The idea Einstein first proposed to explain both the photoelectric effect and the results of double-slit experiments was the particle nature of light, also known as the photon theory.

Here's a breakdown:

* Photoelectric effect: This effect demonstrated that light could knock electrons off a metal surface, but only if the light's frequency exceeded a certain threshold. Classical physics couldn't explain this threshold, as it predicted that the energy of light should depend only on its intensity, not frequency. Einstein proposed that light was made up of tiny packets of energy called photons, each with energy proportional to its frequency. This explained the threshold: only photons with enough energy could knock off an electron.

* Double-slit experiment: This experiment showed that light can exhibit both wave-like and particle-like behavior. When light is passed through two slits, it creates an interference pattern on a screen behind the slits, indicating wave-like behavior. However, it also showed that light can interact with matter like particles, as if individual photons were passing through the slits. Einstein's photon theory helped explain this dual nature, suggesting that light acts as both a wave and a particle.

It's important to note that the wave-particle duality of light is a fundamental concept in quantum mechanics, and while Einstein's photon theory explained the photoelectric effect and provided a framework for understanding the double-slit experiment, it didn't fully explain the wave-like behavior of light. That understanding came with the development of quantum mechanics later.