Question

(a) At what wavelength will we observe a spectral line emitted at 500 nm by a star (b) At what wavelength will we observe the Ca II line (with rest wavelength 397.0 (c) A cloud of neutral hydrogen (HI) emits the so-called "21-cm line" (actually moving toward us at 100 km/s? nm) emitted by a galaxy receding at 60,000 km/s? 21.11 cm, at rest frequency 1420.2 MHz) while moving away at 200 km/s. At what frequency will we observe this line?

Answer 1

From the relativistic doppler effect the wavelength of source measured by an observed which is at rest and the source moving towards the observers = > lambda_observed = lambda_source times squareroot 1 - v/c/1 + v/c = 500 times 10^-9 times squareroot 1 - 100 times 10^3/3 times 10^8/1 + 100 times 10^3/3 times 10^8 m = 499.83 nm For a source receding at 60,000 km/s. For receding object. lambda_observed = lambda_source squareroot c + v/c - v = 397 times 10^-9 squareroot 3 times 10^8 + 60,000 times 10^3/3 times 10^8 - 60,000 times 10^3 m = 486.22 times 10^-9 m = 486.22 nm Freq = 1420.2 MHZ When source moving away, frequency will decrease & wave length will increase, lambda_observed = lambda_source squareroot c + v/c - v = 21.11 times 10^-2 squareroot 3 times 10^8 + 200 times 10^3/3 times 10^8 - 200 times 10^3 therefore v_observed = v_source squareroot c - v/c + v = 1420.2 times 10^6 squareroot 3 times 10^8 - 200 times