Final answer:
The star is moving at a speed of 907.0 km/s away from the Earth, as determined by the redshift of the Calcium H line from 396.9 nm to 398.1 nm using the Doppler effect formula.
Step-by-step explanation:
The H line in Calcium is observed to be shifted from its normal wavelength of 396.9 nm to 398.1 nm in a star's spectrum. To determine the speed of the star and whether it is moving towards or away from the Earth, we can use the Doppler effect formula for light:
v = c × (Δλ / λ), where:
- v is the radial velocity of the star
- c is the speed of light (approximately 3 × 108 m/s)
- Δλ is the change in wavelength (398.1 nm - 396.9 nm)
- λ is the original wavelength (396.9 nm)
First, convert nanometers to meters by multiplying by 10-9. Then calculate Δλ and plug all values into the equation to calculate the star's velocity. Since the observed wavelength is longer than the rest wavelength, the spectral line is redshifted, indicating the star is moving away from Earth. Using the formula allows us to calculate the exact velocity.
Therefore, the correct answer is:
4- 907.0 km/s away from the Earth