Rydberg Atom

A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number. These atoms have a number of peculiar properties including an exaggerated response to electric and magnetic fields, long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons about the nuclei. The core electrons shield the outer electron from the electric field of the nucleus such that, from a distance, the electric potential looks identical to that experienced by the electron in a hydrogen atom.

In spite of its shortcomings, the Bohr model of the atom is useful in explaining these properties. Classically an electron in a circular orbit of radius r, about a hydrogen nucleus of charge +e, obeys Newton's second law:

where k = 1/(4πε₀).

Orbital momentum is quantized in units of ħ:

.

Combining these two equations leads to Bohr's expression for the orbital radius in terms of the principal quantum number, n:

It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as n2 (the n = 137 state of hydrogen has an atomic radius ~1 µm) and the geometric cross-section as n4. Thus Rydberg atoms are extremely large with loosely bound valence electrons, easily perturbed or ionized by collisions or external fields.

Because the binding energy of a Rydberg electron is proportional to 1/r and hence falls off like 1/n2, the energy level spacing falls off like 1/n3 leading to ever more closely spaced levels converging on the first ionization energy. These closely spaced Rydberg states form what is commonly referred to as the Rydberg series. Figure 1 shows some of the energy levels of the lowest three values of orbital angular momentum in lithium.