Spectroscopy & Redshift Explorer

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.

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

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.

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.

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.

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.

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

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.