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.
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.
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