Spectroscopy, Redshift & Hubble Law Lab

Every element leaves a unique fingerprint of spectral lines. When a galaxy moves away from us, those lines shift toward longer wavelengths. Measure redshift, calculate recession velocity, and estimate cosmological distances with Hubble's Law.

Guided Experiment: Emission Spectra & Element Fingerprints

Each element produces a unique set of spectral lines. Can you identify an element by its emission spectrum alone? Do all elements produce the same number of visible lines?

Write your hypothesis in the Lab Report panel, then click Next.

Visible Spectrum

Hα656.3 nmHβ486.1 nmHγ434 nmHδ410.2 nm400450500550600650700750Wavelength (nm)

Controls

Spectral Lines for Hydrogen
Hα: 656.3 nmHβ: 486.1 nmHγ: 434 nmHδ: 410.2 nm

Emission Spectrum

HHydrogen

4 visible emission lines. Each line corresponds to an electron transition between specific energy levels.

LineWavelengthColorSeries
Hα656.3 nmBalmer
Hβ486.1 nmBalmer
Hγ434 nmBalmer
Hδ410.2 nmBalmer
E=hν=hcλE = h\nu = \frac{hc}{\lambda}

Photon energy is inversely proportional to wavelength

Data Table

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#TrialElement/GalaxyRest λ(nm)Observed λ(nm)zVelocity(km/s)Distance(Mpc)
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Reference Guide

Emission & Absorption Spectra

When atoms are excited, electrons jump to higher energy levels. As they fall back down, they emit photons at specific wavelengths determined by the energy difference between levels.

E=hν=hcλE = h\nu = \frac{hc}{\lambda}

Each element produces a unique set of spectral lines. Hydrogen's visible Balmer series includes Hα (656.3 nm, red), Hβ (486.1 nm, cyan), Hγ (434.0 nm, blue), and Hδ (410.2 nm, violet). Astronomers use these fingerprints to identify elements in distant stars and nebulae.

Doppler Effect & Redshift

When a light source moves away from the observer, its wavelengths are stretched (redshifted). Moving toward the observer compresses them (blueshifted). The redshift z quantifies this shift.

z=λobs−λrestλrestz = \frac{\lambda_{\text{obs}} - \lambda_{\text{rest}}}{\lambda_{\text{rest}}}

For non-relativistic speeds (z much less than 1), the recession velocity is v = zc, where c is the speed of light (2.998 × 10⁸ m/s). Positive z means the object is moving away (redshift); negative z means it is approaching (blueshift).

Hubble's Law

Edwin Hubble discovered in 1929 that galaxies are moving away from us with velocities proportional to their distances. This provided the first evidence for an expanding universe.

v=H0 d  ⟹  d=vH0v = H_0 \, d \implies d = \frac{v}{H_0}

The Hubble constant H₀ ≈ 70 km/s/Mpc determines the expansion rate. A galaxy receding at 7,000 km/s is about 100 Mpc (326 million light-years) away. The precise value of H₀ is still actively debated (the "Hubble tension").

Cosmological Distance

Measuring spectral line shifts is the primary tool for determining distances to galaxies beyond the reach of parallax and standard candle methods.

  • Nearby galaxies (z < 0.01) are tens of Mpc away
  • Moderate redshift galaxies (z ≈ 0.1) are hundreds of Mpc away
  • Distant quasars (z > 1) are billions of light-years away
  • The cosmic microwave background has z ≈ 1100

At high redshifts, the simple v = zc formula overestimates velocity because relativistic effects and the expansion history of the universe become important. The lookback time tells us how long ago the light we observe was emitted.