Atomic Structure and Quantum Mechanics

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Context

Scientists are constantly trying to model things that they can't see. The first real model of the atom was the raisin pudding (or plumb pudding) model. In 1907 Ernest Rutherford made new observations that were not consistent with the raisin pudding model and the solar system model was put forward as the atomic theory. New experiments, however, were not consistent with the solar system model and so it too had to be discarded. The current model retains some of the ideas and terminology of the original Bohr model, but it is probabilistic in nature and uses quantum mechanics to describe the atom.

What is quantum mechanics?

Quantum mechanics is a mathematical model of the atom that has agreed with all of our observations for more than 75 years. It is the currently accepted atomic theory.

Explanation

Around 1925 two young scientists, Heisenberg and Schrödinger, independently proposed mathematical models to describe electrons in the atom. The models were equivalent and now are referred to as the original formulations of quantum mechanics. We will concentrate on the part of the theory that describes where the electron is likely to be in space around the nucleus. The theory completely rejects the idea that electrons orbit the nucleus and only gives regions of space where the electron is most likely to be.

This section will help you:

• Better understand the general idea of quantum theory.
• Realize that there is inherent uncertainty in quantum mechanics.
• Realize that a few simplifications of the complicated mathematical theory results in a useable model that allows us to explain much of the chemistry that we observe.

Model

Quantum mechanics is a model that uses probability. It allows us to calculate the probability of finding an electron in a specified region of space for a given energy state. The region of space where the electron is likely to be found changes when the electron changes energy state.

One way of understanding this is to say that the mathematical equations can be used to calculate the most likely spot for an electron to be at a given instant. The time can be changed and the position calculated again. If a dot is placed around the nucleus for each of these calcualations, and it is done many times, we will get a picture of dots around the nucleus. Where there are more dots it will be more likely to find the electron. This process will then allow a calculation of the region in space where the electron is most likely to be. The equations are different for each energy state and so the whole thing must be done again for each energy state.

The result for such an exercise is truely amazing. If the solar system model was correct we would expect dots arranged in circles around the nucleus, but instead we get patterns that make absolutely no sense. The first excited energy state, for instance, ends up being in the shape of a dumbbell! This first excited energy state can actually be formally solved and results in a situation where there is exactly zero probability of finding an electron along a certain plane, but the probability is high both above and below the plane! How does the electron get from below the plane to above the plane? Bohr took care of this by saying that the word "path" should not be used to describe the motion of an electron. He said that electrons don't move in paths!

Feynman quote: It isn't ...
Student probability (in multimedia)

Thinking Questions

1. Does an atomic theory have to make sense?
2. Is science more a set of facts or a set of evolving theories?
3. Do facts exist in science?
4. How does quantum theory describe the position of an electron?
5. What would a picture of dots as described above look like if the solar system model was true.