Year 12 Physics Module 8 ⏱ ~45 min 5 MC · 2 Short Answer Lesson 6 of 17

Spectroscopy and Stellar Classification

In 1925, Cecilia Payne at Harvard analysed absorption spectra from over 300 stars using the Harvard photographic plate collection. Applying Meghnad Saha's 1920 ionisation equation, she concluded that stars are 73% hydrogen and 25% helium by mass, contradicting the accepted view that stellar compositions matched Earth's. Her supervisor Henry Russell initially dismissed the conclusion as "almost certainly wrong." Four years later, Russell independently reached the same finding and published first. Payne-Gaposchkin is now recognised as the founder of stellar astrophysics.

Today's hook: In 1925, Cecilia Payne at Harvard University analysed spectra from over 300 stars using glass photographic plates and calculated that the Sun is 73% hydrogen and 25% helium by mass. Every star she examined showed the same dominant composition, yet the accepted scientific view at the time was that stars had roughly Earth-like compositions. Her supervisor told her the conclusion was "almost certainly not real." She was right. What property of stellar spectra allowed Payne to measure the chemical composition of stars 150 million kilometres away?

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Orient and predict

Set up the spectral vocabulary you will need, then predict what a set of dark lines in a spectrum can tell you.

Warm up first

Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.

Worksheets

Practise this lesson

Four printable worksheets that build from the foundations up to exam-style questions, start at whatever level suits you.

Build Foundations & guided practice Apply Application & data response Master Mastery tasks Exam Exam-style questions

Before you read, predict

When white light passes through a cool gas, dark lines appear at specific wavelengths.

Before reading on, answer:

Why do these dark lines appear at specific wavelengths rather than being spread out?
How could analysing these lines tell us what elements are present in the gas?
What would happen to these lines if the gas were moving toward us?

Warm-up: A stellar spectrum showing dark lines on a continuous background is a(n):

Learning Intentions

goals

Know, Stellar Spectra

Continuous, emission, absorption
Fraunhofer lines
Spectral types OBAFGKM

Understand, Spectroscopic Analysis

Temperature from spectral type
Composition from line identification
Velocity from Doppler shift

Can Do, Interpret Stellar Spectra

Classify spectral type from lines
Calculate radial velocity from $\Delta\lambda$
Estimate surface temperature

Scan these before reading

vocab

Absorption spectrumContinuous spectrum with dark lines where atoms absorb specific wavelengths corresponding to their electron transition energies.

Emission spectrumBright lines at specific wavelengths emitted by excited atoms as electrons drop to lower energy levels.

Spectral typeClassification of stars based on temperature and dominant absorption lines: OBAFGKM from hottest to coolest.

Doppler shiftWavelength shift due to relative motion: blueshift (approaching, $\lambda_{obs} < \lambda_{rest}$), redshift (receding, $\lambda_{obs} > \lambda_{rest}$).

Fraunhofer linesDark absorption lines in the solar spectrum caused by atoms in the Sun's cooler outer atmosphere absorbing specific wavelengths from the photosphere's continuous radiation.

Cross-lesson links: L08 classified stars by HR position. L09 examines the spectral evidence, the absorption lines that allow us to determine a star's temperature, composition, and velocity. Stellar spectroscopy uses diffraction gratings (M7 L04) and the Doppler effect (M7 L01) to extract all the information we know about distant stars.

Core Content

Read the three types of spectra

Use Kirchhoff's laws to work out how each spectrum is produced, and why a star's spectrum is an absorption spectrum.

