Rydberg state

A Rydberg state (after the Swedish physicist Johannes Rydberg ) is a quantum mechanical state of an atom , ion or molecule in which the outermost electron is significantly further away from the center than in the ground state . An atom in such a state is called a Rydberg atom and is well described in the simplest quantum mechanical approach to the hydrogen problem.

In accordance with the correspondence principle , the quantum mechanical description of the Rydberg atom changes to the classical description for large quantum numbers . In fact, the electron can be treated here to a good approximation as a classical particle , as it is based on the Bohr atomic model or the Bohr-Sommerfeld atomic model .

Due to their large size compared to ordinary atoms and the large number of closely spaced or (almost) degenerate energy levels , Rydberg atoms are particularly sensitive to electrical and magnetic fields. For example, a Rydberg atom that flies through a mirrored cavity with a single photon trapped in it shows changes in its wave function. This z. B. the presence of the photon can be detected without influencing it further (so-called quantum non demolition measurement). Serge Haroche and David Wineland received the Nobel Prize in Physics in 2012 for the development of experimental methods based on this, with an otherwise unmatched sensitivity and accuracy .

Mark

One speaks of the Rydberg state when an atom or molecule is excited in such a way that an electron has a principal quantum number that is far above the maximum value that occurs in atoms in the ground state . If the electron also has a correspondingly high angular momentum (maximum angular momentum quantum number ), its probability of being in the vicinity of the nucleus and possibly the other electrons of the atom is very low, so that together they act very precisely like a single point charge and other subtleties of the interactions with the nucleus and the other electrons play a very minor role. Therefore, the Rydberg states of all types of atoms correspond very precisely to the simple relationships in the hydrogen atom . In particular, the energy is well given and degenerate with regard to the orbital angular momentum . ${\ displaystyle n}$ ${\ displaystyle n {\ mathord {=}} 7}$ ${\ displaystyle l {\ mathord {=}} n {\ mathord {-}} 1}$ ${\ displaystyle E_ {n} {\ mathord {=}} - {\ tfrac {13.6 \, eV} {n ^ {2}}}}$ ${\ displaystyle l {\ mathord {=}} 0.1, \ ldots, n {\ mathord {-}} 1}$

The energy of an electron in a Rydberg state is only insignificantly below the vacuum level and is therefore much higher than the energy of electrons further inside, which have a higher binding energy . But this also means that the corresponding electron can be separated ( ionized ) from the atom very easily .

These high energy levels can be occupied by electronic excitation (e.g. with radiation of a suitable wavelength ). Rydberg states can also arise when an ion traps an electron, for example when the ion comes close to a surface and an electron passes from there to the ion.

In the Rydberg state of a molecule, the outermost electron is in a molecular orbital , which is made up of atomic orbitals that do not belong to the valence shell of the molecule.

Proportions

For electrons in Rydberg states far from the nucleus, many properties can be described by classical physics or in Bohr's atomic model . Therefore the following applies to the distance between protons and electrons for a Rydberg hydrogen atom :

{\ displaystyle r_ {n} = n ^ {2} \ cdot a_ {0} = n ^ {2} \ cdot {\ frac {4 \ pi \ varepsilon _ {0} \ hbar ^ {2}} {m_ { e} e ^ {2}}} = n ^ {2} \ times 52 {,} 9 \ times 10 ^ {- 12} \, \ mathrm {m}}

with Bohr's atomic radius . ${\ displaystyle a_ {0}}$

This makes Rydberg atoms very large, e.g. B. for : ${\ displaystyle n = 100}$

{\ displaystyle r_ {100} = 10 ^ {4} \ cdot a_ {0} = 0 {,} 529 \ cdot 10 ^ {- 6} \, \ mathrm {m}.}

The largest quantum numbers achieved are with atomic diameters of around 25 micrometers. ${\ displaystyle n \ approx 500}$

Binding energies

The further away the electron is from the proton , the weaker it is bound or the smaller the required separation energy : ${\ displaystyle E_ {n}}$

{\ displaystyle E_ {n} = - \, {\ frac {E_ {R}} {n ^ {2}}} = - \, {\ frac {13 {,} 6 \ \ mathrm {eV}} {n ^ {2}}}}

with the Rydberg energy ${\ displaystyle E_ {R}.}$

It follows that in already thermal energies sufficient to definitively separate the electron. For this reason, atoms that are so highly excited can only be produced and “stored” in a high vacuum . They arise naturally in the uppermost layers of the earth's atmosphere or that of stars . ${\ displaystyle n = 100}$

Length of stay

Rydberg atoms are classic examples of population inversion because most or even all of the lower states are empty. Especially in the absence of collisions with other atoms and with maximum orbital angular momentum of the electron , the lifetime can be long. The electron can only reduce its orbital angular momentum quantum number by 1 by emitting a photon and therefore has to jump to the next lower shell with the quantum number . Their energy differs so little from that that the emission of the corresponding long-wave photon is severely hindered. Therefore, the spectral lines of Rydberg atoms were first discovered in highly dilute stellar atmospheres or interstellar gases, where the atoms do not collide with another atom for a sufficiently long period of time. ${\ displaystyle l {\ mathord {=}} n {\ mathord {-}} 1}$ ${\ displaystyle n {\ mathord {-}} 1}$ ${\ displaystyle E_ {n-1}}$ ${\ displaystyle E_ {n}}$

example

In the hydrogen atom, the 1s shell is the valence shell. For the molecule, the molecular orbitals and can be constructed from the 1s atomic orbitals of the two atoms . However, such molecular orbitals can also be built up from the vacant 2s, 2p, 3s, ... atomic orbitals in the atom, which are then referred to as Rydberg states. ${\ displaystyle H_ {2}}$ ${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma *}$

Web links

Michael Komma: Circular Rydberg atoms - graphic modeling , status: 2013

Ernst Leitner and Ulrich Finckh: Classical atomic models: Rydberg atoms ( LEIFI ).

F. Camargo et al .: Giant atom takes up neutral neighboring atoms into its shell and binds them . Original article : Creation of Rydberg Polarons in a Bose Gas . In: Physical Review Letters 120, 083401 - February 22, 2018. doi: 10.1103 / PhysRevLett.120.083401 .

Nikola Šibalić and Charles S Adams: Rydberg Physics , IOP Publishing (2018)

literature

H.Dittmar-Ilgen: Generation and manipulation of classical electron orbitals; Naturwissenschaftliche Rundschau 4/2006, p. 206 (H. Maeda; Science 307, 1757 (2005))