Question

A galaxy moves away from the Earth at a speed of 3.9 × 104 km/s.

The speed of light is 3.0 × 105 km/s.
Light from the galaxy is emitted with a wavelength of 6.2 × 10−7 m.
Calculate the change in the wavelength of the light that is received by an observer on the Earth.

Answer 1

The change in the wavelength of light due to the relative motion of the source and observer is given by the equation:

Δλ/λ = v/c

where Δλ is the change in wavelength, λ is the original wavelength, v is the relative velocity between the source and observer, and c is the speed of light.

Plugging in the values given in the problem, we get:

Δλ/6.2 × 10−7 m = 3.9 × 104 km/s / 3.0 × 105 km/s

Simplifying this expression, we get:

Δλ = 1.02 × 10^-7 m

Therefore, the change in the wavelength of light that is received by an observer on the Earth is 1.02 × 10^-7 m.