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In this chapter we break out of the tradition and viewpoint of classical physics and discuss results from quantum theory. In the 1890s, physicists began to realize that the very language of particles and positions, forces and fields was insufficient to discuss the world of the very small, of atoms and molecules. They needed a new language and a new way of thinking, and quantum physics was born.
In classical physics, which we have been studying thus far, if we wanted to talk about a particular electron in an atom, we would specify its position and velocity. Physics would tell us how that position changed in time.
In quantum physics, we do not even talk about position and velocity in this way, because it turns out these terms are impossible to define. Particles simply do not have a definite position nor velocity. Instead we talk about a particular electron in an atom by specifying the orbital it is in. Orbital it is in? An orbital is a state of being for an electron. Knowing an electron's orbital means knowing its energy (generally) and knowing something about its location (often), but not its exact position.
One way to think about it is to think that electrons are tiny particles which move so fast that we do not know where they are, and the area of space they move in is an orbital. That is one way to think about it, but it's the wrong way.
It is not the case that electrons have position and velocity of which we are simply ignorant. An electron truly has no exact position, existing all around the nucleus at once, although it does exist more strongly in some places than in others.
For instance, an electron in the lowest-energy orbital of a hydrogen atom exists throughout the area near the nucleus, but it exists 90% within a radius of 1.4 x 10–10 m and 10% outside of that radius. (That does not mean that it spends 10% of its time outside of 1.4 x 10–10 m. That is thinking classically again.)

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