Atomic Structure and Forces

"If we find the answer to that [why it is that we and the universe exist], it would be the ultimate triumph of human reason - for then we would know the mind of God"
Stephen Hawking

What holds the atom together ?

Consider the simplest atom, that of Hydrogen. Why does the electron stay with the proton ?

The positively charged proton and the negatively charged electron are attracted to each other via the electromagnetic force ( Coulomb's law ), they want to be together. But something stops them from being too close. After all, we have seen that the atom itself (defined by the location of the electron) is much larger than the proton.

There is a similar situation in the gravitational attraction of the Sun and the Earth. In this case what prevents the Earth from falling into the Sun is the Earth's motion with respect to the Sun. The Earth orbits the Sun. Therefore, it is natural to propose that in the Hydrogen atom the electron is orbitting the proton, the electromagnetic force taking the place of the gravitational force in the planetary system. This is known as Rutherford's model of the atom.

Problems ?

Unfortunately, there is a major problem with this interpretation.

Although the electromagnetic and gravitational forces are in many ways similar there are significant differences. Specifically, when objects having electric charge experience acceleration they lose energy (in the form of electromagnetic radiation). The gravitational force has no such property.

Particles moving in orbits are undergoing circular motion. A particle undergoing circular motion has a continuously changing velocity. A particle with a continuously changing velocity is being accelerated. Therefore the orbitting electron feels an acceleration and must lose (radiate) energy. As a result of losing energy the electron will gradually spiral down onto the proton. Calculations indicate that this "gradual" spiral would take a fraction of a second.
Therefore, atoms as we know them should not exist. But they do !!!

Resolving the paradox

The paradox is resolved by the introduction of "New Physics" known as Quantum Mechanics .

Orbits are a term which only make sense in a deterministic framework (Classical Phyiscs); as we have seen, in quantum mechanics we can only predict probablilities, which means the electron moving around the Hydrogen nucleus does not orbit and the radiation problem "magically" dissappears.

But if the electron doesn't orbit around the Hydrogen nucleus, what does it do ? Quantum mechanically we cannot answer this question, all we can say is that there is a certain (calculable) probability that the electron will be at a particular place at a particular time.

The location of the electron is represented by a "cloud" surrouding the nucleus.

becomes

Quantum mechanically, electrons (or more specifically atoms) radiate energy when performing a transition from one state to another. This is the origin of the characteristic spectral lines emitted by excited gases which we will discuss in more detail later.

What about the nucleus ?

The nucleus of an atom contains positively charged protons and neutral neutrons. Coulomb's law tells us that the protons should repel each other. Why then do the protons stay confined within a nucleus ?

Perhaps they are held together by their gravitational attraction ? Unfortunately the gravitational attraction between two protons is one trillion trillion trillion (10^-36) times smaller than the electric repulsion.

The answer is that there is a "new" force involved, the nuclear force (also known as the strong force).

The nuclear force acts on protons and neutrons and is universally attractive (protons and neutrons differ only in their electric charge which the nuclear force does not " see"). The strength of the nuclear force is about 100 times that of the electromagnetic repulsion between two protons, thus causing the atomic nucleus to stay together.

The nuclear force is actually a result of the strong force between the quarks within protons and neutrons. In fact any particles containing quarks will interact via the nuclear/strong force. Electrons do not contain quarks, therefore electrons do not "feel" the nuclear force.

Since the nuclear force is so much stronger than the electromagnetic force, why are we not aware of its existence in our daily experience ?
The answer lies in its "range".

The electromagnetic force is governed by Coulomb's law; it has an inverse square dependence on the distance from the charged particle. The larger the separation of two charges the smaller the force between them, but no matter how far apart the charges are there is always a force. That is, the electromagnetic force has an infinite range.

The nuclear/strong force cannot be described by a simple algebraic expression like Coulomb's law, but one of its properties is that of finite range. Two protons separated by more than about the size of an atomic nucleus (10^-15m) do not "feel" the nuclear force. At scales larger than this we see no direct evidence of the existence of the nuclear/strong force.

Further discussion of the nuclear/strong force and the elementary building blocks of nature is beyond the scope of this course. If you are interested in learning more a good starting point is the " Particle Adventure " presented by the Particle Data Group of the Lawrence Berkeley National Laboratory. Research into elementary particle physics (also known as high energy physics) is ongoing in the Physics Department at UofL.

"To understand something means to derive it from quantum mechanics, which nobody understands."
Proverbial among physicists

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu