Physics

Physics

Problem

In hydrogen spectrum the wavelength of HαH_\alpha line is 656 nm, whereas in the spectrum of a distant galaxy, HαH_\alpha line wavelength is 706 nm. Estimate the speed of the galaxy with respect to earth. a. 2×1082 \times 10^8 m/s b. 2×1072 \times 10^7 m/s c. 2×1062 \times 10^6 m/s d. 2×1052 \times 10^5 m/s
Intuitive explanation

This is a Doppler shift problem—when a light source moves away from you, its wavelength stretches (redshift). The key insight is that the fractional change in wavelength directly tells you the fractional change in velocity: Δλλ≈vc\frac{\Delta \lambda}{\lambda} \approx \frac{v}{c} for speeds much less than light. Since the galaxy's HαH_\alpha line is shifted to a longer wavelength, it's moving away, and you can use this ratio to find its recession speed.

Intuitive explanation

This is a Doppler shift problem—when a light source moves away from you, its wavelength stretches (redshift). The key insight is that the fractional change in wavelength directly tells you the fractional change in velocity: Δλλ≈vc\frac{\Delta \lambda}{\lambda} \approx \frac{v}{c} for speeds much less than light. Since the galaxy's HαH_\alpha line is shifted to a longer wavelength, it's moving away, and you can use this ratio to find its recession speed.

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