The relation that connects photons both as wave motion and as a stream of particles is Option D, $E = hv$. This equation is known as the Planck-Einstein relation. Here, $E$ stands for the energy of a single photon, $h$ is Planck's constant ($6.626 \times 10^{-34}$ m²kg/s), and $v$ (or $f$ in some texts) represents the frequency of the electromagnetic wave associated with the photon.

This equation encapsulates the dual nature of light and all electromagnetic radiation, embodying both wave and particle characteristics. The wave aspect is captured through the frequency ($v$), which is a fundamental property of waves. The particle aspect is represented by quantizing the energy in discrete packets called photons, with each photon having a quantum of energy $E$.

In contrast, Option A (Interference) and Option C (Diffraction) are phenomena that demonstrate the wave nature of light, and Option B ($E = mc^2$), Einstein's mass-energy equivalence, describes how mass and energy are related but is not directly related to the dual characteristic of photons.