primary radical and less stable.
(D) R\(_2\)-C•H: This is a secondary radical and more stable than a primary radical, but less stable than a tertiary radical.
Step 3: Conclusion.
The correct answer is (B) R\(_3\)-C•, as tertiary radicals are the most stable.