**Core Concept**
Wrist drop is a condition characterized by the inability to extend the wrist, resulting from damage to the radial nerve. The radial nerve is responsible for innervating the extensor muscles of the wrist, which are essential for wrist extension.

**Why the Correct Answer is Right**
The radial nerve is a branch of the brachial plexus, specifically originating from the C5-C8 nerve roots and T1 nerve root. It courses down the arm, through the radial tunnel, and into the forearm, where it innervates the extensor muscles of the wrist, including the extensor carpi radialis brevis, extensor carpi radialis longus, and extensor digitorum. Injury to this nerve can result in weakness or paralysis of these muscles, leading to wrist drop.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not specify the nerve responsible for wrist extension. While the ulnar nerve is also a branch of the brachial plexus, it primarily innervates the intrinsic muscles of the hand.
**Option B:** This option is incorrect because it mentions the median nerve, which is responsible for innervating the flexor muscles of the wrist and forearm, but not the extensor muscles.
**Option C:** This option is incorrect because it mentions the musculocutaneous nerve, which is responsible for innervating the biceps brachii and brachialis muscles, but not the extensor muscles of the wrist.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that wrist drop can also be caused by compression of the radial nerve at the radial tunnel, which can occur due to repetitive strain or direct trauma. This can be a common occurrence in individuals who perform repetitive activities, such as typing or using vibrating tools.

**Correct Answer: D. Radial nerve.