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Modern Physics
Modern Physics

Hydrogen-like Atom Energy

En=−13.6 eV×Z2n2E_n = -13.6\text{ eV} \times \frac{Z^2}{n^2}

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

E_n
Energy of level n
eV
Z
Atomic number (nuclear charge)
unitless
n
Principal quantum number
unitless

Derivation

Extended from Bohr model by accounting for nuclear charge Z in the Coulomb potential.

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Common questions

What is the Hydrogen-like Atom Energy formula?

Hydrogen-like Atom Energy is written Eₙ = -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 Eₙ = -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 Eₙ = -13.6 eV ×Z²/n².