Compton Scattering unveils scenarios where classical wave theory reaches its explanatory limits. In classical wave theory, the energy of a wave is spread over a large space, and energy transfer isn't quantised. However, Compton Scattering demonstrates a precise, quantised energy transfer from photons to electrons, leading to a distinct increase in wavelength. This is not explainable by wave theory, as it doesn’t account for such discrete, quantised interactions and energy transitions. Thus, Compton Scattering stands as a testament to the limitations of classical wave theory in explaining quantum phenomena.

Compton Scattering experiments were pivotal in fortifying the empirical foundations of quantum theory. The explicit demonstration of photons transferring quantised energy packets to electrons, leading to an increased wavelength, offered a tangible, experimental corroboration of theoretical propositions. These experiments unveiled a world where energy transitions weren’t continuous, but quantised, and where light exhibited dual characteristics of waves and particles, depending on the observational context. This empirical evidence underpinned the evolution of quantum physics, offering it robust experimental grounding, and catalysing subsequent explorations and discoveries in the field.

The scattering angle in Compton Scattering is intimately linked to the energy transferred during the interaction between photons and electrons. A larger scattering angle correlates with a greater energy transfer to the electron, and correspondingly, a more significant increase in the wavelength of the scattered photon. This relationship is quantifiable and has been instrumental in validating the particle nature of light. It’s a direct manifestation of the conservation of energy and momentum principles at play during the scattering event, underscoring the discrete, quantised interactions that are a hallmark of quantum physics.

The wavelength increase in Compton Scattering is attributed to the energy loss by photons when they interact with electrons. As photons impart energy to electrons, they lose energy, resulting in an increase in their wavelength according to the Planck-Einstein relation. This shift is measurable and provides insights into the dynamics of the photon-electron interaction. It underscores the quantised energy exchange and the particle nature of photons, as they interact with electrons in a manner analogous to particles, offering tangible, empirical evidence that is integral to the comprehension of quantum physics and the dual nature of light.

Compton Scattering unequivocally illustrates the quantised nature of energy transfer during photon-electron interactions. In the event, photons impart a distinct, quantifiable amount of energy to electrons, leading to their recoil and a subsequent increase in the photons’ wavelength. The precision and consistency in this energy transfer, observable and measurable across various experimental settings, echo the narrative of energy quantisation. It underscores the concept that energy is transferred in discrete packets, aligning with the foundational tenets of quantum physics that distinguish it from the continuous energy transitions proposed by classical physics.