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## Shape of orbitals: 1s orbital

The solution of the Schrödinger equation for the hydrogen atom in the ground state with the lowest energy is the 1s orbital. The wave function is spherically symmetric to the atomic nucleus. The square of the wave function, the probability or electron density, has a zero in the origin, the atomic nucleus. The electron density initially increases sharply with a larger nuclear distance and then decreases again. However, the electron density does not become zero with a large nuclear distance. The probability of finding an electron a kilometer from the nucleus, for example, is not zero.

- Tab. 1
- Electron density distribution of the 1s orbital

Wave function | Electron density |
---|---|

The two-dimensional representation in the form of an electron density plot illustrates the spherically symmetrical electron density distribution around the atomic nucleus. The electron density decreases with increasing distance from the atomic nucleus.

The common representation of an s atomic orbital is a sphere. The sphere results from the electron density as follows: A limit value for the electron density (greater than or equal to 90%) is set. The points in space with this electron density form the spherical surface. The three-dimensional electron density distribution can be seen in the truncated sphere. In the further course the s-orbitals are shown as spheres.