How this calculator works
The photon carries the magnitude of the difference between the final and initial atomic energies. A falling atomic energy emits a photon; a rising energy requires absorption. Negative bound-state energies are valid. This energy-bookkeeping tool accepts supplied levels rather than assuming every number is an allowed Bohr orbit. Use the hydrogen energy-level tool to obtain ideal one-electron levels. Recoil, linewidth and selection rules are outside this calculation. Planck constant and light speed use CODATA 2018.
Formula
Delta E = Efinal - Einitial; photon energy = |Delta E|; f = |Delta E|/h; lambda = c/f. Energy inputs are in eV, with 1 eV = 1.602176634e-19 J.
Worked example
A transition from -3 eV to -5 eV releases 2 eV. Its frequency is 4.835978484e14 Hz and its vacuum wavelength is about 619.921 nm.
Frequently asked questions
Why are the energies negative?
The zero can be the separated electron and nucleus. A bound electron then has negative energy.
Can I calculate absorption?
Yes. A final energy above the initial energy gives a positive atomic change and an absorbed photon.
Does this prove a transition is allowed?
No. An actual spectrum also depends on quantum selection rules, recoil and the atomic structure.