Chapter 24, Problem 35 Your answer is partially correct. Try again. Review Inter

Question

Chapter 24, Problem 35 Your answer is partially correct. Try again. Review Interactive Solution 24.35 to see one model for solving this problem. A distant galaxy emits light that has a wavelength of 703.2 nm. On earth, the wavelength of this light is measured to be 708.0 nm. (a) Decide whether this galaxy is approaching or receding from the earth. (b) Find the speed of the galaxy relative to the earth. (Give your answer to 4 significant digits. Use 2.998 x 108 m/s as the speed of light.) (a) The galaxy is [ receding from the earth. (b) Numbe Uni the tolerance is +/-2%

Explanation / Answer

(A)
We start with the Doppler equation : fo = fs (1+-(Vrel/c))

The light is shifted to longer wavelengths, which means smaller frequencies:f = c/

Thus, fo < fs Which means that the parenthesis (1+-(Vrel/c)) must be < 1

Therefore, the correct sign in the parentheses is the – sign: the galaxy is
moving away from earth

(B)

From the Doppler equation:

Vrel = c(1- (fo/fs))

but = f = c /

Thus

Vrel = c(1- (s/o))

= 2.998*10^8 * (1 - (703.2nm/708.0nm) = 2.0325*10^6 m/s

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