Cosmology
5 marks · NormalLight from a galaxy has a measured wavelength of 660 nm. The same absorption line in the Sun's spectrum has a wavelength of 600 nm.
Calculate the change in wavelength observed for the galaxy's light compared to the Sun's light.
Using the Doppler equation, calculate the speed at which the galaxy is moving away from Earth. Use the speed of light as m/s.
State whether this galaxy is moving towards or away from Earth, and explain your answer.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 60 nm · must show correct subtraction
(b) The speed is 3.0×10^7 m/s (or 30,000 km/s), away from Earth. m/s · must show substitution, correct use of formula, final speed
(c) Away from Earth. The observed wavelength is longer (red-shift), indicating the galaxy is receding. · must show correct reasoning
Also accept: accept result in m/s or km/s for calculation
Common mistakes: Confusing change in wavelength direction; Misuse of the Doppler formula
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Correct calculation of change in wavelength (660 - 600 = 60 nm).
M1 (b) · 1 mark · Correct substitution into Doppler equation and rearrangement. (follow-through)
A2 (b) · 1 mark · Accurate calculation of speed value using correct units. (follow-through)
A3 (b) · 1 mark · Correct conversion if necessary (e.g., km/s or m/s accepted). (follow-through)
B1 (c) · 1 mark · Correct statement that galaxy is moving away and clear reference to red-shift.
Worked solution
a) Change in wavelength = 660 nm - 600 nm = 60 nm.
b) Rearranging: = (60 nm / 600 nm) × (3.0 × 10^8 m/s)
c) The observed wavelength is longer than the reference (red-shift), so the galaxy is moving away from Earth.