Hydrogen also produces spectral lines at radio wavelengths,...

Hydrogen also produces spectral lines at radio wavelengths, notably at $21.1 \mathrm{cm} .$ If a galaxy is moving away from us at $10 \%$ of the speed of light, at what wavelength will we detect this line? Convert this into a frequency.

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Key Concepts

Doppler Shift

The Doppler shift describes the change in wavelength (or frequency) of waves, such as light, due to the relative motion between the source and the observer. When an object is moving away, the waves are stretched, leading to longer wavelengths, a phenomenon known as redshift.

Redshift

Redshift is a measure of how much the wavelength of light has been increased due to the recessional motion of an astronomical object. It is quantified by the parameter z, where z = (?_observed - ?_rest) / ?_rest, and provides valuable insight into the speed at which an object is moving away from us.

Wavelength-Frequency Relationship

The relationship between wavelength and frequency in the context of electromagnetic radiation is governed by the equation c = ??, where c is the speed of light. This inverse relationship means that an increase in wavelength due to redshift corresponds to a decrease in frequency.

Relativistic Doppler Shift

At velocities that are appreciable fractions of the speed of light, the relativistic Doppler shift formula must be used to accurately account for time dilation and other relativistic effects. This ensures that the computed observed wavelengths and frequencies are precise, even when the motion involves significant fractions of c.

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