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Question

With what speed should a galaxy move outward with respect to earth so that the Sodium-D line at wavelength 5890 Å is observed at 5896 Å?


A

306 km/sec

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B

322 km/sec

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C

296 km/sec

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D

336 km/sec

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Solution

The correct option is A

306 km/sec


Step 1: Speed and Wavelength.

  1. Speed- The pace at which an object's location changes in any direction.
  2. Wavelength- The wavelength is the distance between successive crests or troughs.
  3. We know that speed of light is 3×108m/s

Step 2: Calculations

f=f0=1+β1β

ff0=1+β1β

[1+Δff0]2=(1+β)(1β)1

[1+2Δff0]2=(1+2β)

β=Δff0=vc

v=6×c5890=6×3×108ms5890=0.003056×108=305.6kms306kms

Final Answer: The correct option is (a)306 km/sec


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