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The atomic energy-level diagram established in the previous lesson explains not only the line spectra of glowing gases but also a familiar piece of everyday technology — the fluorescent tube. By accelerating electrons through a low-pressure gas and observing the resulting light, physicists in the early 20th century confirmed the existence of discrete energy levels, and electrical engineers in the mid-20th century turned the same physics into one of the most energy-efficient lighting technologies ever developed. This lesson covers the energetics of electron-atom collisions, the distinction between excitation and ionisation, and the detailed physics of the fluorescent tube — placing it in the context of incandescent and LED alternatives.
Specification mapping. This lesson develops AQA A-Level Physics (7408) Particles and Radiation strand, sub-strand 3.2.2.2 (excitation and ionisation by electron impact) and 3.2.2.3 (the fluorescent tube as an application; mercury-vapour excitation, ultraviolet emission, phosphor down-conversion). Refer to the official AQA 7408 specification document for the authoritative wording. The lesson is the closing lesson of the Particles and Radiation strand because it integrates the photon model, the energy-level picture, the electron-impact mechanism and the macroscopic engineering application into a single coherent narrative.
Synoptic links. Three principal synoptic threads run through this content. First, atomic energy levels and line spectra (3.2.2.2, our order 8) — the same quantised energy levels that explain emission/absorption spectra are the targets of electron-impact excitation in fluorescent tubes; mercury's prominent 254 nm UV line is the source of the energy that ultimately becomes visible light. Second, electric current and resistivity (course 5) — the electrons in a fluorescent tube are accelerated by a potential difference, gaining kinetic energy eV that they then deposit in atomic excitations; the connection between electrical energy and atomic-scale energy transfers is direct. Third, the photoelectric effect (3.2.2.1, our order 7) — both the photoelectric effect and electron-impact excitation are quantum-energy-transfer processes, but with energy flowing in opposite directions: photoelectric (photon → electron kinetic energy), electron impact (electron kinetic energy → photon or excited atom).
When a free electron with kinetic energy E_k collides with an atom, three things can happen depending on the relationship between E_k and the atomic energy-level structure:
If E_k is less than the smallest excitation energy of the atom (i.e. less than the energy gap between the ground state and the first excited state), the electron cannot excite the atom. The collision is elastic: the electron bounces off the atom, transferring almost no energy (because the atom is so much more massive than the electron). The atom remains in its ground state.
If E_k is greater than or equal to the energy gap to some excited state (call it E_excitation), the electron can transfer energy E_excitation to the atom, promoting an electron in the atom from the ground state to that excited state. The colliding electron leaves with kinetic energy E_k − E_excitation. The atom is now in an excited state and will return to the ground state by emitting a photon (or a cascade of photons) of total energy E_excitation.
If E_k exceeds the ionisation energy of the atom, the colliding electron can knock an atomic electron entirely free, leaving behind a positive ion. The total energy E_k is shared between (i) the ionisation energy (absorbed by the atom-becoming-ion), (ii) the kinetic energy of the freed atomic electron, and (iii) the kinetic energy of the colliding electron after the collision.
flowchart TD
A["Electron with KE E_k collides with atom"] --> B{"Compare E_k to atomic levels"}
B -->|"E_k < smallest gap"| C["Elastic scattering<br/>(atom unaffected)"]
B -->|"E_k ≥ gap to excited state"| D["Excitation<br/>(electron loses E_excitation,<br/>atom emits photon)"]
B -->|"E_k ≥ ionisation energy"| E["Ionisation<br/>(atom becomes ion,<br/>second electron freed)"]
D --> F["Atom returns to ground state<br/>emitting photon of energy hf = E_excitation"]
Hydrogen has ground state −13.6 eV, first excited state −3.40 eV. Gaps from the ground state:
An electron with kinetic energy:
The first experimental confirmation that atoms have discrete energy levels accessible through electron impact came in 1914 from James Franck and Gustav Hertz, who passed accelerated electrons through low-pressure mercury vapour and measured the current arriving at a collector electrode.
The current I increases steadily with V — until V reaches about 4.9 V, at which point the current drops sharply. As V is increased further, the current rises again, then drops sharply at V ≈ 9.8 V, then rises and drops at V ≈ 14.7 V, and so on. The drops are evenly spaced.
At V = 4.9 V, electrons reaching the grid have kinetic energy 4.9 eV — exactly equal to the energy of the first excited state of mercury above the ground state. They can collide with mercury atoms, transfer 4.9 eV of energy, and emerge with essentially zero kinetic energy — too little to overcome the retarding potential, so the collector current drops. At V = 9.8 V, electrons can excite two mercury atoms (4.9 eV each) before reaching the collector; at V = 14.7 V, three atoms; and so on. The evenly spaced current drops are direct evidence of a discrete atomic energy level at 4.9 eV.
The 1925 Nobel Prize was awarded to Franck and Hertz for this experiment.
An electron is accelerated through a potential difference of 6.0 V and collides with a mercury atom (first excited state 4.9 eV above ground state, ionisation energy 10.4 eV). Can the electron excite the atom? Can it ionise the atom?
