Final answer:
A Vagus nerve (CN X) lesion leads to a drooping of the soft palate with the uvula deviating to the unaffected side, as it affects the palatoglossus muscle responsible for elevation of the soft palate.
Step-by-step explanation:
The lesion that leads to drooping of the arch of the soft palate with the uvula deviating to the unaffected side is a Vagus nerve (CN X) involvement. When there is damage to the vagus nerve, it can result in an asymmetrical soft palate response due to paralysis of the palatoglossus muscle on the affected side. The uvula, which is a fleshy bead of tissue at the center of the posterior edge of the soft palate, points away from the side of the lesion because the opposite side of the soft palate is still functioning and pulls the uvula towards it.
The hypoglossal nerve (CN XII) is the motor nerve that controls the muscles of the tongue, and testing for hypoglossal function involves asking the patient to stick out their tongue. Observing the direction the tongue deviates when protruded can help identify damage to the nerve, as it will point towards the side with the deficit. The facial nerve (CN VII) is responsible for taste, as well as salivation, in the anterior oral cavity. Finally, the accessory nerve (CN XI) primarily controls the sternocleidomastoid and trapezius muscles and would not cause asymmetry in the soft palate.