A star is moving away from an observer at 1% of the speed of light. At what wavelength would the observer find an emission line which would occur at a wavelength of 6000 Angstroms if the star were at rest?
a. 6060 Angstroms
b. 6010 Angstroms
c. 6000 Angstroms
d. 5940 Angstroms
C
To find the wavelength observed by the observer when the star is moving away, we can use the formula for the Doppler effect:
Δλ/λ = v/c
where Δλ is the change in wavelength, λ is the rest wavelength, v is the velocity of the star, and c is the speed of light.
Given that the speed of the star is 1% of the speed of light, we can calculate the change in wavelength:
Δλ/λ = 0.01
Δλ = 0.01 * λ
Substituting the values given, we find:
Δλ = 0.01 * 6000 Angstroms
Δλ = 60 Angstroms
Now, to find the observed wavelength, we add the change in wavelength to the rest wavelength:
Observed wavelength = λ + Δλ
Observed wavelength = 6000 Angstroms + 60 Angstroms
Observed wavelength = 6060 Angstroms
Therefore, the correct answer is:
a. 6060 Angstroms
To solve this question, we can use the formula for the Doppler effect, which relates the observed wavelength to the actual wavelength of light emitted by a moving source. The formula is given as:
λ(observed) = λ(actual) * (1 + v/c)
Where:
- λ(observed) is the observed wavelength
- λ(actual) is the actual wavelength emitted by the source
- v is the speed of the source relative to the observer
- c is the speed of light in a vacuum
In this case, the observed wavelength (λ(observed)) is given as 6000 Angstroms, and the speed of the star relative to the observer (v) is 1% of the speed of light.
To find the actual wavelength (λ(actual)), we can rearrange the formula:
λ(actual) = λ(observed) / (1 + v/c)
Substituting the given values:
λ(actual) = 6000 Angstroms / (1 + 0.01)
Calculating this:
λ(actual) = 6000 Angstroms / 1.01
λ(actual) ≈ 5940 Angstroms
Therefore, the observer would find an emission line at an actual wavelength of approximately 5940 Angstroms. Hence, the correct answer is option d.
Relative change in frequency = v/c
Where v is the speed that the body moves away at, and c is the speed of light.
Relative change in frequency = - (Relative change in Wavelength)
=> - (Relative change in Wavelength) = v/c
=> -(Change in wavelength/Original Wavelength) = v/c
Plug in your values.