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Spec mapping: OCR H556 Module 4.5 — Quantum physics (atomic emission and absorption line spectra as direct evidence of discrete energy levels; relationship between transition energies and observed wavelengths via hf=Eupper−Elower; the hydrogen Lyman / Balmer / Paschen series; applications of spectroscopy to identify elements and probe stellar atmospheres). Refer to the official OCR H556 specification document for exact wording.
In the last lesson we established that atoms possess discrete energy levels, and that transitions between those levels involve photon emission or absorption at specific frequencies hf = E_upper - E_lower. In this final lesson of the course we apply this theoretical framework to what is perhaps its most direct experimental manifestation: line spectra.
When you look at the light emitted or absorbed by a gas, you do not see a smooth continuum of wavelengths. You see discrete lines — narrow, sharp features at very specific wavelengths — on an otherwise featureless background. Each element produces its own characteristic pattern of lines, as unique as a fingerprint. This is the evidence, visible and measurable, for the existence of quantised atomic energy levels.
Line spectra are central to the OCR A-Level Physics A specification (H556), Module 4.5, and the OCR examiners frequently set questions that require you to (a) relate a spectral line's wavelength to an energy-level transition, (b) explain why line spectra are evidence for quantisation, and (c) distinguish emission and absorption spectra. This lesson develops each of these skills thoroughly.
Before we focus on atomic line spectra, it is useful to set them in context. In 1859, Kirchhoff and Bunsen established three basic categories of optical spectra:
flowchart TB
H["Hot dense body<br/>(filament, Sun’s photosphere)"] --> C["Continuous spectrum<br/>all wavelengths present"]
HG["Hot thin gas<br/>(discharge tube)"] --> E["Emission line spectrum<br/>bright lines on dark background"]
CG["Cool thin gas<br/>in front of continuous source"] --> AB["Absorption line spectrum<br/>dark lines on continuous background"]
These three Kirchhoff-Bunsen laws established — decades before Bohr — that atoms interact with light in ways that reveal something about their internal structure. What the discrete lines meant remained a mystery until quantum theory explained them.
When an atom is excited (by collisions, by absorbed photons, or by electric discharge), its electron is promoted to a higher energy level. After a brief time (~10⁻⁸ s), the electron drops back down to a lower level, emitting a photon whose energy exactly equals the energy difference:
Each possible downward transition corresponds to a specific photon wavelength, and these wavelengths appear as bright lines in the emission spectrum. The number of lines, their positions, and their relative intensities are all characteristic of the element.
For hydrogen, the visible emission lines belong to the Balmer series — transitions that end on n = 2. The strongest four are:
| Transition | Wavelength | Colour |
|---|---|---|
n = 3 → 2 (H-α) | 656.3 nm | red |
n = 4 → 2 (H-β) | 486.1 nm | cyan-blue |
n = 5 → 2 (H-γ) | 434.1 nm | violet |
n = 6 → 2 (H-δ) | 410.2 nm | deep violet |
These four lines are easy to see in a simple hydrogen discharge tube with a diffraction grating. They are direct, visible evidence that the hydrogen atom has a discrete set of energy levels and that transitions between them produce sharp emission lines.
For helium, the emission spectrum shows a different but equally characteristic pattern. For sodium, the familiar yellow "sodium D lines" at 589.0 and 589.6 nm dominate. For neon, a rich pattern of red and orange lines gives a neon sign its distinctive colour. Every element is unique.
When white light — containing all wavelengths — passes through a cool gas, atoms in the gas can absorb photons that match their allowed upward transitions. Photons of the right wavelength are absorbed and the atoms jump to an excited state. The excited atoms then re-emit in random directions, so from the original forward direction these wavelengths appear missing — dark lines against the otherwise continuous background.
