1. Given data

• Original wavelength of sodium-D line: $\lambda = 5890\,\mathring{A}$
• Observed wavelength: $\lambda' = 5896\,\mathring{A}$

Since the observed wavelength is greater, the galaxy is moving away from Earth, so this is a red shift.

2. Use Doppler shift formula for light

For small speeds compared to the speed of light, $\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$ where $\Delta \lambda = \lambda' - \lambda = 5896 - 5890 = 6\,\mathring{A}$

Thus, $\frac{v}{c} = \frac{6}{5890}$

3. Calculate the speed

Taking $c = 3 \times 10^5\ \text{km/s}$ we get $v = 3 \times 10^5 \times \frac{6}{5890}$

$v \approx 3 \times 10^5 \times 0.0010187$

$v \approx 305.6\ \text{km/s}$

So, $v \approx 306\ \text{km/s}$

4. Match with options

• A: $306$ km/s ✅
• B: $322$ km/s
• C: $296$ km/s
• D: $336$ km/s

Therefore, the correct option is A.