Ritz's combination principle

Article By:

Gerjuoy, Edward Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania.

Last reviewed:August 2020

DOI:https://doi.org/10.1036/1097-8542.590900

The empirical rule, formulated by W. Ritz in 1905, that sums and differences of the frequencies of spectral lines often equal other observed frequencies. The rule is an immediate consequence of the quantum-mechanical formula h f = E_i − E_f relating the energy h f of an emitted photon to the initial energy E_i and final energy E_f of the radiating system; h is Planck's constant and f is the frequency of the emitted light. For example, the illustration shows the photon energies h f₃₂, h f₃₁, h f₃₀ associated with transitions from level 3 to lower-lying levels, and so on. Level 3 may radiate directly to the ground state 0, emitting f₃₀, or it may first make a transition to level 2, which subsequently radiates to the ground state, and so on. Since the total energy emitted in these two alternative means of making transitions from 3 to 0 is exactly the same, namely E₃ − E₀, it follows that h f₃₀ = h f₃₂ + h f₂₀. Similarly, h f₃₀ = h f₃₂ + h f₂₁ + h f₁₀, and so forth. See also: Atomic structure and spectra; Energy level (quantum mechanics); Quantum mechanics

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