A pulsar lies 1000 light years from Earth. The average plasma concentration is 1 el/cc (note units!). Using the plasma dispersion relationship for group speed, what is the group delay between a pulsar pulse received at 1 GHz and at 800 MHz??? Please show the analytical solution where you have expanded (using a Taylor series keeping the constant and first order terms) the solutions at both frequencies about a total transit time of 1000 years (speed of light in a vacuum result) such that subtracting one from the other leaves just the delay that is of order of 1 second.