Rydberg atom

A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number, n.^[1][2] The higher the value of n, the farther the electron is from the nucleus, on average. Rydberg atoms have a number of peculiar properties including an exaggerated response to electric and magnetic fields,^[3] long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons about the nuclei.^[4] 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.^[5]

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:

${\displaystyle \mathbf {F} =m\mathbf {a} \Rightarrow {ke^{2} \over r^{2}}={mv^{2} \over r}}$

where k = 1/(4πε₀).

Orbital momentum is quantized in units of ħ:

${\displaystyle mvr=n\hbar }$.

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

${\displaystyle r={n^{2}\hbar ^{2} \over ke^{2}m}.}$

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 2 shows some of the energy levels of the lowest three values of orbital angular momentum in lithium.