Physics › Quantum phenomena › Energy levels and photon emission
Energy levels and photon emission
Heated gases refuse to glow with a rainbow. They emit a few sharp colours and nothing between, and that pattern of lines is direct evidence that the energy inside an atom comes in fixed rungs.
Builds on Collisions of electrons with atoms.
IN THIS TOPIC
- Interpret line spectra as evidence for transitions between discrete energy levels.
- Use hf = E1 − E2 for photon emission, with levels quoted in J or eV.
- Explain why each element's line spectrum is unique.
WHAT YOU PROBABLY THINK
An atom can emit any colour it likes.
The evidence: lines, not rainbows
Pass the light from a glowing gas, hydrogen in a discharge tube say, through a diffraction grating and the result is not a continuous rainbow but a line spectrum: a handful of sharp, bright colours with darkness between.
Each line is light of one photon energy, so the atom is evidently emitting only certain exact energies. The inescapable conclusion: the electron's possible energies inside the atom are discrete levels, and light is emitted only when an electron drops from one to another.
The transition equation
When an electron falls from a level of energy E1 to a lower level E2, the atom emits one photon carrying exactly the difference:
Level diagrams quote energies as negative numbers, measured down from zero at ionisation: a bound electron sits in an energy debt, and the ground state is the deepest rung. The subtraction in hf = E1 − E2 handles the signs by itself, always delivering a positive photon energy. Questions quote levels in J or in eV, so the conversion habit from the last lesson is on duty throughout.
Fingerprints
Every element has its own set of levels, so every element has its own set of gaps, so every element emits its own set of lines. A spectrum identifies an element as surely as a fingerprint identifies a person, which is how astronomers read the composition of a star they will never touch: the starlight carries the atomic barcodes of everything burning in it.
The same levels absorb as they emit. White light shone through a cool gas comes out missing exactly the frequencies the gas would emit, a barcode of dark lines at the same positions.
THE EXAM BIT
- “Explain how line spectra provide evidence for energy levels” wants the full chain: sharp lines mean only certain photon energies, photon energy equals a level difference, therefore the levels themselves are discrete.
- One transition, one photon, carrying exactly the gap. Two small drops make two photons, never one photon of the combined energy.
- Level energies are negative; the ground state is the most negative. “Lowest level” means deepest in the well, not smallest in magnitude.
- hf = E1 − E2 with the levels in joules before h gets involved. Substituting eV straight into hf is the unit slip this topic exists to punish.
- The bigger the gap, the higher the frequency: transitions to the ground state give the most energetic photons, often ultraviolet.
CHECK YOURSELF
In hydrogen, an electron falls from the −3.4 eV level to the −13.6 eV ground state. Find the frequency of the emitted photon. (h = 6.63 × 10−34 J s.)
Show a hint
Gap first, in eV; then joules; then h.
Show the answer
Gap: E1 - E2 = (−3.4) − (−13.6) = 10.2 eV. The signs take care of themselves.
In joules: 10.2 × 1.60 × 10−19 = 1.63 × 10−18 J.
Frequency: f = E/h = 1.63 × 10−18 / 6.63 × 10−34 = 2.5 × 1015 Hz, in the ultraviolet, as a drop to the ground state usually is.
Discrete lines, discrete gaps, discrete levels.
One transition makes one photon.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.