Theme E — Nuclear and Quantum Physics
E.5.5 The Hertzsprung–Russell (HR) Diagram — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 42 of 45 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
E.5.5 The Hertzsprung–Russell (HR) Diagram — IB PHYSICS SL notes: Interpret the HR diagram using luminosity, temperature and mass relationships to place stars and follow their evolution.Hertzsprung and Russell independently plotted luminosity against temperature.Luminosity L = to…
- Temperature T is surface temperature in kelvin
- The Sun is class G
- The diagram shows only stable phases
- A star radiates as a black body
- What the symbols mean
- For two stars L1/L2
Part 1 of 7Axes of the diagram
1
Hertzsprung and Russell independently plotted luminosity against temperature.
2Luminosity L
Luminosity L total power radiated by a star, in watts or relative to the Sun (L☉ = 3.83 × 1026 W).
- The axis is logarithmic — each gridline is a factor of ten or more, not an equal addition.
3Temperature T is surface temperature in kelvin
- Temperature T is surface temperature in kelvin plotted backwards, hot on the left, cool on the right.
- Hot stars are about 40 000 K and cool stars about 3000 K.
4
The temperature axis may be labelled by spectral class O, B, A, F, G, K, M or by colour from blue to red.
Part 2 of 7Regions of the diagram
| Region | Position | Features |
|---|---|---|
| Main sequence | Diagonal band, top left to bottom right | Stars fusing hydrogen; about 90% of stars; luminosity rises with surface temperature |
| Red giants | Above the main sequence, right | Cool but luminous, so very large |
| Red supergiants | Very top right | Luminosity up to 106 L☉; larger still |
| White dwarfs | Bottom left | Hot but dim, so very small |
1The Sun is class G
- 5800 K and 1 L☉.
2The diagram shows only stable phases
- The diagram shows only stable phases transitions are short; black holes emit no light.
Part 3 of 7Stefan–Boltzmann law and radius
Stefan–Boltzmann law and radius
A star radiates as a black body
- L = σAT4 = 4πR2σT4.What the symbols mean: L = luminosity, the total power emitted (W) · σ = 5.67 × 10−8 W m−2 K−4 · r = radius of the star (m) · A = surface area (m2) · T = surface temperature (K)
- σ = 5.67 × 10-8 W m-2 K-4, R is the radius and T is in kelvin.
For two stars L1/L2
(R1/R2)2(T1/T2)4.
Giants are large
- Giants are large they have similar or lower temperature than the Sun yet far greater luminosity, so their area is large.
Lines of constant radius run diagonally
- Lines of constant radius run diagonally with larger radii toward the top right.
Two stars at the same point have the same radius
- Two stars at the same point have the same radius whatever their mass.
Part 4 of 7Mass–luminosity relation
1For main-sequence stars L ∝ M3.5
- For main-sequence stars L ∝ M3.5 with M in solar masses.
- A star of twice the Sun's mass is about 23.5, roughly 11 times as luminous.
2Lifetime goes as M/L ∝ M-2.5
- Lifetime goes as M/L ∝ M-2.5 so heavy stars live short lives.
3
Mass increases from bottom right to top left along the main sequence.
4
The relation does not apply to giants, supergiants or white dwarfs.
Part 5 of 7Evolution on the diagram
1
A protostar moves down and left toward the main sequence.
2After leaving the main sequence a star moves up and right
- After leaving the main sequence a star moves up and right it expands and cools to the giant region.
3
A low-mass star later moves left across the diagram, then down to the white dwarf region as it fades.
4
A massive star moves across to the supergiant region.
5Cluster turn-off point
- Cluster turn-off point stars above it have left the main sequence; its position gives the cluster's age.
- A turn-off at lower luminosity means an older cluster.
Part 6 of 7Using the diagram
1
Use temperature, colour or class for the horizontal position.
2
Use luminosity for the vertical position.
3
Find the radius from L = 4πR2σT4.
4
Classify the star as main sequence, giant or white dwarf.
1Plot a star by temperature and luminosity relative to the Sun
- Plot a star by temperature and luminosity relative to the Sun the Sun is at 1 on the luminosity axis.
2Stars in a cluster are at the same distance
- Stars in a cluster are at the same distance matching apparent brightness against a standard main sequence gives the cluster distance.
Part 7 of 7More from the specification
Stellar spectra and energy levels
- Stellar spectra and energy levels absorption line classifications on HR diagrams correspond to quantum electron jumps between distinct atomic energy levels.
The Hertzsprung-Russell (HR) Diagram and Stellar Classes
- The HR diagram plots stellar luminosity against surface temperature (or spectral class, in reverse temperature order); main sequence stars occupy a diagonal band, red giants and supergiants lie at the upper right,
- (or absolute magnitude)
- and white dwarfs lie at the bottom left.
Nuclear Fusion and Hydrostatic Equilibrium in Main Sequence Stars — In main sequence stars, hydrogen nuclei undergo nuclear fusion reactions in the core to produce helium nuclei (via the proton-proton chain or CNO cycle); the vast thermal energy released creates outward gas and radiation pressure that balances inward gravitational collapse.
Stellar Evolution and Post-Main-Sequence Core Collapse
- When core hydrogen is exhausted, fusion ceases and radiation pressure drops,
- causing gravitational contraction of the helium core; outer layers expand and cool into a giant star,
- where stellar atmospheres produce characteristic dark absorption lines in their continuous emission spectra.
Wavelength
- Distance between a point on one wave and the same point on the next wave
Stellar parallax
- Apparent shift of a nearby star against distant stars as Earth orbits the Sun.
Binding energy
- The minimum energy required to separate the nucleons of a nucleus to infinity.
Emission spectrum
- The set of discrete wavelengths emitted by excited atoms of an element.
Energy level
- A discrete energy an electron in an atom can have
Kinetic energy
- K = ½mv2, energy of motion.
Continuous spectrum
- Spectrum with no gaps between the regions.
Fusion
- Joining of light nuclei into a heavier one.
Pressure
- Force per unit area, P = F/A.What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Helium
- Product of the fusion of hydrogen in stars.
Nucleus
- Small, dense, positively charged centre of the atom.
Absorption
- The conversion of wave energy to internal energy of the medium.
Reaction
- The partner force acting on the other object.
Parallax
- Apparent shift between objects caused by viewing from different positions
Photon
- A quantum of electromagnetic energy, E = hfWhat the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Key terms
| Term | Meaning |
|---|---|
| Luminosity | Total power radiated by a star. |
| HR diagram | Plot of luminosity against surface temperature or spectral class. |
| Main sequence | Band of stars fusing hydrogen in their cores. |
| Stefan–Boltzmann law | L = σAT4 for a black body. |
| Turn-off point | Place where cluster stars leave the main sequence, showing the age. |
| Spectral class | Classification O, B, A, F, G, K, M by temperature. |
Avoid these mistakes
1
Reading the temperature axis left to right as increasing — it decreases.
2
Thinking giants are hot — they are cool and large, luminous because of their area.
3
Applying L ∝ M3.5 to white dwarfs and giants — it is only for main-sequence stars.
4
Using temperature in degrees Celsius in L = 4πR2σT4 — use kelvin.
5
Treating the luminosity scale as linear — it is logarithmic.
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