Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- The system is the atom: electron plus nucleus. A change of state is a change in their interaction energy.
- Energy levels are negative because zero is set at “electron free and at rest”. The ground state (n = 1) is the lowest.
- Absorption: a photon whose energy equals a gap lifts the atom to a higher state.
- Emission: an excited atom drops spontaneously to a lower state and emits one photon equal to the gap.
- One transition gives one frequency and one wavelength, so atoms give line spectra.
- Emission spectrum: bright lines from a hot, low-density gas. Absorption spectrum: dark lines in a continuous spectrum after it passes through a cooler gas.
- Each element has its own levels, so its own lines. Emission spectra identify elements in a source; absorption spectra identify elements in a gas the light crossed.
- Binding energy = energy to free the electron from a given state. Largest from the ground state.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| E_photon = |E_upper − E_lower| | energies in eV or J | find the photon for a transition |
| E = hf = hc/λ | h = 6.63 × 10⁻³⁴ J·s = 4.14 × 10⁻¹⁵ eV·s | link photon energy, frequency and wavelength |
| λ (nm) ≈ 1240 ÷ E (eV) | hc ≈ 1.24 × 10³ eV·nm | convert quickly |
| 1 eV = 1.60 × 10⁻¹⁹ J | change units | |
| Binding energy from level n = 0 − E_n | eV | find the minimum ionizing energy |
| K_electron = E_photon − binding energy | eV | find the energy of the freed electron |
| Number of lines from N levels = N(N − 1)/2 | count possible emission lines |
Assumptions behind the numbers
- Energy level diagrams are for atoms with one electron only.
- A cool gas has almost all atoms in the ground state, so it absorbs only transitions that start at n = 1.
- Each photon interacts with one atom; energy is conserved in each event.
Mistakes to avoid
- Absorbing a photon with “enough” energy. For a bound-to-bound jump the energy must match a gap exactly.
- Forgetting ionization. Any photon at or above the binding energy can free the electron.
- Inverting the wavelength link. Larger gap → higher f → shorter λ.
- Expecting identical emission and absorption line sets. A cool gas shows fewer absorption lines.
- Thinking dark lines contain no light at all. Re-emitted light goes in all directions, so the beam is only much weaker there.
- Naming an element from one line. Check the whole pattern.
Quick self-check
- What is the wavelength of a 4.0 eV photon? (About 310 nm, ultraviolet)
- An atom has levels at −6.0 eV and −2.5 eV. What wavelength does it emit when it drops between them? (Gap 3.5 eV, so about 354 nm)
- A single-electron atom has five levels. How many emission lines can it produce? (5 × 4 ÷ 2 = 10)
- Which state needs the most energy to ionize? (The ground state)
Next: practice questions.