Final answer:
The Heisenberg uncertainty principle and the Schrödinger wave equation led to the idea of atomic orbitals by introducing the concept of a cloud of probability and describing electron behavior as waves.
Step-by-step explanation:
The Heisenberg uncertainty principle and the Schrödinger wave equation were crucial in developing the idea of atomic orbitals. The uncertainty principle states that we cannot know both the position and momentum of a particle simultaneously. This means that the exact path and speed of an electron cannot be determined precisely, leading to the concept of a cloud of probability.
Schrödinger's wave equation, on the other hand, describes the behavior of particles, such as electrons, as waves. The equation provides a mathematical description of how these waves vary in space and time. By solving the equation for the hydrogen atom, Schrödinger derived a set of wavefunctions, known as atomic orbitals. These orbitals represent the probability of finding an electron in a particular region around the nucleus.