Final answer:
The removal of an impacted mandibular third molar tooth carries a significant risk of damaging the alveolar nerve due to its proximity to the nerve within the mandibular canal. Other mentioned dental procedures generally possess a lower risk to the alveolar nerve.
Step-by-step explanation:
The question concerns the potential risk to the alveolar nerve during various dental surgical procedures. The alveolar nerve runs within the mandible and supplies sensation to the lower teeth and parts of the oral cavity. When considering the procedures mentioned, the removal of an impacted mandibular third molar tooth is the one that poses a significant risk to the alveolar nerve due to its close proximity to the nerve's location within the mandibular canal. The mandibular third molar, commonly known as the wisdom tooth, is located at a point where the nerve is at a higher risk of being disturbed or damaged.
Other procedures such as the removal of a torus mandibularis, forceps removal of a mandibular second molar, or distal wedge periodontal surgery do not typically carry the same level of risk to the alveolar nerve as the extraction of an impacted third molar does.