**Core Concept**
The underlying principle being tested is the management of a closed injury to the extensor tendon of the finger, specifically the **mallet finger** injury. This injury typically occurs when an object, such as a ball, strikes the tip of the finger, causing disruption of the extensor tendon at the distal interphalangeal (DIP) joint.

**Why the Correct Answer is Right**
Since the X-ray is normal, indicating no fracture, the next step involves treating the soft tissue injury. The correct management approach for a mallet finger injury without fracture is immobilization of the DIP joint in extension to allow the tendon to heal. This is typically achieved with a splint.

**Why Each Wrong Option is Incorrect**
**Option A:** This choice is not provided, but generally, immediate surgical intervention is not the first line for mallet finger injuries without fracture.
**Option B:** Similarly, this option is not specified, but applying a cast might not be the best initial approach for isolated tendon injuries.
**Option C:** Again, the specific option is missing, but generally, options that do not involve immobilization in extension are less likely to be correct.
**Option D:** This option is also not provided, but if it involved neglecting immobilization or inappropriate management, it would be incorrect.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that mallet finger injuries should be immobilized in extension for several weeks to ensure proper healing of the tendon. Failure to do so can result in permanent deformity.

**Correct Answer:** D. Immobilize the DIP joint in extension.