To determine the speed at which the distant galaxy is receding from us, we can make use of the concept of redshift. The formula for calculating the redshift is given by:
z = (observed wavelength - rest wavelength) / rest wavelength
where z is the redshift. In this case, the observed wavelength is 400 nm, and the rest wavelength is 300 nm.
Plugging in the values into the formula:
z = (400 nm - 300 nm) / 300 nm z = 100 nm / 300 nm z = 1/3
The redshift (z) is equal to the velocity of recession (v) divided by the speed of light (c), according to the Hubble's law:
z = v / c
Rearranging the equation, we can solve for the velocity of recession:
v = z * c v = (1/3) * c
The speed of light (c) is approximately 299,792 kilometers per second.
v ≈ (1/3) * 299,792 km/s v ≈ 99,930.67 km/s
Therefore, the galaxy is receding from us at a speed of approximately 99,930.67 kilometers per second.