Types of Spectra

+5 XP

Kirchhoff's laws of spectroscopy

Pass sunlight through a glass prism and you see a continuous rainbow. Now look more carefully: running across that rainbow are hundreds of thin dark lines at precise wavelengths, wavelengths where specific elements in the Sun's outer atmosphere have absorbed light. Pass light through a glowing gas of pure hydrogen and you see the opposite: a black background with a few bright lines at exactly those same wavelengths where hydrogen absorbs. These observations are described by Kirchhoff's three laws of spectroscopy:

Continuous spectrum: A complete rainbow of colours with no gaps. Produced by hot, dense objects (stellar photospheres, incandescent solids).
Absorption (line) spectrum: A continuous spectrum with dark lines at specific wavelengths. Produced when light from a hot source passes through a cooler gas. The gas atoms absorb photons at wavelengths corresponding to their electron transition energies.
Emission (line) spectrum: Bright coloured lines on a dark background. Produced by hot, low-density gas. Excited atoms emit photons as electrons drop to lower energy levels.

Stellar spectra are absorption spectra: the hot photosphere produces continuous radiation, and cooler atoms in the star's atmosphere absorb specific wavelengths. The pattern of absorption lines is unique to each element and depends on temperature, different ions dominate at different temperatures.

Figure 1, Three spectral types and the Doppler shift effect on absorption lines. The dark lines in the absorption spectrum shift toward blue (shorter wavelength) when the source approaches, and toward red when it recedes.

Stop and check

Explain why stellar spectra are absorption spectra rather than emission spectra. What produces the continuous background and what produces the dark lines?

Kirchhoff's three laws: (1) hot dense source → continuous spectrum; (2) cool gas in front → absorption spectrum (dark lines at element-specific wavelengths); (3) hot low-density gas → emission spectrum (bright lines at same wavelengths). Stellar spectra are absorption: the photosphere produces continuous radiation and the cooler outer atmosphere absorbs specific wavelengths.

Pause, copy the highlighted laws and stellar application into your book before moving on.

Stellar spectra are absorption spectra because cooler gas in the star's outer atmosphere absorbs specific wavelengths from the photosphere's continuous radiation.

An emission spectrum contains a complete rainbow with no gaps, produced by a hot, dense source.

The dark absorption lines in a stellar spectrum occur at the same wavelengths as the bright emission lines for the same element.

Classify a star with OBAFGKM

Order the spectral types by temperature and match each one to the absorption features that identify it.

Spectral Classification

+5 XP

The OBAFGKM sequence

We just saw that stellar spectra are absorption spectra produced by Kirchhoff's three laws. That raises a question: since every star shows absorption lines, how do we systematically classify stars from their spectra? This card answers it → via the OBAFGKM sequence, which orders stars from hottest to coolest by their dominant absorption features (He II → H Balmer → Ca II → TiO).

Stars are classified by spectral type based on their absorption line patterns, which depend on temperature. The sequence, from hottest to coolest, is O B A F G K M. Remember it with: "Oh Be A Fine Girl/Guy, Kiss Me"

Spectral Types, Temperature and Dominant Features

O ($>30{,}000$ K): Ionised He lines. Blue, massive. E.g. Mintaka.

B ($10{,}000–30{,}000$ K): Neutral He, some H. Blue-white. E.g. Rigel.

A ($7{,}500–10{,}000$ K): Strong H Balmer lines. White. E.g. Sirius.

F ($6{,}000–7{,}500$ K): H weaker, ionised metals appear. Yellow-white. E.g. Procyon.

G ($5{,}200–6{,}000$ K): Ionised Ca (H & K lines), neutral metals. Yellow. E.g. Sun (G2).

K ($3{,}700–5{,}200$ K): Strong metal lines, molecular bands begin. Orange. E.g. Arcturus.

M ($<3{,}700$ K): Molecular bands (TiO) dominate. Red. E.g. Betelgeuse.

Each spectral type is subdivided 0–9 (hottest to coolest within type). The Sun is G2V spectral type G, subclass 2, luminosity class V (main sequence dwarf). The luminosity class indicates evolutionary stage: I = supergiant, II = bright giant, III = giant, IV = subgiant, V = main sequence.

Figure 2, The OBAFGKM spectral sequence from hottest (O) to coolest (M), with characteristic colours, temperature ranges, dominant absorption features, and example stars.

