Read the Bohr Model Before Ranking Spectral Lines
Bohr-model questions reduce to one formula, applied carefully: Eₙ is proportional to -Z²/n², so every energy, radius or wavelength comparison is really a comparison of Z²/n² across two states.
Chemistry questions first require the material, particles or reaction condition to be identified before a formula or rule is selected.
Separate the nucleus from the electron shell
Nucleus identifies the element · outer shell sets valency
Protons and neutrons are in the nucleus; electrons occupy shells. Atomic number identifies the element, while valency concerns outer-shell electrons.
Comparing transitions across hydrogen-like ions
For matching transition energies across H and a hydrogen-like ion like He+, equate Z²(1/n1² − 1/n2²) for each species rather than computing each energy separately and comparing — this avoids compounding rounding error.
Wavelength ratios need the energy difference, not the energy itself
A wavelength ratio between two electronic transitions comes from inverting the ratio of their (1/n1² − 1/n2²) energy terms — longer wavelength always means the smaller energy gap, which is the lowest-energy transition among the options, not necessarily the one with the largest n.
Line spectra are a fingerprint, not a headcount
Each element's line spectrum is unique, but the number of lines observed depends on which transitions are populated and resolvable — it is not simply equal to the number of electrons in the atom.
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- ✓Eₙ ∝ −Z²/n² — every Bohr-model comparison reduces to comparing this ratio across states.
- ✓Match transition energies across different hydrogen-like species by equating Z²(1/n1² − 1/n2²), not by computing and rounding each energy separately.
- ✓Longer wavelength = smaller energy gap between the two levels involved.
- ✓The number of spectral lines is not the number of electrons in the atom — it depends on which transitions actually occur.
Don't assume more electrons automatically means more spectral lines — line count depends on which transitions are populated, not on electron count.
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