Reading Starlight: Spectra, Composition, and the Doppler Shift
Lumi floats beside a glowing prism in a dim observatory, splitting a star's white beam into a rainbow band crossed by dark lines, gesturing toward a labeled wavelength scale on the dome wall.
- Distinguish emission spectra from absorption spectra by their bright versus dark lines.
- Explain how the pattern of spectral lines identifies which elements are present in a glowing object.
- Relate a continuous spectrum's peak wavelength to the object's surface temperature using Wien's Displacement Law.
- Predict whether a spectrum is redshifted or blueshifted from an object's line-of-sight motion.
- Interpret a shifted line set to state both direction and meaning of an object's radial velocity.
Key terms
- Absorption spectrum
- A continuous band of color crossed by dark lines where cooler intervening gas has removed its characteristic wavelengths.
- Emission spectrum
- Bright lines on a dark background produced when a thin hot gas radiates only its characteristic wavelengths.
- Wien's displacement law
- The relation λ_max = b ÷ T, with b ≈ 2.898 × 10⁻³ m·K, linking a blackbody's peak wavelength to its temperature.
- Doppler shift
- The shift of an object's whole line pattern to shorter (blue) or longer (red) wavelengths revealing its line-of-sight velocity.
Three Messages in One Spectrum
A single stellar spectrum simultaneously encodes composition, temperature, and radial velocity. The pattern of dark absorption lines or bright emission lines matches the quantum-defined wavelengths of specific elements, naming what the star is made of. The wavelength at which the underlying continuous spectrum peaks reveals surface temperature through Wien's law. Finally, any uniform shift of the entire line pattern records motion toward or away from us. Reading a spectrum is therefore a matter of asking these three separate questions of the same band of light.
Why Doppler Preserves the Fingerprint
A common worry is that a shifted spectrum signals changed composition, but the Doppler shift multiplies every wavelength by the same factor, sliding the whole pattern while keeping the relative spacing of the lines intact. Because the fingerprint's internal geometry is unchanged, the same elements remain identifiable; only the lines' absolute positions move. Contrast this with stellar rotation, which broadens each line symmetrically rather than displacing the whole set, showing that line shape and line position carry different physical information.
Worked examples
A star's continuous spectrum peaks at 450 nm. Estimate its surface temperature using Wien's law.
- Write Wien's law solved for temperature: T = b ÷ λ_max.
- Convert the peak to meters: 450 nm = 4.5 × 10⁻⁷ m.
- Divide: T = (2.898 × 10⁻³ m·K) ÷ (4.5 × 10⁻⁷ m) ≈ 6,440 K.
Answer: About 6,400 K — hotter than the Sun's 5,778 K, consistent with a peak shifted toward the blue end.
Activity
Match each spectral clue to the property of the star it reveals.
Practice
A star shows the hydrogen line pattern but every line is displaced toward longer wavelengths. State both the direction and meaning of its radial motion.
Explain why an emission spectrum and an absorption spectrum of the same element show lines at the same wavelengths despite looking opposite.
Common mistakes to avoid
- A redshifted star is made of different elements.The Doppler shift slides the whole fingerprint while preserving relative line spacing, so the same elements are still identified.
- Stellar rotation shifts the whole spectrum like recession.Rotation broadens each line symmetrically rather than displacing the entire pattern in one direction as Doppler recession does.
Check your understanding
A spectrum shows several dark lines cutting across an otherwise continuous rainbow band. What kind of spectrum is this?
Two stars have identical line patterns, but Star B's entire pattern is shifted toward longer wavelengths compared to Star A. Star B is made of completely different elements than Star A — true or false?
A classmate says a star's redshifted lines mean the star is now made of different elements than before. Which response best corrects this reasoning?
Wien's Displacement Law shows that a star's continuous spectrum peaks near 450 nm (blue end of the visible band). What does this most directly indicate about the star?
Recap
A single spectrum yields three measurements at once: composition from the line pattern, temperature from the peak wavelength via Wien's law, and radial velocity from how far the whole line set has Doppler-shifted while keeping its spacing.
Reflect
Which of the three properties a spectrum reveals do you find most surprising that light can carry, and why?