Stop and check

A star shows strong ionised helium lines but weak hydrogen Balmer lines. What is its approximate spectral type and surface temperature? What colour would this star appear?

Spectral sequence OBAFGKM (hottest → coolest; mnemonic: "Oh Be A Fine Girl/Guy, Kiss Me"): O ($>30\,000$ K, He II); A (H Balmer); G (Ca II; Sun = G2V); M ($<3\,700$ K, TiO). Luminosity class: I supergiant → V main sequence dwarf (the Roman numeral after the spectral type).

Add the highlighted sequence and dominant features to your notes before the check below.

Which spectral type shows strong molecular TiO absorption bands in its spectrum?

Measure motion from a wavelength shift

Turn a measured shift in a spectral line into a radial velocity, and check the direction and the low-speed condition.

Doppler Spectroscopy and Radial Velocity

+5 XP

Measuring motion from wavelength shifts

We just saw how the OBAFGKM sequence classifies stars from their absorption line patterns. That raises a question: can spectral lines do more than identify a star's temperature, can they reveal how fast a star is moving? This card answers it → yes, via the Doppler formula $\Delta\lambda/\lambda_{\text{rest}} = v_r/c$, which also underlies the radial velocity method for detecting exoplanets.

The Doppler effect causes spectral lines to shift when a star moves relative to Earth. The radial velocity formula is:

$$\dfrac{\Delta\lambda}{\lambda_{\text{rest}}} = \dfrac{v_r}{c}$$

where $v_r$ is the radial velocity (positive for recession, negative for approach). This technique enables astronomers to:

Measure stellar radial velocities: Used to study galactic rotation and binary star orbits.
Detect exoplanets: A star's periodic wobble due to an orbiting planet produces oscillating Doppler shifts in its spectrum. This was the first successful exoplanet detection method (1995-51 Pegasi b).
Measure galaxy recession: Cosmological redshift from Hubble expansion ($z = v/c$ for small $z$).

For cosmological redshifts, the simple Doppler formula is only an approximation. The full relativistic relation is:

$$1 + z = \sqrt{\dfrac{1 + v/c}{1 - v/c}}$$

For small $z$ ($< 0.1$), the non-relativistic approximation $z \approx v/c$ is adequate for HSC purposes.

Figure 3, Doppler shift of spectral lines. Approaching sources compress wavelengths (blueshift); receding sources stretch them (redshift). The shift magnitude gives the radial velocity via $\Delta\lambda/\lambda_{\text{rest}} = v_r/c$.

Doppler Spectroscopy Equations

$z = \Delta\lambda/\lambda_{\text{rest}} = v_r/c$, redshift / radial velocity (non-relativistic, $v \ll c$)

$\Delta\lambda = \lambda_{\text{obs}} - \lambda_{\text{rest}}$, wavelength shift (positive = redshift)

$v_r = c\,\Delta\lambda/\lambda_{\text{rest}}$, radial velocity from spectral shift

$1 + z = \sqrt{(1+v/c)/(1-v/c)}$, relativistic Doppler (large $z$)

Stop and check

A spectral line at rest wavelength 656.3 nm is observed at 658.1 nm from a distant galaxy. Calculate its redshift $z$ and approximate recession velocity.

Doppler radial velocity: $\Delta\lambda/\lambda_{\text{rest}} = v_r/c$ (positive $v_r$ = recession/redshift; negative = approach/blueshift). For HSC use $z \approx v/c$ for $z < 0.1$. Exoplanet radial velocity method (1995): periodic Doppler wobble in the host star's spectrum reveals the orbiting planet's gravitational tug.

Pause, write the highlighted formula and application into your book before the check below.

A star's H$\alpha$ line ($\lambda_{\text{rest}} = 656.3$ nm) is observed at 659.0 nm. The radial velocity is $v_r = c \times \Delta\lambda / \lambda_{\text{rest}}$. Using $c = 3.00 \times 10^5$ km/s, the radial velocity is approximately _____ km/s (round to nearest 100).

