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Suppose you had a single hydrogen atom and at a particular instant plotted the position of its electron. Soon afterwards, you do the same thing, and find that it is in a new position. You have no idea how it got from the first place to the second. You keep on doing this over and over again, and gradually build up a sort of 3D map of the places that the electron is likely to be found.

The Heisenberg Uncertainty Principle  says - loosely - that you can’t know with certainty both where an electron is and where it’s going next. That makes it impossible to plot an orbit for an electron around a nucleus, but we have a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom’s nucleus.

In the hydrogen case, the electron can be found anywhere within a spherical space surrounding the nucleus. Such a region of space is called an orbital. Orbits and orbitals sound similar, but they have quite different meanings. It is essential that you understand the difference between them. You can think of an orbital as being the region of space in which the electron lives. The GIF animation shows the probability densities for the electron of a hydrogen atom in different quantum states. These orbitals form an orthonormal basis for the wave function of the electron. These shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found.


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