Transition Combinations and Ritz Principle
Because each photon frequency equals a level-energy difference divided by h, transition frequencies obey the Ritz combination principle. For ordered levels E_A > E_B > E_C, nu_AC = nu_AB + nu_BC.
Why this shows up in the exam
Finding an unknown transition wavelength · Comparing photon momenta · Checking energy-level diagrams
Learn the idea
Atomic transition frequencies combine through energy differences, not by directly adding wavelengths. If A to C equals A to B plus B to C in energy, the same is true for frequencies and wavenumbers. Wavelengths must first be inverted.
🧠 Memory hook: Add gaps as frequencies; invert before handling wavelengths.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- nu_AC = nu_AB + nu_BC — frequency combination for consecutive downward gaps
- 1/lambda_AC = 1/lambda_AB + 1/lambda_BC — vacuum-wavelength form of the same relation
- p_photon = h/lambda — photon momentum for comparing spectral lines
How to approach it
- 1Order the levels by energy
- 2Write the energy-gap identity
- 3Convert wavelength to wavenumber before combining
Common slip-ups that cost marks
- •Adding wavelengths directly
- •Ignoring transition direction
- •Using electron orbital momentum as photon momentum
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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