Please help me solve this!
The spectrum of the sodium atom is detected in the light from a distant galaxy. If the 590.0 nm line is redshifted to 658.5 nm, at what speed is the galaxy receding from the Earth?
To solve this problem, we can use the formula for Doppler effect:
(Δλ / λ) = (v / c)
Where Δλ is the change in wavelength, λ is the original wavelength, v is the velocity of the source or observer, and c is the speed of light.
In this case, the original wavelength (λ) is 590.0 nm, and the redshifted wavelength (Δλ) is 658.5 nm. We need to solve for v, the velocity of the galaxy.
First, let's rearrange the formula to solve for v:
v = (Δλ / λ) * c
Substituting the values:
v = (658.5 nm - 590.0 nm) / 590.0 nm * c
Now, let's calculate the velocity:
v = (68.5 nm / 590.0 nm) * 299,792,458 m/s
v ≈ 34,416 km/s
Therefore, the galaxy is receding from the Earth at a speed of approximately 34,416 km/s.