Identify stars, watching the traps

Check which lines actually mark each temperature range, then classify real stars from their described spectra.

HSC Tip, Spectral Analysis

Remember the spectral type sequence with "Oh Be A Fine Girl/Guy, Kiss Me", OBAFGKM from hottest to coolest. A common trap: confusing which lines dominate at which temperature. O stars show ionised helium (He II), not hydrogen. M stars show molecular bands (TiO), not hydrogen. For Doppler calculations, use $z = \Delta\lambda/\lambda_{\text{rest}} = v_r/c$ for non-relativistic velocities. Always check whether the line is blueshifted (shorter wavelength, approaching) or redshifted (longer wavelength, receding). When classifying a star from its spectrum, the presence/absence of specific lines is more reliable than line strength alone.

Activity 1, Spectral Classification

ApplyBand 4

Identify spectral types from absorption line descriptions

A star's spectrum shows strong hydrogen Balmer lines with very weak ionised calcium lines. Identify the most likely spectral type and surface temperature range.
A star shows no hydrogen lines, but strong ionised helium (He II) lines. State its spectral type and give an example star.
The Sun's spectrum shows strong Ca II (H and K) lines and neutral metal lines, with weak hydrogen Balmer lines. Confirm the Sun's spectral type and explain why its Balmer lines are weaker than those of an A-type star, even though the Sun contains hydrogen.
Arrange these stars from hottest to coolest surface temperature: Arcturus (K), Rigel (B), Betelgeuse (M), Sirius (A), the Sun (G).

Calculate radial velocities and test the limits

Run the Doppler calculations yourself, then separate what a shift tells you from what it does not.

Activity 2, Doppler Velocity Calculations

ApplyBand 5

Practice calculating radial velocity from wavelength shifts

A galaxy's H$\alpha$ line ($\lambda_{\text{rest}} = 656.3$ nm) is observed at 660.9 nm. Calculate: (a) $\Delta\lambda$, (b) redshift $z$, (c) recession velocity $v_r$, (d) state whether the galaxy is approaching or receding.
A binary star's spectral line at 500.0 nm oscillates between 499.5 nm and 500.5 nm as the star orbits. Calculate the maximum orbital speed of this star component.
An exoplanet host star shows a periodic Doppler wobble of $\pm 50$ m/s. Explain how this is used to infer the existence and properties of the planet.
A star's Ca II K line ($\lambda_{\text{rest}} = 393.3$ nm) is observed at 394.5 nm. Calculate its radial velocity and state whether it is approaching or receding.

Misconceptions, Final Check

Wrong: "Spectral type depends only on chemical composition, stars of the same composition must have the same spectral type."

Right: Spectral type depends primarily on surface temperature, not composition. Two stars with identical compositions but different temperatures will show completely different dominant absorption features. The same element can appear as neutral atoms, ions, or be absent from the spectrum depending on temperature.

Wrong: "A blueshifted line means the star's light has higher energy, so the star must be hotter."

Right: Blueshift indicates the star is moving toward us, not that it is hotter. Temperature is inferred from which spectral lines are present and their relative strengths, not from a global wavelength shift. A hot star moving away from us shows redshifted lines.

Three of these statements about stellar spectroscopy are correct. Pick the odd one out.

Independent practice

Show what you can do without prompts

Complete a shuffled question-bank set, then write full spectroscopy responses in HSC style.

Quick recall, spectroscopy and stellar classification

+5 XP

A fresh five-question set drawn from this lesson's bank, feedback shown immediately. +5 XP per correct · +25 XP all correct

Pick your answer, then rate your confidence, that tells the system what to drill next.

Short Answer, 8 marks

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ApplyBand 4(3 marks) 1. A galaxy's H$\alpha$ emission line ($\lambda_{\text{rest}} = 656.3$ nm) is observed at 658.1 nm. (a) Calculate the redshift $z$. (b) Estimate the recession velocity. (c) State whether the galaxy is approaching or receding, and justify using the wavelength values.

