Physics • Year 12 • Module 8 • Lesson 8
The Hertzsprung-Russell Diagram
Lock in the core vocabulary, the structure of the HR diagram, and the key formulas 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: main sequence, red giant, supergiant, white dwarf, spectral type, luminosity, absolute magnitude, Stefan-Boltzmann law, Wien's displacement law, main sequence turn-off point. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The diagonal band on the HR diagram where stars spend approximately 90% of their lives fusing hydrogen in their cores; mass increases from bottom-right to top-left. | |
| 1.2 | A cool, highly luminous evolved star that has left the main sequence; its enormous radius compensates for its low surface temperature. | |
| 1.3 | An extremely luminous, cool star found in the upper-right of the HR diagram; among the largest stars by radius. | |
| 1.4 | A hot but very dim stellar remnant found in the lower-left of the HR diagram; approximately Earth-sized, the end state of low-to-intermediate mass stars. | |
| 1.5 | A classification scheme (O, B, A, F, G, K, M) based on stellar absorption lines and surface temperature; O is hottest, M is coolest. | |
| 1.6 | The total power output of a star, typically measured in watts or solar luminosities; plotted on the vertical axis of the HR diagram. | |
| 1.7 | A measure of a star's intrinsic brightness; defined as the apparent magnitude the star would have at a standard distance of 10 parsecs. | |
| 1.8 | The relation L = 4πR²σT&sup4; relating a star's luminosity, radius, and surface temperature. | |
| 1.9 | The relation λmaxT = 2.898 × 10−3 m K, which links peak emission wavelength to surface temperature. | |
| 1.10 | The position on a star cluster's HR diagram where the most massive stars still undergoing core hydrogen fusion depart from the main sequence; used to determine cluster age. |
2. True or false — with correction
Circle T or F. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 On the HR diagram, temperature increases from left to right (hot stars are on the right). T / F
2.2 A star with the same temperature as the Sun but 100 times its luminosity must have a radius 10 times larger, because R ∝ √L at fixed T. T / F
2.3 White dwarfs are found in the upper-right of the HR diagram because they are very bright. T / F
2.4 The spectral sequence from hottest to coolest is O, B, A, F, G, K, M. T / F
2.5 The main sequence turn-off point of a star cluster indicates the distance to that cluster. T / F
2.6 A red giant is cool but luminous; from L = 4πR²σT&sup4;, this implies it must have a very large radius. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word or phrase is used once. 8 marks (1 per blank)
Word bank:
luminosity · left · main sequence · radius · spectroscopic parallax · Stefan-Boltzmann · temperature · turn-off point
The HR diagram plots ___________ on the vertical axis against surface ___________ on the horizontal axis, with temperature increasing to the ___________. Stars spend most of their lives on the ___________, fusing hydrogen in their cores. The ___________ law, L = 4πR²σT&sup4;, explains how a star’s ___________ accounts for the position of red giants and white dwarfs. The age of a star cluster can be estimated from its ___________, the most massive point still on the main sequence. The technique of ___________ uses a star’s spectral type and HR diagram position to determine its distance.
4. Function recall
Answer each question in 1–2 sentences using precise physics terms. 8 marks (2 each)
4.1 What does the Stefan-Boltzmann law tell us about two stars that have the same surface temperature but different luminosities?
4.2 How does Wien’s displacement law allow astronomers to determine a star’s surface temperature from its spectrum?
4.3 Why does a more massive star on the main sequence have a shorter lifetime than a less massive star?
4.4 Why are star clusters particularly useful for testing stellar evolution theory?
5. Label the HR diagram
The diagram below shows the HR diagram with five regions marked A–E. Identify each region and give one characteristic property. 10 marks (1 name + 1 property each)
| Region | Name of stellar group | One characteristic property |
|---|---|---|
| A | ||
| B | ||
| C | ||
| D | ||
| E |
Q1 — Term–definition match
1.1 main sequence • 1.2 red giant • 1.3 supergiant • 1.4 white dwarf • 1.5 spectral type • 1.6 luminosity • 1.7 absolute magnitude • 1.8 Stefan-Boltzmann law • 1.9 Wien’s displacement law • 1.10 main sequence turn-off point.
Q2 — True / false with correction
2.1 False. Temperature increases to the left on the HR diagram — hot O-type stars are on the left; cool M-type stars are on the right. This is a common exam trap.
2.2 True. From L = 4πR²σT&sup4; at fixed T, L ∝ R², so R ∝ √L. If L = 100 L⊙, then R = √100 = 10 R⊙.
2.3 False. White dwarfs are found in the lower-left of the HR diagram. They are hot (high T, blue-white colour) but very dim (low L) due to their tiny, Earth-sized radius.
2.4 True. The sequence O, B, A, F, G, K, M runs from hottest (~30 000 K) to coolest (~3 000 K). Mnemonic: “Oh Be A Fine Girl/Guy Kiss Me.”
2.5 False. The main sequence turn-off point indicates the age of the cluster, not its distance. Distance can be found by spectroscopic parallax.
2.6 True. A red giant has low T but high L. Since L = 4πR²σT&sup4;, a large L with small T&sup4; requires a very large R (hundreds to thousands of solar radii).
Q3 — Cloze paragraph
In order: luminosity / temperature / left / main sequence / Stefan-Boltzmann / radius / turn-off point / spectroscopic parallax.
Q4.1 — Stefan-Boltzmann and radius
Two stars with the same surface temperature (same T&sup4; term) but different luminosities must differ in radius. From L = 4πR²σT&sup4;, the more luminous star has a larger radius, since R ∝ √L at constant T. For example, a subgiant and a red giant both at ~4 500 K but at different luminosities differ only in size.
Q4.2 — Wien’s law and temperature
Wien’s displacement law states λmaxT = 2.898 × 10−3 m K. By measuring the peak wavelength (λmax) of a star’s continuous spectrum (the wavelength at which it emits most intensely), astronomers can solve for T = 2.898 × 10−3 / λmax. A blue star peaking at ~300 nm has T ≈ 10 000 K; a red star peaking at ~700 nm has T ≈ 4 100 K.
Q4.3 — Why massive stars live shorter lives
More massive main sequence stars are far more luminous (L ∝ M3.5), meaning they consume their hydrogen fuel at a much faster rate. The main sequence lifetime scales as t ∝ M/L ∝ M−2.5. A 10 M⊙ star burns its fuel ~102.5 ≈ 316 times faster than the Sun relative to its mass, giving it a lifetime of only ~30 Myr compared to ~10 Gyr for the Sun.
Q4.4 — Why star clusters are useful
All stars in a cluster formed at the same time from the same molecular cloud, so they share the same age and initial chemical composition. When plotted on the HR diagram, their main sequence turn-off point directly reveals the cluster age: the most massive stars still on the main sequence define how long the cluster has been evolving. This removes the uncertainty of comparing stars with unknown ages or different initial compositions.
Q5 — HR diagram labels
A: Upper main sequence — hot, luminous, massive O/B-type stars (T > 10 000 K; L > 100 L⊙). B: Main sequence (Sun’s position) — G-type star; T ≈ 5 800 K; L = 1 L⊙; hydrogen-burning in core. C: Red giants — cool (T ≈ 3 000–5 000 K), luminous (L ≈ 10–1 000 L⊙), enormous radius (10–100 R⊙). D: Supergiants — very high luminosity (>10 000 L⊙), large range of temperatures; very large radii (>100 R⊙). E: White dwarfs — hot (T = 10 000–100 000 K) but very dim (L < 0.01 L⊙); very small radius (~R⊕); electron-degenerate remnants.