Which of the following is the most stable free radical?

Step-by-step solution

The stability of free radicals is determined by factors such as resonance, hyperconjugation, and inductive effects. Option (1) is a vinyl radical, which is highly unstable due to the sp^2 hybridized carbon atom having the unpaired electron in an sp^2 orbital. Option (2) is a methyl radical, which has no alkyl groups to provide stability through hyperconjugation. Option (3) is a tertiary butyl radical, which is stabilized by hyperconjugation from nine -hydrogen atoms. Option (4) is a diphenylmethyl radical, which is