1 mark: correct $z$ · 1 mark: correct velocity · 1 mark: correct direction with justification

AnalyseBand 6(5 marks) 2. (a) Distinguish between continuous, absorption, and emission spectra. Give one astrophysical example of each. (b) Explain why spectral type is determined by surface temperature rather than chemical composition. (c) A star shows strong TiO molecular bands. Identify its spectral type and approximate temperature range. (d) Explain how the radial velocity method detects exoplanets. (e) State one limitation of the radial velocity method for exoplanet detection.

1 mark each for (a) three spectra + examples · (b) temperature mechanism · (c) type M + temp · (d) Doppler wobble · (e) valid limitation

Show all answers

Multiple choice

MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set drawn from the lesson bank.

Short Answer, Model Answers

Q1 (3 marks): (a) $z = (658.1 - 656.3)/656.3 = 1.8/656.3 = 0.00274$ (1 mark). (b) $v_r = cz = 3.00\times10^5 \times 0.00274 = 820\ \text{km/s}$ (1 mark). (c) The galaxy is receding the observed wavelength (658.1 nm) is longer than the rest wavelength (656.3 nm), indicating a redshift, meaning the source is moving away from us (1 mark).

Q2 (5 marks): (a) Continuous: unbroken rainbow, produced by a hot dense source (e.g. stellar photosphere). Absorption: continuous spectrum with dark lines, produced when light passes through cooler gas (e.g. stellar atmosphere). Emission: bright lines on dark background, produced by hot low-density gas (e.g. nebula) (1 mark). (b) The electron energy levels that are populated, and therefore which transitions produce absorption lines, depend on temperature, not just which elements are present. A G-star and an O-star could have similar hydrogen content, but the O-star is hot enough to ionise hydrogen completely, removing Balmer lines, while the G-star shows Ca II lines (1 mark). (c) Strong TiO bands indicate spectral type M, surface temperature $<3{,}700$ K, cool enough for molecules to survive in the stellar atmosphere (1 mark). (d) The orbiting planet exerts a gravitational force on its host star, causing the star to "wobble" periodically. This wobble produces periodic Doppler shifts in the star's spectral lines; measuring the period and amplitude of these shifts reveals the planet's orbital period and a lower bound on its mass (1 mark). (e) Valid limitations include: only detects the component of motion along the line of sight (misses face-on orbits); biased toward massive, close-in planets; cannot directly reveal planet size or atmosphere (1 mark).

Final step

Retrieve, reflect and finish

Check what stuck, revisit your opening spectrum prediction and record the method you will reuse.

Check what actually stuck

How did your thinking change?

At the start you were asked about the property of stellar spectra that allowed Cecilia Payne in 1925 to determine that the Sun is 73% hydrogen and 25% helium, a finding her supervisor initially dismissed but which is now the foundation of stellar astrophysics.

Did you predict dark absorption lines appear at specific wavelengths because atoms absorb only photons matching their electron transition energies? Correct, Payne used the positions and strengths of these lines, combined with Saha's ionisation equation, to calculate stellar compositions from over 300 photographic spectra.
Did you predict that line patterns identify elements because each element has unique electron energy levels? Correct, the absorption spectrum is an elemental fingerprint, appearing at the same wavelengths in emission and absorption.
Did you predict approaching gas causes blueshift (shorter wavelengths)? Correct, the Doppler effect compresses wavelengths for approaching sources, shifting lines toward blue.

Extend: A star classified as B2V is compared to a G2V star. (a) Which is hotter, and what dominant spectral features distinguish them? (b) The B2V star's H$\beta$ line ($\lambda_{\text{rest}} = 486.1$ nm) is observed at 485.7 nm, is this star approaching or receding, and at what speed? (c) Explain why the radial velocity method would fail to detect an Earth-mass planet orbiting a sun-like star at 1 AU using current technology.

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