Energy Levels and Line Spectra
An atom holds only certain electron energies, so a jump between two of them emits or absorbs a photon of one exact energy. That is why a hot gas gives bright lines and a cool gas in front of a lamp gives dark ones.
What a learner can do afterwards
- Calculates the wavelength emitted by a jump between two stated levels
- Reads an energy level diagram, including why the levels are given as negative numbers
- Explains an absorption spectrum as the same set of jumps taken the other way
1 · Read
An atom lets its electrons hold only fixed energies, like rungs on a ladder. When an electron drops to a lower rung, the atom emits a photon carrying exactly the gap. A drop from -1.5 eV to -3.4 eV gives a 1.9 eV photon. For its wavelength, turn the gap into joules and use wavelength = h c / E: 1.9 x 1.6e-19 = 3.04e-19 J, and 6.6e-34 x 3.0e8 / 3.04e-19 = 6.5e-7 m, about 650 nm.
Levels are negative because the electron is trapped, and zero is the escape point where it just breaks free. Hydrogen sits deepest at -13.6 eV. Swallowing a 10.2 eV photon lifts the electron to -3.4 eV, since -13.6 plus 10.2 is -3.4.
Absorption is the same jump taken upward. White light passing through a cooler gas loses photons with exactly a gap energy, leaving dark lines. An atom can only climb from a level it is in. Cool hydrogen sits almost all at -13.6 eV, so its dark lines are ultraviolet. In a star's hot outer layers some hydrogen sits at -3.4 eV, and 656 nm light lifts it to the third level.
Read a spectrum like a fingerprint: bright lines from hot gas, dark lines from cooler gas in front of a lamp. Each element owns a unique set of gaps, so its lines name it in stars and lamps.
Electrons jump between fixed levels, and each gap sends or swallows one photon of matching energy.
The rewritten readings were written for this dataset. Practice item x3 adapted from OpenStax College Physics (CC BY 4.0) and x5 from OpenStax Astronomy (CC BY 4.0), openstax.org. Practice items x1, x2 and x4 are original to this dataset.
2 · Watch
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Where it sits
Optional connections
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
13 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.