Question

The most stable free radical among the following is
$
  (1){C_6}{H_5}C{H_2}\dot C{H_2} \\
  (2){C_6}{H_5}\dot CHC{H_3} \\
  (3)C{H_3}\dot CHC{H_3} \\
  (4){{\dot C}_6}{H_5} \\
    \\
 $

Answer 1

Hint: As we know that radical is an atom, molecule or an ion with an unpaired valence electron. Free radicals are very reactive and they have a very short lifetime. They spontaneously combine with other radicals to form dimers.
Complete step by step solution:
We know that stability of a radical depends on the internal energy of the radical. If the internal energy of the radical is very high then it is unstable and if the internal energy of the radical is low then it will be stable. It is important to note that the electron donating groups increases the stability of the radical. That means a radical is stabilised by hyperconjugation and resonance . So a benzylic radical will be very much stable as compared to other radicals. In ${C_6}{H_5}C{H_2}\dot C{H_2}$, the free radical is not stabilized by resonance. In $C{H_3}\dot CHC{H_3},{\dot C_6}{H_5}$ the radical cannot undergo resonance . But in ${C_6}{H_5}\dot CHC{H_3}$, the radical can undergo resonance with the benzyl ring. So it will be the most stable free radical .
So from the above explanation it is clear that the correct option of the question is : $(2){C_6}{H_5}\dot CHC{H_3}$

So the the correct answer is option (2)

Additional information:
Carbocation is also stabilized by the electron donating groups. The free radical has only seven electrons in their valence shell for this reason the electron donating groups stabilizes the free radical because it will increase the seven valence electron to eight valence electrons.

Note:
Always remember that electron donating groups increase the stability of free radicals as well as carbocations. Resonance and hyperconjugation increases the stability of a free radical and carbocations. If a radical or carbocation can undergo resonance with a benzene ring then it will be exceptionally stable.