Spectroscopy & Redshift Explorer

Two modes. Emission Spectra displays the visible spectral lines of five elements on an interactive spectrum diagram. Redshift Calculator computes cosmological redshift, recession velocity, and Hubble-law distance from rest and observed wavelengths. Six presets from nearby galaxies to distant quasars.

Mode

Presets

Element

Hydrogen Emission Spectrum

Hydrogen (H) Spectral Lines

Line	Wavelength	Color
Hδ	410.2 nm	Visible
Hγ	434.0 nm	Visible
Hβ	486.1 nm	Visible
Hα	656.3 nm	Visible

Element

Hydrogen (H)

Visible Lines

Min Wavelength

410.2 nm

Max Wavelength

656.3 nm

Reference Guide

Electromagnetic Spectrum

Light is electromagnetic radiation. The visible portion spans roughly 380 nm (violet) to 750 nm (red). Shorter wavelengths carry more energy per photon according to the Planck-Einstein relation.

E = h\nu = \frac{hc}{\lambda}

Where $h$ is Planck's constant (6.626 × 10⁻³⁴ J·s), $\nu$ is frequency, and $\lambda$ is wavelength.

Violet380 - 450 nm Blue450 - 490 nm Green490 - 570 nm Yellow570 - 590 nm Orange590 - 620 nm Red620 - 750 nm

Emission & Absorption Lines

When electrons in an atom transition between energy levels, they emit (or absorb) photons at specific wavelengths. These produce bright emission lines or dark absorption lines in a spectrum, acting as a fingerprint for each element.

\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)

The Rydberg formula for hydrogen, where $R_H = 1.097 \times 10^7 \text{ m}^{-1}$ . The Balmer series (visible) has $n_1 = 2$ , giving lines at 410.2, 434.0, 486.1, and 656.3 nm.

Doppler Effect & Redshift

When a light source moves away from the observer, its wavelengths are stretched (redshifted). When it approaches, wavelengths are compressed (blueshifted). The cosmological redshift $z$ quantifies this shift.

z = \frac{\lambda_{\text{obs}} - \lambda_{\text{rest}}}{\lambda_{\text{rest}}}

For recession velocities much less than the speed of light, $v \approx zc$ . At higher redshifts the relativistic Doppler formula is needed. Most distant galaxies and quasars show positive $z$ , confirming the expansion of the universe.

Hubble's Law & the Expanding Universe

Edwin Hubble discovered that galaxies are receding from us at speeds proportional to their distance. This relationship is the foundation of modern cosmology.

v = H_0 \, d

The Hubble constant $H_0 \approx 67.4 \text{ km/s/Mpc}$ (Planck 2018). One megaparsec (Mpc) is about 3.26 million light-years. Combined with redshift measurements, Hubble's law lets us estimate the distance and lookback time to remote objects.

d = \frac{v}{H_0} = \frac{zc}{H_0}