Astronomers use the Doppler shift in the Balmer series ofthe hydrogen spectrum t

Question

Astronomers use the Doppler shift in the Balmer series ofthe

   hydrogen spectrum to determine the radial speed ofa galaxy. The

   fractional change in the wavelength of the spectralline is given by Z= / o = - o /o = (1+v/c /(1-v/c)) -1 .

Once this quantity is measured for a

   particular receding galaxy, the speed of recessioncan be found by

   solving for v. One measured Z value of Z = 2.8 hasbeen measured for

   several quasars(squasi-stellar radio sources). Howfast are these

   quasars moving away from us?

Explanation / Answer

.      Z = / o = - o /o = (1+v/c /(1-v/c)) - 1 . For Z = 2.8 : .       2.8 = (1+v/c /(1-v/c)) -1 . or (1+v/c /(1-v/c)) = 2.8 + 1 =3.8 . or   (1+v/c /(1-v/c)) = (3.8)2  = 14.44 . or   (1+v/c )    = 14.44 * (1-v/c) . or v/c + 14.44 (v/c) = 14.44 - 1 = 13.44 . or 15.44 (v/c)   = 13.44 . or v/c    = 0.870 . or v = 0.870 c . Hope this helps u!

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