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Hydrogen-like ions
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Energy scales as Z².
Ions with one electron (He⁺, Li²⁺) have E_n = −13.6 Z²/n² eV and radii a₀n²/Z; spectral lines shift to shorter wavelength.
He⁺ ground state: −54.4 eV.
Applies only to single-electron ions.
In more detail
Hydrogen-like ions have one electron, such as He⁺ or Li²⁺, and their energy levels scale with the square of the nuclear charge. They are used to test quantum theory.
Real-world uses
- Hydrogen-like ions are used in astrophysical spectroscopy.
- They provide precise tests of quantum electrodynamics.
- Astrophysicists study hydrogen-like ions in hot plasmas, where the energies scale strongly with nuclear charge.
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Frequently asked questions
How do their energies compare with hydrogen?
They scale with Z squared, so they are more tightly bound.
Why are they useful?
They are simpler than multi-electron atoms, giving clearer tests of theory.
Why does the energy depend on Z squared?
A higher nuclear charge pulls the electron more strongly, so its binding energy grows with the square of Z.
Related topics in Atomic & Nuclear Physics
Nuclear magnetic resonance · Mössbauer effect · Nuclear waste · Positronium · Muonic atoms · Atomic clocks