To determine the motion of a star based on the measured wavelength, we can use the concept of redshift and blueshift. When an object is moving away from us, its light is shifted towards longer wavelengths, known as redshift. Conversely, when an object is moving towards us, its light is shifted towards shorter wavelengths, known as blueshift.
In this case, if the measured wavelength is 410 nm instead of the expected 411 nm, we observe a blueshift. This indicates that the star is moving towards us. To estimate the star's speed, we can use the formula for Doppler shift:
v = (Δλ / λ) * c,
where v is the velocity of the star, Δλ is the difference between the measured wavelength and the expected wavelength, λ is the expected wavelength, and c is the speed of light.
Using this formula, we can calculate the velocity as follows:
v = (411 nm - 410 nm) / 411 nm * c.
To obtain a numerical value, we need to know the value of c, the speed of light. In a vacuum, the speed of light is approximately 299,792 kilometers per second (km/s). Plugging in this value, we can calculate the star's velocity.
v = (1 nm / 411 nm) * 299,792 km/s.
Calculating this expression, we find:
v ≈ 729.9 km/s.
Therefore, based on the measured blueshift of 410 nm instead of the expected 411 nm, the star is moving towards us at an estimated speed of approximately 729.9 kilometers per second.