**Core Concept**
The removal of hard carious dentin in dentistry requires a precise technique to prevent further damage to the surrounding tooth structure. This process involves the use of rotary instruments, specifically burs, which are designed to effectively remove decayed dentin while maintaining the integrity of the tooth.

**Why the Correct Answer is Right**
The correct answer is **C. Bur at high speed** because high-speed burs are specifically designed for efficient removal of hard tissues, such as carious dentin. When used at high speed, these burs can effectively remove the decayed dentin while minimizing the risk of further damage to the surrounding tooth structure. The high-speed motion also helps to prevent the bur from binding in the dentin, reducing the risk of fracture.

**Why Each Wrong Option is Incorrect**
**Option A:** Excavators are typically used for the removal of softer, more decayed dentin or for shaping and smoothing the dentin surface. They are not suitable for the removal of hard carious dentin.
**Option B:** Low-speed burs are generally used for more delicate procedures, such as removing decayed dentin in areas where high-speed burs may be too aggressive. However, they are not as effective as high-speed burs for removing hard carious dentin.

**Clinical Pearl / High-Yield Fact**
When using high-speed burs to remove hard carious dentin, it is essential to maintain a steady, gentle hand motion and to use a water coolant to prevent overheating and damage to the surrounding tooth structure.

**✓ Correct Answer: C. Bur at high speed**