$$(C_7H_5O_2)_2 \xrightarrow{h\nu} [X] \to 2\dot{C}_6H_5 + 2CO_2$$
Consider the above reaction and identify the intermediate 'X'

We are given the photolysis of benzoyl peroxide:

$$(C_6H_5COO)_2 \xrightarrow{h\nu} [X] \to 2\dot{C}_6H_5 + 2CO_2$$

We need to identify the intermediate X.

Structure of benzoyl peroxide

Benzoyl peroxide has the structure:

$$C_6H_5-\overset{O}{\underset{||}{C}}-O-O-\overset{O}{\underset{||}{C}}-C_6H_5$$

It contains a weak O-O peroxide bond.

Photolysis (homolytic cleavage)

When benzoyl peroxide absorbs UV light ($$h\nu$$), the weak O-O bond undergoes homolytic cleavage (since it is photolysis, which favors homolytic bond breaking).

$$C_6H_5COO-OOCC_6H_5 \xrightarrow{h\nu} 2 \cdot C_6H_5COO\dot{}$$

This produces two benzoyloxy radicals: $$C_6H_5-\overset{O}{\underset{||}{C}}-\dot{O}$$

Further decomposition

Each benzoyloxy radical then decomposes to give a phenyl radical and $$CO_2$$:

$$C_6H_5-\overset{O}{\underset{||}{C}}-\dot{O} \to \dot{C}_6H_5 + CO_2$$

Identify intermediate X

The intermediate X is the benzoyloxy radical: $$C_6H_5-\overset{O}{\underset{||}{C}}-\dot{O}$$

This is a free radical species with an unpaired electron on oxygen.

The correct answer is Option C: $$C_6H_5-\overset{O}{\underset{||}{C}}-\dot{O}$$.