What speed should a galaxy move with respect to us so that the sodium line at `589.0 nm` is observed at `589.6 nm` ?

Explanation

To solve the problem, we need to determine the speed at which a galaxy must move away from us so that the sodium line originally at a wavelength of \( 589.0 \, \text{nm} \) is observed at a wavelength of \( 589.6 \, \text{nm} \). We will use the formula for the Doppler effect for light, which relates the change in wavelength to the velocity of the source.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Original wavelength (\( \lambda_0 \)): \( 589.0 \, \text{nm} \)
- Observed wavelength (\( \lambda \)): \( 589.6 \, \text{nm} \)
- Change in wavelength (\( \Delta \lambda \)):
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