Kinetic energy of electron after acceleration: E_k = eV = 1.60 × 10⁻¹⁹ × 6.0 = 9.6 × 10⁻¹⁹ J = 6.0 eV.
The colliding electron can transfer 4.9 eV to the atom (exciting it to the first excited state) and leave with 6.0 − 4.9 = 1.1 eV.
After the excitation in Example 1, the mercury atom returns to its ground state by emitting a photon. Calculate the photon's wavelength.
Photon energy = excitation energy = 4.9 eV = 4.9 × 1.60 × 10⁻¹⁹ = 7.84 × 10⁻¹⁹ J
λ = hc / E = (6.63 × 10⁻³⁴)(3.00 × 10⁸) / (7.84 × 10⁻¹⁹) = 2.54 × 10⁻⁷ m ≈ 254 nm
This is in the ultraviolet — invisible to the human eye. (Approximate value 254 nm corresponds to the established figure for the dominant mercury UV line.)
What is the minimum potential difference needed to ionise mercury from its ground state by electron impact?
E_k(min) = ionisation energy = 10.4 eV
V_min = E / e = 10.4 V
A free electron accelerated through 10.4 V or more has sufficient kinetic energy to ionise mercury.
An electron with 14 eV kinetic energy collides with a mercury atom and ionises it. The freed electron has 1.5 eV of kinetic energy, and the colliding electron has 2.1 eV after the collision. Check energy conservation.
E_k(initial) = 14 eV (incoming electron) E_k(final) = 2.1 eV (incoming electron, after) + 1.5 eV (freed electron) = 3.6 eV Energy absorbed by atom = 14 − 3.6 = 10.4 eV ✓ (this matches the ionisation energy)
An electron with 11.0 eV kinetic energy collides with a hydrogen atom. Which excited states are accessible?
E_k = 11.0 eV. Compare with hydrogen excitation energies:
Only the n = 2 excitation is energetically allowed. After excitation, the atom emits a 10.2 eV (~122 nm UV) photon as it returns to the ground state.
A fluorescent tube is a glass tube containing low-pressure mercury vapour (with some argon) and coated on the inside with a thin layer of phosphor (a fluorescent material). Electrodes at each end provide the electrons; a starter circuit and ballast (modern tubes use electronic ballasts) provide the right voltage and current to sustain the discharge.
Without the phosphor, the tube would emit mostly UV — useless for illumination and harmful to skin and eyes. The phosphor acts as a down-converter: each high-energy UV photon (4.9 eV) is converted to one or more lower-energy visible photons (1.5–3 eV). The energy difference is dissipated as heat.
graph LR
A["Mains voltage<br/>(~230 V)"] --> B["Ballast<br/>(limits current)"]
B --> C["Heated electrodes<br/>(thermionic emission)"]
C --> D["Accelerated electrons<br/>(KE ~5–10 eV)"]
D --> E["Collide with Hg atoms"]
E --> F["Hg* excited"]
F --> G["Emit UV photon<br/>(254 nm, 4.9 eV)"]
G --> H["Phosphor coating<br/>absorbs UV"]
H --> I["Re-emits broad-spectrum visible light"]
Commercial fluorescent-tube phosphors are typically mixtures of rare-earth-doped compounds (e.g. europium-activated yttrium oxide for red emission, terbium-activated lanthanum phosphate for green, europium-activated barium magnesium aluminate for blue). The mixture is adjusted to produce a colour temperature appropriate to the application (warm white ~2700 K, neutral white ~4000 K, cool white ~6500 K).
| Technology | Mechanism | Luminous efficacy (lm/W) | Notes |
|---|---|---|---|
| Incandescent (filament) | Thermal radiation from hot tungsten | 10–17 | Most energy lost as infrared (heat); banned for general lighting in many jurisdictions since the 2010s |
| Halogen (incandescent variant) | Higher filament temperature with halogen gas to prevent tungsten deposition | 16–24 | Slightly more efficient than standard incandescent |
| Fluorescent (compact or tube) | Electron-impact UV → phosphor visible | 50–100 | 4–6× more efficient than incandescent; contains small amount of mercury (disposal concern) |
| LED (light-emitting diode) | Direct electron-hole recombination in semiconductor junction | 80–150+ | Most efficient; no UV intermediate stage; long lifetime (>20,000 hours) |
The fluorescent tube held the efficiency crown for general lighting from the 1940s to the 2010s, when LED technology surpassed it on both efficacy and lifetime. Fluorescent tubes are still widely used in older installations but new fluorescent products are being phased out in many markets.
A tungsten filament heated to ~2800 K (the temperature of the filament in a typical incandescent bulb) emits a continuous blackbody spectrum. The peak of the spectrum lies in the infrared, not the visible — most of the radiated energy is heat rather than light. Only about 10% of the input electrical energy emerges as visible light.
A fluorescent tube, by contrast, has no thermal emission as part of its design — the visible light comes from a quantum-mechanical down-conversion of UV photons emitted at one specific frequency. Each UV photon could in principle yield one visible photon at ~50% efficiency, with the remaining energy as heat in the phosphor. Real tubes achieve about 25% luminous efficiency, much higher than incandescent.
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