A hydrogen line emitted at 656 nm is observed at 672.4 nm in a galaxy's spectrum. Calculate the galaxy's recession speed in km/s, taking c = 3.0 x 10^5 km/s.

Astrophysics Challenge #1 — Red Shift

The red shift
of a galaxy.

Astrophysics Medium

Problem

In a distant galaxy’s spectrum, a hydrogen line normally emitted at 656 nm is observed at 672.4 nm. Calculate the galaxy’s recession speed, in km/s.

Emitted wavelength\( \lambda = 656\ \mathrm{nm} \)
Observed wavelength\( 672.4\ \mathrm{nm} \)
Speed of light\( c = 3.0 \times 10^5\ \mathrm{km/s} \)
Answer inkm/s

The non-relativistic Doppler formula is accurate at these speeds.

Hint: the red shift is the fractional stretch: \( z = \tfrac{\Delta\lambda}{\lambda} \). Find z first — the recession speed is that same fraction of the speed of light.

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Up next · Measurements Convert the Rocket's Speed Keep the streak going — a fresh problem in Measurements.

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The red shiftof a galaxy.

Problem

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The red shift
of a galaxy.