Hydrogen-like Atom Energy
Generalized Bohr energy formula for hydrogen-like atoms (single electron). Energy scales with Z² making inner electrons in heavy atoms much more tightly bound.
Variables
Derivation
Extended from Bohr model by accounting for nuclear charge Z in the Coulomb potential.
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- Z = 2 (Atomic number (nuclear charge))
- n = 3 (Principal quantum number)
Result: En = -6.0444444 eV
Where this formula is listed
- Modern Physics formulas, under Atomic Physics, alongside Bohr Radius, Hydrogen Spectrum (Rydberg) and Moseley's Law.
- In the modern physics list it comes after Hydrogen Spectrum (Rydberg) and before Electron Orbital Radius.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Hydrogen-like Atom Energy formula?
Hydrogen-like Atom Energy is written E_n = −13.6 eV × Z²/n². Generalized Bohr energy formula for hydrogen-like atoms (single electron). Energy scales with Z² making inner electrons in heavy atoms much more tightly bound. It belongs to Modern Physics, under Atomic Physics.
What are the units in E_n = −13.6 eV × Z²/n²?
In SI units, E_n is energy of level n, measured in eV; Z is atomic number (nuclear charge) (dimensionless); n is principal quantum number (dimensionless).
How is the Hydrogen-like Atom Energy formula derived?
Extended from Bohr model by accounting for nuclear charge Z in the Coulomb potential. The result is E_n = −13.6 eV × Z²/n².