Explanation: For a phase-modulated (PM) emission, the modulation index is defined as the maximum phase deviation of the carrier from its unmodulated angle. This maximum phase deviation (often denoted as $\Delta\phi_{max}$ or $m_p$) is directly proportional to the amplitude of the modulating signal and the sensitivity of the phase modulator. The RF carrier frequency determines the base frequency around which the phase is being shifted. However, the *amount* of phase shift itself (e.g., a shift of $\pi/2$ radians) is an angular quantity and is independent of how rapidly the carrier wave is oscillating. Whether the carrier is at 100 kHz or 100 MHz, a given modulating signal will cause the same maximum phase deviation, assuming the modulator sensitivity remains constant. Therefore, the modulation index of a phase-modulated emission does not depend on the RF carrier frequency. Options B, C, and D are incorrect as they suggest a dependency that does not exist for pure phase modulation.