**Core Concept:** Anatomical snuff box is a region on the volar surface of the forearm, located between the tendons of the extensor carpi radialis brevis and extensor digiti minimi muscles. It is a landmark used in clinical examination and surgical procedures.

**Why the Correct Answer is Right:**
The correct answer, **C. Radial Nerve**, is responsible for the sensation to the skin over the anatomical snuff box and motor function to the extensor muscles of the thumb. The radial nerve arises from the brachial plexus and contains fibers from the C5, C6, and C7 spinal nerves. It passes through the radial tunnel, a space formed by the radial head, the annular ligament, and the triangular fibrocartilage complex.

**Why Each Wrong Option is Incorrect:**

A. **Ulnar Nerve (Ulnar Nerve)** is responsible for sensation to the skin over the medial half of the forearm and motor function to the flexor muscles of the thumb. It does not pass through the radial tunnel or innervate the extensor muscles of the thumb.

B. **Radial Artery**: Although the radial artery is located in the radial fossa, it is an artery and not a nerve responsible for sensation or motor function.

D. **Median Nerve**: The median nerve is responsible for sensation to the skin over the medial half of the forearm and motor function to the muscles of the thumb. It does not pass through the radial tunnel or innervate the extensor muscles of the thumb.

**Clinical Pearl:** Understanding the relationship between nerves, arteries, and landmarks like the anatomical snuff box enables accurate clinical examination and surgical planning, preventing unnecessary damage to vital structures.