We observe an absorption line of Oxygen at 504 nm in Star A and at 508 nm in Star B. We know in the lab
this line has a wavelength of 500 nm. Which statement correctly describes the motions of Star A and B?
Group of answer choices
Star B is moving towards us half as fast as Star A
Star B is moving away from us half as fast as Star A
Star B shares the same motion as Star A
Star B is moving towards us twice as fast as Star A
Star B is moving away from us twice as fast as Star A
Based on the observed wavelengths of the absorption line, we can conclude that Star B is moving away from us twice as fast as Star A.
To determine the motions of Star A and Star B based on the observed absorption line wavelengths, we can use the concept of redshift and blueshift.
The observed wavelength of an absorption line is determined by the Doppler effect, which occurs when the light source and the observer are moving relative to each other. When an object is moving towards the observer, the observed wavelength of light is compressed, resulting in a blueshift (shift to shorter wavelengths). On the other hand, when an object is moving away from the observer, the observed wavelength is stretched, resulting in a redshift (shift to longer wavelengths).
In this case, Star A shows the oxygen absorption line at 504 nm, which is longer than the laboratory wavelength of 500 nm. This indicates a redshift, implying that Star A is moving away from us. Similarly, Star B shows the oxygen absorption line at 508 nm, also longer than the laboratory wavelength. So, Star B is also moving away from us.
To determine the relative speeds of Star A and Star B, we compare their wavelengths. The difference between the observed wavelength and the laboratory wavelength of the absorption line is proportional to the velocity of the star. Assuming a linear relationship, we can say that the velocity is directly proportional to the wavelength difference.
Star A has a wavelength difference of 504 nm - 500 nm = 4 nm.
Star B has a wavelength difference of 508 nm - 500 nm = 8 nm.
Since the velocity is directly proportional to the wavelength difference, we can conclude that Star B is moving away from us twice as fast as Star A. Therefore, the correct statement is:
Star B is moving away from us twice as fast as Star A.
To determine the motions of Star A and B based on the observed absorption line shifts, we can use the Doppler effect equation, which states that the observed wavelength shift is directly related to the motion of the source relative to the observer:
Δλ/λ = V/C,
where Δλ is the observed wavelength shift, λ is the laboratory wavelength, V is the velocity of the source, and C is the speed of light.
In this case, the observed absorption line of Oxygen in Star A is at 504 nm, while in Star B it is at 508 nm. The laboratory wavelength for this line is 500 nm.
Let's determine the velocity of Star A first. By substituting the values into the Doppler effect equation:
(504 nm - 500 nm) / 500 nm = V_A / C.
4 nm / 500 nm = V_A / C.
V_A = (4 nm / 500 nm) * C.
Now let's determine the velocity of Star B by using the same equation:
(508 nm - 500 nm) / 500 nm = V_B / C.
8 nm / 500 nm = V_B / C.
V_B = (8 nm / 500 nm) * C.
Comparing the velocities V_A and V_B, we can see that Star B has a higher velocity than Star A. However, to determine the ratio between their velocities, we need to calculate the ratio:
V_B / V_A = [(8 nm / 500 nm) * C] / [(4 nm / 500 nm) * C].
Canceling out the common factors:
V_B / V_A = 8 nm / 4 nm.
V_B / V_A = 2.
This means that Star B is moving away from us twice as fast as Star A. Therefore, the correct statement is:
Star B is moving away from us twice as fast as Star A.