Quantum Defect in Rydberg Atoms
The quantum defect of a Rydberg atom refers to a correction applied to the equations governing Rydberg atom behavior to take into account the fact that the inner electrons do not entirely screen their associated charge in the nucleus. It is used particularly for the alkalis that contain a single electron in their outer shell.
The perfect 1/r potential in the hydrogen atom leads to an electron binding energy given by
- ,
where R is the Rydberg constant, h is Planck's constant, c is the speed of light and n is the principal quantum number.
For multi-electron atoms in Rydberg states with a low value of the orbital angular momentum, there is a high probability of finding the excited electron near the nucleus where it can polarize or even penetrate the ion core, modifying the potential. The resulting shift of the energy levels is represented mathematically as an angular momentum dependent quantum defect, δl:
- .
The largest shifts occur when the orbital angular momentum is equal to 0 (normally labelled 's') and these are shown in the table for the alkali metals:
| Element | Configuration | n* | δs |
|---|---|---|---|
| Li | 2s | 1.59 | 0.41 |
| Na | 3s | 1.63 | 1.37 |
| K | 4s | 1.77 | 2.23 |
| Rb | 5s | 1.81 | 3.19 |
| Cs | 6s | 1.87 | 4.13 |
Read more about this topic: Quantum Defect
Famous quotes containing the words quantum, defect and/or atoms:
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“Well, I had gone and spoiled it again, made another mistake. A double one in fact. There were plenty of ways to get rid of that officer by some simple and plausible device, but no, I must pick out a picturesque one; it is the crying defect of my character.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“No imperfection in budded mountain,
Valleys breathe, heaven and earth move together,
daisies push inches of yellow air, vegetables tremble,
green atoms shimmer in grassy mandalas,
sheep speckle the mountainside, revolving their jaws with empty eyes,
horses dance in the warm rain,”
—Allen Ginsberg (b. 1926)