Step 1: Concept
One mole of any substance contains Avogadro's number ($N_A = 6.022 \times 10^{23}$) of constituent particles (atoms, molecules, or ions).
Step 2: Analysis of $CO_2$
One molecule of $CO_2$ consists of one Carbon (C) atom and two Oxygen (O) atoms.
Step 3: Calculation
- One mole of $CO_2$ molecules contains $1 \times N_A$ Carbon atoms.
- One mole of $CO_2$ molecules contains $2 \times N_A$ Oxygen atoms.
Step 4: Conclusion
Thus, one mole of $CO_2$ contains $6.02 \times 10^{23}$ atoms of Carbon.
Final Answer: (D)