To calculate the speed of a star based on the observed shift in the wavelength of a spectral line, we can use the formula for the Doppler effect:
v = (Δλ / λ) * c
Where: v is the velocity of the star, Δλ is the change in wavelength (observed wavelength - rest wavelength), λ is the rest wavelength, and c is the speed of light.
Given: Rest wavelength (λ) = 121.6 nm Observed wavelength (λ') = 122.4 nm Speed of light (c) = 3 × 10^8 m/s
First, let's calculate the change in wavelength:
Δλ = λ' - λ Δλ = 122.4 nm - 121.6 nm Δλ = 0.8 nm
Now we can calculate the velocity of the star:
v = (Δλ / λ) * c v = (0.8 nm / 121.6 nm) * (3 × 10^8 m/s)
Converting nm to meters: v = (0.8 × 10^-9 m) / (121.6 × 10^-9 m) * (3 × 10^8 m/s) v = (0.8/121.6) * 3 m/s
v ≈ 0.0198 * 3 m/s v ≈ 0.0594 m/s
Therefore, the speed of the star based on the observed shift in the wavelength of the spectral line is approximately 0.0594 meters per second.