For a hydrogen-like ion of nuclear charge Z, the energy levels scale as:

For a hydrogen-like ion of nuclear…

Answer: Z².

A Z²
B Z
C 1/Z
D Z³

Correct answer: A. Z²

Explanation: E<sub>n</sub> = −13.6 Z²/n² eV, so the levels scale as Z².

Comparison of the Thomson model and the Rutherford model of the atom: in the Thomson plum pudding model alpha particles pass almost straight through a diffuse positive sphere, while in the Rutherford model a concentrated central nucleus deflects some alpha particles through large angles, with the lower panels showing the alpha particle source and gold foil and the observed result of wide-angle scattering

The Geiger–Marsden alpha-scattering result: a few alpha particles bounce back at large angles, which rules out Thomson’s diffuse model and demands a tiny, massive, positively charged nucleus. Image: Kurzon, CC BY 3.0, via Wikimedia Commons.

Concept context

Thomson's plum-pudding model, Rutherford's nuclear model from alpha-scattering, Bohr's postulates and hydrogen spectrum, spectral series (Lyman to Pfund), Rydberg formula, and limitations of each model.

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For a hydrogen-like ion of nuclear charge Z, the energy levels scale as:

Concept context

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