An electron in an atom can sit only at fixed energy levels. When it drops between them, it emits a photon of an exact energy, producing the sharp bright lines of a line spectrum.
Electrons in an isolated atom occupy discrete energy levels (negative, because they are bound). A jump down emits a photon and a jump up absorbs one, with hf = E₁ − E₂. Because only fixed energy gaps are allowed, only certain photon energies appear, giving a line spectrum rather than a continuous one.
Choose two hydrogen levels and watch the photon. Drop an electron to n = 2 from a higher level and you land on the visible Balmer lines; read the wavelength straight off the spectrum. Switch to absorption and the same energy is taken in.
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Energy levels are negative, so always take the difference carefully: the gap is E₁ − E₂ with E₁ the higher (less negative) level. Convert the gap from eV to joules before using hf or hc/λ. A line spectrum is itself the evidence that the levels are discrete.
Four quick checks on energy levels and line spectra. Each correct answer earns XP and lights this skill on your star map.
The existence of a line spectrum is evidence that atomic energy levels are:
When an electron moves from a higher to a lower energy level, the atom:
The energy of the photon emitted in a transition between two levels is:
An absorption line spectrum appears as:
The bright emission lines and the dark absorption lines of an element lie at exactly the same wavelengths, because both correspond to the same set of energy gaps. To find a wavelength, work out the gap in joules, then use λ = hc/ΔE.
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