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Hydrogen-like species: wavelength ratio, atomic number and ionic charge

Build a hydrogen-like ion proton by proton, fire tuned photons at it and watch the electron jump, hunt the pair of atomic numbers that makes one wavelength exactly nine times the other, then count the particles to turn Z into the ionic charge.

Sub-topics covered

• Hydrogen-like species and the one-electron condition
• Energy levels and the Z-squared scaling
• Absorption and emission transitions
• Rydberg equation and the ratio of two wavelengths
• Wavelength versus photon energy
• Atomic number versus ionic charge

What it teaches

• Hydrogen-like means exactly one electron, not one proton
• The Bohr result E = -13.6 Z^2 / n^2 holds only for a one-electron species
• Dividing two Rydberg equations cancels the constant and the wavelength alike
• Longer wavelength means lower photon energy, never higher
• The charge on a hydrogen-like ion is Z - 1, so the question is one subtraction longer than it looks

Simulation ID

• ADV-2026-P2-CHE-Q10 · revision 1

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