Question:
With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 \(\mathring{A}\) is observed at 5896 \(\mathring{A}\) ?
With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 \(\mathring{A}\) is observed at 5896 \(\mathring{A}\) ?
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For speeds much smaller than c, \(\frac{\Delta\lambda}{\lambda} = \frac{v}{c}\) (red shift for a receding source).
Updated On: Nov 4, 2026
- 306 km/sec
- 322 km/sec
- 296 km/sec
- 336 km/sec
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The Correct Option is A
Solution and Explanation
For a receding source with \(v \ll c\): \(\frac{\Delta\lambda}{\lambda} = \frac{v}{c}\).
\(\Delta\lambda = 5896 - 5890 = 6\ \mathring{A}\).
\(v = c\,\frac{\Delta\lambda}{\lambda} = 3 \times 10^5\ \text{km/s} \times \frac{6}{5890} \approx 305.6\ \text{km/s} \approx 306\ \text{km/s}\).
Answer: (1) 306 km/sec
\(\Delta\lambda = 5896 - 5890 = 6\ \mathring{A}\).
\(v = c\,\frac{\Delta\lambda}{\lambda} = 3 \times 10^5\ \text{km/s} \times \frac{6}{5890} \approx 305.6\ \text{km/s} \approx 306\ \text{km/s}\).
Answer: (1) 306 km/sec
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