Final answer:
The C₃H₅ ion likely exhibits asymmetry since it does not have a geometry that allows it to be split into two equal mirror-image halves and it doesn't display radial or spherical symmetry. This conclusion is based on the described trigonal planar and linear geometries within the ion.
Step-by-step explanation:
When determining the symmetry of the C₃H₅ ion, we look at the atomic arrangement and electron distribution. For this particular ion, the description given indicates that the terminal carbon atoms are trigonal planar, the central carbon is linear, and the C-C-C angle is 180°. This leads us to conclude that the ion displays molecular geometries associated with planar and linear shapes rather than spherical or radial symmetry. However, the question as stated does not provide a perfect match to any of the options, as it lacks the required context to make a definitive determination. A likely assumption would be that the C₃H₅ ion exhibits asymmetry since it cannot be split into two equal mirror-image halves through any plane of symmetry, which is supported by previous knowledge of organic molecular structures. However, without additional structural details, this is an informed hypothesis rather than a definitive conclusion.