Short on time? This page is the recap. For explanations, a diagram and worked examples, use the full study guide.
Recap
- Light comes in photons. Each photon’s energy depends only on its frequency.
- Absorbing a photon raises the energy of an atom or molecule by exactly the photon’s energy. Emitting a photon lowers it by exactly that amount.
- Photon energy = difference between two levels: E(photon) = E(upper) − E(lower).
- Only photons whose energy matches a gap are absorbed or emitted, so spectra show sharp lines.
- Brightness = number of photons. It does not change the energy of each photon.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| c = λν | c = 2.998 × 10⁸ m s⁻¹; λ in m; ν in s⁻¹ (Hz) | convert between wavelength and frequency |
| E = hν | E in J per photon; h = 6.626 × 10⁻³⁴ J s | find the energy of one photon from its frequency |
| E = hc/λ | λ in m | go straight from wavelength to energy |
| E(per mol) = E(per photon) × N_A | N_A = 6.022 × 10²³ mol⁻¹; ÷ 1000 for kJ | compare with bond energies in kJ mol⁻¹ |
Proportions: λ and ν are inversely proportional; E and ν are directly proportional; E and λ are inversely proportional.
Assumptions behind the numbers
- The light travels at c, its speed in a vacuum (air changes it by less than 0.1%, too little to matter here).
- Each absorption or emission involves one photon and one atom or molecule.
- The energy levels are fixed values, so each gap gives one sharp wavelength.
Mistakes to avoid
- Not converting nm to m. 1 nm = 10⁻⁹ m. Do it first.
- Per photon vs per mole. E = hν is per photon; multiply by N_A for per mole.
- Forgetting J → kJ. Divide by 1000 at the end.
- Using the level energy instead of the gap. Always subtract: upper − lower.
- Negative photon energy. If you get one, you subtracted the wrong way round.
- Thinking brighter light can reach a bigger gap. One photon, one transition: energy per photon decides.
Quick self-check
- What is the frequency of light with λ = 5.00 × 10⁻⁷ m? (6.00 × 10¹⁴ s⁻¹)
- What is the energy of one photon of frequency 1.00 × 10¹⁵ s⁻¹? (6.63 × 10⁻¹⁹ J)
- An atom drops from a level at −3.0 × 10⁻¹⁹ J to one at −7.0 × 10⁻¹⁹ J. What is the energy of the emitted photon? (4.0 × 10⁻¹⁹ J)
Next: practice questions.