**Core Concept**
The question pertains to the interaction of X-rays with matter, specifically the Compton scattering effect. Compton scattering is a type of inelastic scattering where an X-ray photon collides with a free electron, resulting in a transfer of energy and a change in the wavelength of the X-ray. This phenomenon is crucial in understanding the attenuation of X-rays as they pass through tissues.

**Why the Correct Answer is Right**
Compton scattering is the primary mechanism by which X-rays interact with soft tissues, given that most of the atoms in biological tissues have low atomic numbers. The amount of X-rays that undergo Compton scattering is significant because it depends on the density and composition of the material the X-rays are passing through. Compton scattering is responsible for the majority of the scattered radiation in medical imaging, affecting image quality.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the photoelectric effect, while an important interaction, is more significant in materials with higher atomic numbers and at lower energies.
**Option B:** This option is incorrect as the photoelectric effect and Compton scattering both play roles but are not the correct answer to the question about the amount of X-rays undergoing Compton scattering.
**Option D:** This option is incorrect because the amount of X-rays that undergo Compton scattering is not negligible, especially in the context of medical imaging and the interaction with soft tissues.

**Clinical Pearl / High-Yield Fact**
Compton scattering is a critical concept in radiology, affecting the dose and image quality in X-ray-based imaging modalities. Understanding Compton scattering helps in optimizing imaging protocols to improve diagnostic accuracy while minimizing radiation exposure to patients.

**Correct Answer:** Correct Answer: C. 80% of X-rays.