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CHEM 121 Studioby Learn4Less · UBC CHEM 121

CHEM 121 glossary

One-electron species

An atom or ion with a single electron (H\ce{H}, HeX+\ce{He+}, LiX2+\ce{Li^2+}, …). Its levels follow En=−Z2RH/n2E_n = -Z^2R_H/n^2 exactly, so every energy and line position scales with Z2Z^2 compared with hydrogen.

Energy levels of the He⁺ ionn = 1: −8.72 × 10⁻¹⁸ J; n = 2: −2.18 × 10⁻¹⁸ J; n = 3: −9.68 × 10⁻¹⁹ J; n = 4: −5.45 × 10⁻¹⁹ J.n = ∞0 Jn = 1−8.72 × 10⁻¹⁸ Jn = 2−2.18 × 10⁻¹⁸ Jn = 3−9.68 × 10⁻¹⁹ Jn = 4−5.45 × 10⁻¹⁹ J

HeX+\ce{He+}: every level is 4 times deeper than hydrogen's.

Example

HeX+\ce{He+} (Z=2Z = 2), 2→12 \to 1: 1/λ=4(1.097×107)(34)1/\lambda = 4(1.097\times10^{7})(\tfrac{3}{4}), so λ=30.4\lambda = 30.4 nm, a quarter of hydrogen's 122 nm.

See alsoRydberg equationEnergy levelEffective nuclear charge