Question

How much of a gravitational redshift should you expect for a spectral line of the Sun observed in deep space if it has a rest wavelength of 121.6nm?

Answer 1

According to the gravitational redshift
   
where, R is the radius of the sun. And by definition
   is the Schwarzschild radius of the sun. So, we get
  
  
Now the radius of the sun and the Schwarzschild radius of the sun are
    ,   
so, we see that
  
hence we use the Binomial expansion

  
Hence the redshift defined as
  
is given by
   
Now putting the given values for the sun, we get
  
   
So, the wavelength of the spectral line on the sun is
  
  so, the shift is
  
  

Now as , so, to first order in z, we have
  
  
And for the given values
   and.     
we get the shift in the wavelength