The correct increasing order of stability of the free radicals among the following is:

(C_{6} H_{5})_{2} ∙ C H < (C_{6} H_{5})_{3} ∙ C < (C H_{3})_{3} ∙ C < (C H_{3})_{2} ∙ C H

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(C H_{3})_{2} ∙ C H < (C H_{3})_{3} ∙ C < (C_{6} H_{5})_{2} ∙ C H < (C_{6} H_{5})_{3} ∙ C

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(C H_{3})_{3} ∙ C < (C H_{3})_{2} ∙ C H (C_{6} H_{5})_{2} ∙ C H < (C_{6} H_{5})_{3} ∙ C

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(C_{6} H_{5})_{3} ∙ C < (C_{6} H_{5})_{2} ∙ C H < (C H_{3})_{3} ∙ C < (C H_{3})_{2} ∙ C H

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Solution

The correct option is C $(C H_{3})_{3} ∙ C < (C H_{3})_{2} ∙ C H (C_{6} H_{5})_{2} ∙ C H < (C_{6} H_{5})_{3} ∙ C$
The correct order of stability of free radicals is:
$(C H_{3})_{2} ∙ C H < (C H_{3})_{3} ∙ C < (C_{6} H_{5})_{2} ∙ C H < (C_{6} H_{5})_{3} ∙ C$

More the number of phenyl ring, more the number of resonating structure and hence more is the stability.
Similarly, more the number of $α H$ , more will be the hyperconjugative structure and hence stability will be more.

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