Physics • Year 12 • Module 8 • Lesson 9
Spectroscopy and Stellar Classification
Lock in the core vocabulary, Kirchhoff’s three spectral types, the OBAFGKM sequence, and the Doppler radial-velocity formula before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: continuous spectrum, absorption spectrum, emission spectrum, spectral type, Fraunhofer lines, luminosity class, Doppler shift, redshift, blueshift, radial velocity. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A complete rainbow of colours with no gaps, produced by a hot dense source such as a stellar photosphere. | |
| 1.2 | A continuous background with dark lines at specific wavelengths where cooler atmospheric gas has absorbed photons. | |
| 1.3 | Bright coloured lines on a dark background, produced when excited atoms in a hot low-density gas emit photons. | |
| 1.4 | A star’s classification based on its surface temperature, which determines the dominant absorption lines in its spectrum. | |
| 1.5 | Specific dark absorption lines in the solar spectrum, catalogued by Joseph von Fraunhofer in 1814, each labelled by a letter. | |
| 1.6 | A roman-numeral code (I–V) appended to a spectral type indicating a star’s size: I = supergiant, V = main-sequence dwarf. | |
| 1.7 | A change in the observed wavelength of light caused by relative motion between source and observer. | |
| 1.8 | A shift of spectral lines to longer wavelengths, indicating the source is moving away from the observer. | |
| 1.9 | A shift of spectral lines to shorter wavelengths, indicating the source is approaching the observer. | |
| 1.10 | The component of a star’s velocity directed along the line of sight to the observer, measurable via spectral line shifts. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 Stellar spectra are emission spectra because the star’s photosphere emits light. T / F
2.2 The spectral sequence OBAFGKM runs from coolest to hottest. T / F
2.3 O-type stars show strong ionised helium lines because their surface temperature exceeds 30 000 K. T / F
2.4 A star whose spectral lines are shifted to shorter wavelengths is moving away from us. T / F
2.5 M-type stars are characterised by molecular TiO bands in their spectra because they are very cool (below 3 700 K). T / F
2.6 The simple Doppler formula \(z = v_r/c\) is a good approximation when the recession velocity is greater than 50% of the speed of light. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
absorption · atmosphere · blueshift · continuous · electron · photosphere · radial velocity · temperature
A stellar spectrum is an ___________ spectrum. The hot, dense ___________ of the star produces ___________ radiation covering all visible wavelengths. Cooler gas in the star’s outer ___________ absorbs photons at wavelengths that exactly match the ___________ transition energies of the atoms present, leaving dark lines. The pattern of these lines reveals the star’s surface ___________ and chemical composition. When a star moves toward the observer its lines undergo a ___________, and the formula \(\Delta\lambda/\lambda = v_r/c\) allows us to calculate the star’s ___________.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What physical property of a star primarily determines its spectral type, and why?
4.2 What does the luminosity class (e.g. the “V” in G2V) tell us about a star?
4.3 State the Doppler radial-velocity formula and define each symbol.
4.4 Why must the full relativistic Doppler formula be used for galaxies with large cosmological redshifts (\(z > 0.1\))?
5. Complete the OBAFGKM summary table
Complete the missing cells in the spectral classification table. 12 marks (1 per cell)
| Type | Temperature range | Dominant feature | Colour | Named example |
|---|---|---|---|---|
| O | > 30 000 K | Ionised helium (He II) | Mintaka | |
| B | Blue-white | Rigel | ||
| A | 7 500–10 000 K | Strong hydrogen Balmer lines | White | |
| F | Hydrogen weaker; ionised metal lines | Procyon | ||
| G | 5 200–6 000 K | Yellow | The Sun (G2V) | |
| K | 3 700–5 200 K | Strong metal lines; molecular bands begin | ||
| M | Red | Betelgeuse |
Q1 — Term–definition match
1.1 continuous spectrum • 1.2 absorption spectrum • 1.3 emission spectrum • 1.4 spectral type • 1.5 Fraunhofer lines • 1.6 luminosity class • 1.7 Doppler shift • 1.8 redshift • 1.9 blueshift • 1.10 radial velocity.
Q2 — True / false with correction
2.1 False. Stellar spectra are absorption spectra. The photosphere produces continuous radiation; the cooler outer atmosphere absorbs specific wavelengths, creating dark lines.
2.2 False. OBAFGKM runs from hottest (O) to coolest (M).
2.3 True.
2.4 False. Shorter wavelengths (blueshift) indicate the source is approaching the observer. Moving away produces longer wavelengths (redshift).
2.5 True.
2.6 False. The simple formula is valid only for small velocities (\(v \ll c\), typically \(z < 0.1\)). At large fractions of \(c\) the full relativistic formula must be used.
Q3 — Cloze paragraph
In order: absorption / photosphere / continuous / atmosphere / electron / temperature / blueshift / radial velocity.
Q4.1 — What determines spectral type
Surface temperature primarily determines spectral type because temperature controls which atomic species are ionised and which electron transitions are populated, determining which absorption lines appear most strongly in the star’s spectrum.
Q4.2 — Luminosity class
The luminosity class indicates the star’s size and evolutionary stage: class I = supergiant, II = bright giant, III = giant, IV = subgiant, V = main-sequence (dwarf). The “V” in G2V means the Sun is a main-sequence star.
Q4.3 — Doppler formula
\(\dfrac{\Delta\lambda}{\lambda_\text{rest}} = \dfrac{v_r}{c}\), where \(\Delta\lambda = \lambda_\text{obs} - \lambda_\text{rest}\) is the shift in wavelength, \(\lambda_\text{rest}\) is the laboratory rest wavelength, \(v_r\) is the radial velocity (positive = receding), and \(c\) is the speed of light.
Q4.4 — Why relativistic formula needed for large z
The simple approximation \(z \approx v/c\) assumes \(v \ll c\). For \(z > 0.1\) (i.e. \(v > 10\%\) of \(c\)), relativistic time dilation and length contraction become significant; the full formula \(1+z = \sqrt{(1+v/c)/(1-v/c)}\) is required to avoid underestimating recession velocities by substantial margins.
Q5 — OBAFGKM summary table
O: colour = blue. B: 10 000–30 000 K; neutral helium lines, some hydrogen; blue-white; Rigel (already given). A: example = Sirius. F: 6 000–7 500 K; yellow-white. G: dominant feature = ionised calcium H and K lines, neutral metal lines. K: colour = orange; example = Arcturus. M: below 3 700 K; molecular bands (TiO) dominate; example = Betelgeuse (already given).