Crucially, the dark lines in an absorption spectrum appear at exactly the same wavelengths as the bright lines in an emission spectrum of the same element. The transitions are the same; only the direction (upward for absorption, downward for emission) is reversed.
flowchart LR
W["White light<br/>all wavelengths"] --> CG["Cool gas (Na)"]
CG --> AB["Transmitted light<br/>missing at 589.0, 589.6 nm"]
CG -. re-emits .-> S["Radiation in all directions"]
The most famous absorption spectrum is that of the Sun. When Joseph von Fraunhofer mapped the solar spectrum in 1814, he found thousands of dark lines at discrete wavelengths. These lines are caused by absorption in the Sun's cool outer atmosphere, and each corresponds to a specific element. By matching the wavelengths to laboratory spectra, astronomers have identified the chemical composition of the Sun — and, by extension, of every star and galaxy we can observe.
This technique, astronomical spectroscopy, is one of the most powerful tools in astrophysics. The helium atom was first identified in the spectrum of the Sun (helios = Sun) in 1868 — twenty-seven years before it was isolated in a laboratory on Earth. Today, every discovery about the composition, motion, and history of distant objects in the universe ultimately traces back to the same equation: hf = E_upper - E_lower.
The discrete nature of atomic spectra is direct evidence that atomic energy levels are themselves discrete. If the energy levels formed a continuum — any energy allowed — then transitions between them would produce photons of any energy, and the spectrum would be continuous (like the blackbody spectrum). The fact that we see sharp lines instead of a smeared continuum is evidence — overwhelming and unambiguous — that atoms possess only a discrete set of allowed energies.
This is the key point that OCR exam questions often test, and it is worth rehearsing explicitly:
Emission line spectra are evidence for discrete atomic energy levels because each observed line corresponds to a specific photon energy
hf = E_upper - E_lower. Since only certain discrete photon energies are observed (not a continuous range), only certain discrete energy differences — and therefore only certain discrete energy levels — can exist within the atom.
This kind of concise, logically clear explanation is exactly what is expected in a 5- or 6-mark exam question.
Exam Tip: When OCR asks "explain how line spectra provide evidence for discrete energy levels", make sure your answer explicitly includes: (1) each line corresponds to a transition between two specific levels, (2) the photon energy is
hf = E_upper - E_lower, (3) sharp discrete lines (not a continuum) imply discrete energy differences, which in turn imply discrete energy levels. All three steps in the logical chain are needed for full marks.
A hydrogen atom makes a transition from n = 4 to n = 2. What is the wavelength of the emitted photon? Which of the named Balmer lines is this?
Solution.
E_4 = -13.6/4² = -0.85 eV; E_2 = -13.6/4 = -3.40 eV.
(Writing E_upper - E_lower as always — a positive number.)
Wavelength:
λ=1240/2.55≈486nmAnswer: 486 nm — this is the H-β line of the Balmer series, in the cyan-blue part of the visible spectrum.
A beam of white light passes through a cloud of cold hydrogen atoms in their ground state. Which wavelengths are absorbed? Which are not?
Solution. From the ground state (n = 1, E = -13.6 eV), the available upward transitions are to n = 2, n = 3, n = 4, ... Each requires a specific photon energy:
1 → 2: ΔE = 10.20 eV, λ = 121.6 nm (Lyman-α, UV)1 → 3: ΔE = 12.09 eV, λ = 102.6 nm (Lyman-β, UV)1 → 4: ΔE = 12.75 eV, λ = 97.3 nm (Lyman-γ, UV)1 → ∞: ΔE = 13.60 eV, λ = 91.2 nm (Lyman limit, UV)Notice that all Lyman absorption lines are in the ultraviolet. Ground-state hydrogen does not absorb visible light — this is why pure hydrogen gas is transparent and colourless. The visible Balmer lines (red, blue, violet) would require the atom to start in the n = 2 excited state, which is only populated at very high temperatures or in active discharge tubes. Cold hydrogen in space shows Lyman absorption in the UV but is invisible in visible wavelengths.
Answer: Only UV wavelengths at 121.6, 102.6, 97.3, ... nm are absorbed. Visible light passes through unchanged.
