Atomic Orbitals and Nodes

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Orbitals are important becuase they determine the distribution of electrons in molecules, which in turn determines the electronic and optical properties of materials. Atomic orbitals are wave functions that are solutions to the Schrödinger equation. This equation allows us to figure out the wave functions and associated energies in atomic orbitals. The square of the wave function gives the probability of finding an electron at a certain point. The integral of the wavefunction over a voluem gives the enclosed electron density within that volume. The most likely position to find the 1s electron is at the nucleus.However the most likely radius is at some distance from the nucleus. The graph of wavefunction vs distance falls off exponentially as you move away from the nucleus. The electron density builds quadratically with distance from the nuclues. The peak electron density will be the product of the these two functions. This results in a curve with a density peak at a certain distance.