Step 1: Understanding the Concept:
A molecule has a zero dipole moment if the vector sum of all individual bond dipoles cancels out, which happens due to its symmetrical geometry. Step 2: Detailed Explanation:
• CH\(_2\)Cl\(_2\): Tetrahedral but not symmetric (H and Cl differ). Net dipole moment is non-zero.
• NH\(_3\): Trigonal pyramidal. The lone pair causes a net dipole moment.
• CH\(_4\): Tetrahedral with identical C-H bonds. The vector sum of bond dipoles is zero.
• PH\(_3\): Similar to NH\(_3\), has a net dipole moment.
Step 3: Final Answer:
CH\(_4\) has a zero dipole moment, which corresponds to option (C).