The wavelength of a particular spectrum line is 6000 A in the laboratory. The wavelength of the same line is observed to be 6020 A in the spectrum of a star. Then which of the following is correct?

  1. The star is moving away from earth with a speed of 105 m/s
  2. The star is moving towards earth with a speed of 105 m/s
  3. The star is moving towards earth with a speed of10m/s
  4. The star is moving away from earth with a speed of 10m/s

Answer (Detailed Solution Below)

Option 3 : The star is moving towards earth with a speed of10m/s
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Detailed Solution

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CONCEPT:Doppler effect of light

  • Doppler shift is also known as the Doppler effect is defined as the change in the wavelength or frequency of the waves with respect to the observer who is in motion relative to the wave source.
  • The phenomenon was described in the year 1842 by the Austrian physicist Christian Doppler.

CALCULATION:

Given λA = 6020 Å and λs = 6000 Å

  • Doppler's shift is given by,

     -----(1)

Where, Δλ = doppler shift(Å), v = velocity(m/s), λS = wavelength of source(Å), and c = speed of light = 3×108 m/s

     -----(2)

By equation 1 and equation 2,

  • The negative sign shows that the star is moving towards the earthHence, option 3 is correct.

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