Galaxies that are 400 million light years away have a red shift of 0.03 approximately. A radio wave coming from one of these galaxies has an observed wavelength of 125 meters. What is the emitted wavelength in meters and the observed frequency in Megahertz

Respuesta :

Answer:

The correct answer is "121.36 meters and 2.40 MHz".

Explanation:

Given:

Red shift,

[tex]\frac{v}{c}=\frac{\lambda - \lambda_0}{\lambda_0} = 0.03[/tex]

Wavelength,

[tex]\lambda = 125 \ meters[/tex]

The observed frequency will be:

⇒ [tex]f = \frac{c}{\lambda}[/tex]

      [tex]=\frac{3\times 10^8}{125}[/tex]

      [tex]=24\times 10^5[/tex]

      [tex]= 2.40\times 10^6[/tex]

      [tex]=2.40 \ MHz[/tex]

hence,

The Emitted wavelength will be:

⇒ [tex]\frac{125-\lambda_0}{\lambda_0} =0.03[/tex]

   [tex]\frac{125}{\lambda_0}-1 =0.03[/tex]

         [tex]125=1.03 \ \lambda_0[/tex]

           [tex]\lambda_0=\frac{125}{1.03}[/tex]

                [tex]=121.36 \ m[/tex]