23.4 Spectra of Light

Types of Spectra

When light from a source is passed through a prism or diffraction grating, the resulting pattern of wavelengths is called a spectrum. There are three main types:

1. Continuous Spectrum

A continuous spectrum contains all wavelengths of visible light (like a rainbow). It is produced by hot, dense objects such as the filament of an incandescent bulb or the interior of a star.

2. Emission Line Spectrum

An emission line spectrum consists of discrete bright lines on a dark background. It is produced when atoms of a hot, low-pressure gas are excited (e.g., by an electric discharge). Electrons in the excited atoms jump from higher energy levels to lower ones, emitting photons of specific wavelengths:

$E=hf=\frac{hc}{\lambda }$

Because energy levels are quantised, only specific wavelengths are emitted — giving a unique spectral "fingerprint" for each element.

3. Absorption Line Spectrum

An absorption line spectrum consists of dark lines on a continuous (rainbow) background. It is produced when white light passes through a cool, low-pressure gas. The gas atoms absorb photons whose energies exactly match the energy differences between their quantised levels, removing those wavelengths from the continuous spectrum.

Hydrogen Spectral Series

Hydrogen produces several series of spectral lines, each corresponding to electron transitions ending at a particular energy level $n_f$:

The Balmer series is the only series visible to the naked eye and is the most important for astronomical observations.

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Redshift

Redshift is the observed increase in the wavelength (shift toward the red end of the spectrum) of light received from a distant astronomical object compared to the wavelength emitted by the same element in a laboratory.

If a galaxy is moving away from Earth, the light waves are stretched, increasing their wavelength. This is the Doppler effect applied to light.

The fractional redshift $z$ is defined as:

$z=\frac{\Delta \lambda }{{\lambda }_0}=\frac{{\lambda }_{\text{observed}}-{\lambda }_{\text{emitted}}}{{\lambda }_{\text{emitted}}}$

For recession speeds $v\ll c$, the Doppler formula gives:

$z\approx \frac{v}{c}$

So the recession velocity of a galaxy can be calculated from its redshift:

$v=z\cdot c=\frac{\Delta \lambda }{{\lambda }_0}\cdot c$

Worked Example

A hydrogen absorption line normally at ${\lambda }_0=486\text{ nm}$ is observed at $\lambda =491\text{ nm}$ in a distant galaxy's spectrum.

$z=\frac{491-486}{486}=\frac{5}{486}\approx 0.0103$

$v=zc=0.0103\times 3\times 10^8\approx 3.1\times 10^6{\text{ m s}}^{-1}$

The galaxy is receding at approximately $3.1\times 10^6{\text{ m s}}^{-1}$.

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Redshift and the Expanding Universe

Edwin Hubble observed that virtually all distant galaxies show redshift — they are all moving away from us. Furthermore, the more distant the galaxy, the greater its redshift (and hence recession speed). This is summarised in Hubble's Law.

The universal observation of redshift leads to the conclusion that the universe is expanding — not that Earth is at the centre, but that space itself is stretching, carrying galaxies apart from one another.

This expanding universe, traced back in time, implies that all matter originated from a single point in an event known as the Big Bang.

Key Points:

• Redshift of spectral lines in distant galaxies → galaxies are receding
• Greater distance → greater redshift → faster recession
• Expansion is uniform in all directions
• Running the expansion backwards → Big Bang origin