Bond dissociation energy of CH₃-H bond is 103 kcal mol^-1 and heat of formation of CH₄(g) as - 17.88 kcal mol^-1. The heat of formation of methyl radical is

$\begin{array}{l}{\mathrm{CH}}_4\left(\mathrm{g}\right)={\mathrm{CH}}_3\left(\mathrm{g}\right)+\mathrm{H}\left(\text{ atom, }\mathrm{g}\right)\\ {\left(\mathrm{\Delta }{H}_{\mathrm{f}}\right)}_{{\mathrm{CH}}_3-\mathrm{H}}{\mathrm{CH}}_3-\mathrm{H}=103=\mathrm{\Delta }{H}_{\mathrm{f}}\left({\mathrm{CH}}_3,\mathrm{g}\right)+\mathrm{\Delta }{H}_{\mathrm{f}}(\mathrm{H}\text{ atom },\\ \mathrm{g})-\mathrm{\Delta }{H}_{\mathrm{f}}\left({\mathrm{CH}}_4,\mathrm{g}\right)\\ {\left(\mathrm{\Delta }{H}_{\mathrm{f}}\right)}_{{\mathrm{CH}}_3,\mathrm{g}}=103-\frac{103}{2}+(-17.889)=33.611\mathrm{kcal}{\mathrm{mole}}^{-1}\end{array}$

$\therefore \mathrm{Heat} \mathrm{of} \mathrm{formation} \mathrm{of} \mathrm{methyl} \mathrm{radical} \mathrm{is}$

$\mathrm{\Delta }H=33.611\mathrm{kcal}{\mathrm{mol}}^{-1}$