A spectral line from an unknown source has wavelength 589.0 nm. This matches the sodium D line. What is the energy difference between the corresponding sodium levels, in eV?
Solution.
E=1240/589.0≈2.105eVSo the transition involves an energy difference of about 2.1 eV. The sodium atom has many levels, but the 3p \to 3s transition in the outer electron configuration gives exactly this value — and is the origin of the bright yellow emission you see in sodium street lamps and flame tests.
A hydrogen atom is excited to the n = 4 level. It then cascades down to the ground state. How many different photon wavelengths might it emit on the way down? List the possible transitions.
Solution. The atom must reach n = 1, but it can get there by various routes. The possible transitions from n = 4 to lower levels are:
4 → 1n = 2: 4 → 2 then 2 → 1n = 3: 4 → 3 then 3 → 1, or 4 → 3 then 3 → 2 then 2 → 1All the individual transitions between any two of the four levels {1, 2, 3, 4} are possible, and each has a distinct photon energy:
4 → 3: 0.66 eV (IR, 1875 nm)4 → 2: 2.55 eV (visible, 486 nm)4 → 1: 12.75 eV (UV, 97.3 nm)3 → 2: 1.89 eV (visible, 656 nm)3 → 1: 12.09 eV (UV, 102.6 nm)2 → 1: 10.20 eV (UV, 121.6 nm)That is 6 distinct wavelengths. For an atom excited to level n, the number of possible transitions is n(n-1)/2. For n = 4, this is 4 \cdot 3/2 = 6. The pattern generalises: level n = 5 gives 10 lines, n = 6 gives 15 lines, and so on.
Note: not every transition is equally probable — quantum mechanics gives selection rules and transition rates. But all six wavelengths will be observed in a sample of many such atoms.
Spectroscopy — the systematic measurement and analysis of line spectra — is one of the most productive techniques in physics, chemistry and astronomy. Some of its applications:
9 192 631 770 Hz, from a caesium hyperfine transition).All of these applications exploit the same principle: atomic transitions involve specific, discrete, characteristic photon energies. The universal currency of quantum physics — hf = \Delta E — turns out to be one of the most powerful measurement tools we possess.
Before closing this lesson, it is worth pointing out the connections back through everything we have covered in this course:
E = hf makes spectral lines possible. In a classical wave theory, a continuous range of photon energies would give a continuous spectrum; only quantisation gives discrete lines.hf units. Atomic absorption lines are the exact counterpart for atoms: energy absorption in discrete units corresponding to atomic transitions.hf = E_upper - E_lower connects them to observed photon wavelengths.Every topic in this module ultimately converges on line spectra. They are where the photon model, the wave-particle duality of matter, and the quantisation of atomic energy levels all come together to produce something directly observable in a laboratory or through a telescope.
The following SVG contrasts the appearance of an emission spectrum (bright lines on a dark background) with an absorption spectrum (dark lines superposed on a continuous rainbow background). Both arise from the same set of atomic transitions in the same element, but the direction (down for emission, up for absorption) determines the visual appearance.
The four lines shown are the visible Balmer transitions of hydrogen (H-α red, H-β cyan, H-γ violet, H-δ deep violet). The bright/dark difference encodes only the direction of the transition (down vs up); the underlying atomic structure is identical.
Question (10 marks): A hydrogen discharge tube emits visible light. When this light is viewed through a diffraction grating, four bright lines are seen at wavelengths 656 nm, 486 nm, 434 nm and 410 nm.
(a) Identify, with reasoning, which atomic series these lines belong to and which transitions they correspond to. [3]
(b) Explain in detail how line spectra provide evidence for discrete energy levels in atoms. Your answer should include both the photon-energy equation and the contrast with what a continuous-energy-level model would predict. [4]
(c) A different hydrogen sample, this time cool and placed in front of a white-light source, is observed to produce an absorption spectrum. Will the dark lines appear at the same four wavelengths as in part (a), or at different wavelengths? Justify your answer with reference to (i) which atomic level the absorbing atoms start from, and (ii) which level they reach. [3]
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