Question:
A galaxy is moving away from the Earth so that a spectral line at 6000 Å is observed at 6300 Å. Then the speed of the galaxy with respect to the Earth is
A galaxy is moving away from the Earth so that a spectral line at 6000 Å is observed at 6300 Å. Then the speed of the galaxy with respect to the Earth is
Updated On: Dec 26, 2024
- 500 km/s
- 150 km/s
- 200 km/s
- 1500 km/s
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The Correct Option is A
Solution and Explanation
The observed shift in wavelength \( \Delta \lambda = 6300 - 6000 = 300 \, \text{Å} \) is due to the Doppler effect.
The formula for the Doppler shift in wavelength for light is:
\( \Delta \lambda = \frac{v}{c} \lambda \)
where \( v \) is the velocity of the galaxy,
\( c \) is the speed of light, and
\( \lambda \) is the initial wavelength.
Substituting the known values, we calculate the speed of the galaxy as 500 km/s.
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