Hydrogen Atom

"The physicists have known sin; and this is a knowledge which they cannot lose"
J. Robert Oppenheimer

In order to provide a full theoretical description of the Hydrogen atom (or any other atom) we must use Quantum Mechanics. However, before quantum mechanics was fully developed the Danish physicist Niels Bohr proposed a model of the Hydrogen atom which relied primarily on classical ideas. This "Bohr model" was successful in describing some of the basic properties of the Hydrogen atom.

The Bohr model assumes that the Hydrogen atom electron moves in cirular orbits about the proton, but that only orbits of particular radii, r_n are allowed where,

r₁ is the radius of the smallest allowed orbit and n can take on integer values and is called the principal quantum number . The value of r₁ is 5.3 x 10^-11 m (called the Bohr radius) and provides a measure of the size of the Hydrogen atom.

The fact that only orbits of particular radii are allowed seems strange when compared to a "planetary" system; there is nothing special about the distance at which the earth orbits the sun, it could easily be somewhat smaller or larger. But we have already seen one situation where an apparently continuous variable is constrained to have only certain values. The standing wave patterns on a stretched string allow only certain frequencies of vibration.

The deBroglie wavelength of the Hydrogen electron in the smallest radius orbit is equal to the circumference of that orbit (both about 3.3 x 10^-10 m). The electron can be thought of as behaving in a similar manner to the stretched string which exhibits a standing wave pattern. Only orbits with a circumference equal to an integer multiple of electron wavelengths will be allowed.

Why did the chicken cross the road ?
Albert Einstein: "Whether the chicken crossed the road or the road moved beneath the chicken depends on your frame of reference."

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