E.1 · IB Physics
Atomic energy levels and spectra
Electrons in hydrogen occupy discrete energy levels. Choose a transition, release the photon and see where its spectral line falls; tick the box to show every line of that series.
Predict first
Start from the default settings (From level n = 3, To level n = 2). Move To level n down to 1. What happens to the photon's wavelength?
ΔE = 13.6 (1/1² − 1/3²) = 12.1 eV instead of 1.89 eV. Since λ = hc ÷ ΔE, a larger photon energy means a shorter wavelength: about 103 nm instead of 656 nm.
Check it in the model: Drag the To level n slider from 2 to 1 and compare the Wavelength λ readout (656 nm before, 103 nm after).
Top: energy levels in eV (zero at n = ∞). Bottom: spectrum on a logarithmic wavelength scale; the thick line is the chosen transition.
ΔE = 13.6 (1/nf² − 1/ni²) eV = hf = hc/λ
λ = hc ÷ ΔE, hc = 1240 eV nm
f = ΔE × e ÷ h
Try this
- Press "Balmer α (3→2)" then "Lyman (2→1)". Compare ΔE, λ and the region of the spectrum for the two photons.
- Keep "To level" at 2 and raise "From level" from 3 to 7. How do the lines in the series bunch up, and what happens to the photon wavelengths?
- Set the transition to 3→1 and check that its photon energy equals the sum of the energies for 3→2 and 2→1.
Exam tip: a photon from a transition carries exactly ΔE = hf, so a line spectrum is evidence for discrete energy levels; work in eV for ΔE, then convert with λ = hc/ΔE.