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

Solution

Physics sir · 4 steps

Red shift means the galaxy recedes: the fractional change in wavelength equals v over c.

1. Doppler shift. The observed wavelength is longer than the emitted one, so the light is red-shifted and the galaxy is moving away. When v ≪ c, the fractional shift in wavelength equals the speed divided by the speed of light.

   Δλ/λ = v/c

2. Find the shift. Δλ = 5896 - 5890 = 6 Å, and the emitted wavelength is λ = 5890 Å.
3. Put in numbers. v = c Δλ/λ = 3 × 10⁸ × 6/5890 ≈ 3.06 × 10⁵ m s⁻¹.
4. So. The galaxy recedes at about 306 km s⁻¹, which is option (a).

The idea to keep. For light from moving sources, use Δλ/λ = v/c. A longer observed wavelength means the source is moving away, and a shorter one means it is approaching.

Answer from the NTA final answer key. Solution by PrepWiser.