For a specific wavelength $$670$$ nm of light coming from a galaxy moving with velocity $$v$$, the observed wavelength is $$670.7$$ nm. The value of $$v$$ is

We use the Doppler effect for light to find the velocity of the galaxy.

Actual wavelength: $$\lambda_0 = 670$$ nm

Observed wavelength: $$\lambda = 670.7$$ nm

Since $$\lambda > \lambda_0$$, the galaxy is moving away (redshift).

For a source moving away at non-relativistic speed:

$$\frac{\Delta\lambda}{\lambda_0} = \frac{v}{c}$$

$$\Delta\lambda = 670.7 - 670 = 0.7 \text{ nm}$$

$$v = \frac{\Delta\lambda}{\lambda_0} \times c = \frac{0.7}{670} \times 3 \times 10^8$$

$$v = \frac{7}{6700} \times 3 \times 10^8 = \frac{21 \times 10^8}{6700}$$

$$v = 3.134 \times 10^5 \text{ m s}^{-1}$$

$$v \approx 3.13 \times 10^5 \text{ m s}^{-1}$$

Hence, the correct answer is Option B.