Hydrogen-like Atom

A hydrogen-like atom or ion has one nucleus and exactly one bound electron, with nuclear Coulomb attraction governing its leading structure.

Version

v1 · 2026-10-07 · History

Domain-specific #

13907

Domain group

Natural Sciences

Origin domain

Physics

Subdomain

Atomic Physics → Physics

Core Idea

A hydrogen-like atom is a whole atom or atomic ion with one nucleus and exactly one bound electron. Attraction between that nucleus and electron is the dominant binding interaction. Neutral hydrogen (H I) and singly ionized helium (He II) both meet this test, even though their nuclei, masses and net charges differ. They are two carriers of one basic mechanism, not two different mechanisms.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

A simple Bohr formula describes the leading level pattern: \(E_n=-Z^2/n^2\) in Rydberg units appropriate to the nuclear mass. The formula is a model, not the physical atom and not an exact value for every measured or tabulated level.[^ref-0bbfc7ac0718]

Scope of Application

The class includes neutral H I and one-electron ions such as He II. For any proposed member, identify its atomic nucleus, count all its bound electrons, and ask whether nuclear Coulomb attraction dominates the one-electron bound-state problem. \(Z\), isotope and net charge may differ. An atom with only one outer electron but additional core electrons fails the whole-species count.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

Detailed spectral claims need more care than class membership. NIST's He II level data include theoretical and evaluated values, so appearing in the table does not mean every entry was directly observed. NIST's familiar 21-cm hyperfine example concerns ordinary hydrogen-1 and its proton–electron magnetic moments; it is not a universal line for hydrogen-like ions.[^{ref-9688428ceb9b][}ref-0bbfc7ac0718]

Clarity

Keep three questions separate: Is the species hydrogen-like? What does the leading model predict? What does a particular source report about its levels? The first question concerns a physical one-nucleus, one-bound-electron carrier. The second uses an approximation with stated units. The third depends on observed, calculated or evaluated data and may include fine, relativistic or Lamb-shift corrections.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

This separates a strict member from an alkali near miss. An alkali can have one valence electron with approximately hydrogenic labels, while its filled inner shells make the whole atom multielectron and introduce core effects and quantum defects.[^ref-0bbfc7ac0718]

Manages Complexity

The nucleus–one-electron–Coulomb test sorts many species before their detailed spectra are compared. Within the class, nuclear charge \(Z\) and the appropriate mass scale organize a leading energy comparison. This saves the reader from treating every isotope, charge state or level as a new atomic kind, while leaving room for the corrections needed by a precise question.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

Abstract Reasoning

1. Count the whole species' bound electrons, not just its outer electrons.
2. Identify the atomic nucleus and dominant attraction to the sole electron.
3. State the member's \(Z\), nuclear-mass context and net charge before comparing it with another member.
4. Use the Bohr expression for a leading model; for a specific level or line, consult its source and correction provenance. Do not carry hydrogen-1's 21-cm example over to He II.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

Knowledge Transfer

The same membership test works for H I and He II despite their different nuclear charges and neutral versus positive charge states. The test transfers within atomic physics. A one-particle central-force equation elsewhere may be analogous, but without an atomic nucleus and exactly one bound electron it is not another hydrogen-like atom under this entry.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

Example

H I. The single atomic nucleus has \(Z=1\); exactly one electron is bound to it; and nucleus–electron Coulomb attraction dominates the leading level structure. H I is neutral. The 21-cm hyperfine line belongs to the specific hydrogen-1 isotope example, not to the membership test. Mapped back: nucleus, complete one-electron inventory, and dominant binding all appear.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

He II. A helium nucleus has \(Z=2\); first ionization leaves exactly one bound electron; and the same nucleus–electron Coulomb attraction supplies the leading one-electron problem. He II has positive net charge and a different nuclear-mass context. Its NIST levels include theoretical and evaluated data, rather than being uniformly direct observations. Mapped back: the same three required roles recur in a different ionic carrier, without importing the hydrogen-1 hyperfine line.[^{ref-0bbfc7ac0718][}ref-9688428ceb9b]

Neighborhood in Abstraction Space

Hydrogen-like Atom sits in a sparse region of the domain-specific corpus (97^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Molecular & Atomic Electronic Structure (12 abstractions)

Nearest neighbors

• Molecular Hamiltonian — 0.78
• Mirror nuclei — 0.77
• Relativistic quantum chemistry — 0.77
• Periodic Trends — 0.77
• Fukui function — 0.76

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

• An alkali atom with one valence electron: it has additional bound core electrons, so the whole atom fails the strict count.[^ref-0bbfc7ac0718]
• The Bohr model: its leading \(-Z^2/n^2\) rule is a representation in nuclear-mass Rydberg units, not the atom or its complete observed spectrum.[^ref-0bbfc7ac0718]
• A spectral table or spectroscopy method: those describe or study atoms; the physical carrier is not itself a table, model or method.[^ref-9688428ceb9b]
• A presumed universal 21-cm line: NIST's cited hyperfine example is specific to ordinary hydrogen-1.[^ref-0bbfc7ac0718]

References

[^ref-0bbfc7ac0718]: W. C. Martin and W. L. Wiese, Atomic Spectroscopy A Compendium of Basic Ideas, Notation, Data, and Formulas, National Institute of Standards and Technology. The official title prints a colon after “Spectroscopy”; it is omitted only from the linked title for work-ID parsing. Full authoritative text: §4, “Hydrogen and Hydrogen-like Ions,” and §5, “Alkalis and Alkali-like Spectra”; §13, “Term Series, Quantum Defects, and Spectral-line Series,” Eq. 10–11. §4 gives dominant Coulomb interaction, the ^1H 21-cm hyperfine example, spin-orbit and Lamb separations; §13 gives the leading \(-Z^2/n^2\) value in the Rydberg for the appropriate nuclear mass. The NIST page names Martin and Wiese as authors; no publication year is asserted here. [^ref-9688428ceb9b]: A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (2024), NIST Atomic Spectra Database. DOI: https://doi.org/10.18434/T4W30F. Version 5.12, National Institute of Standards and Technology; official H I levels and He II levels, accessed 6 October 2026. The outputs label H I as \(Z=1\) and He II as \(Z=2\) in the H-isoelectronic sequence. The He II primary-data note reports theoretical Erickson and Yerokhin–Shabaev values, scaling and additional evaluation; do not treat its level table as uniformly direct observation.