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A line spectrum includes the wavelength 382 nm. When analysing light from a distant galaxy, this line is measured to be at 396 nm. Calculate the recessional speed of the galaxy in km s-1. Give the unit in the form "km s-1". Give your answer to three significant figures.

Question

A line spectrum includes the wavelength 382 nm. When analysing light from a distant galaxy, this line is measured to be at 396 nm. Calculate the recessional speed of the galaxy in km s-1. Give the unit in the form "km s-1". Give your answer to three significant figures.

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Solution

To calculate the recessional speed of the galaxy, we can use the formula for redshift:

z = Δλ/λ0

where:

  • z is the redshift,
  • Δλ is the change in wavelength (396 nm - 382 nm), and
  • λ0 is the original wavelength (382 nm).

First, calculate the change in wavelength:

Δλ = 396 nm - 382 nm = 14 nm

Then, calculate the redshift:

z = Δλ/λ0 = 14 nm / 382 nm = 0.03665

The redshift is related to the recessional speed v by the formula:

v = z * c

where c is the speed of light (approximately 3.00 x 10^5 km/s).

So, the recessional speed of the galaxy is:

v = 0.03665 * 3.00 x 10^5 km/s = 10995 km/s

Rounding to three significant figures, the recessional speed of the galaxy is 11000 km s-1.

This problem has been solved

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