A highly energetic cosmic event in a distant galaxy simultaneously emits a pulse of radio waves with wavelength λradio=1.5 km\lambda_{\text{radio}} = 1.5\text{ km}λradio=1.5 km and a pulse of gamma rays with wavelength λgamma=3.0 pm\lambda_{\text{gamma}} = 3.0\text{ pm}λgamma=3.0 pm. Both pulses travel through the vacuum of interstellar space to a detector on Earth.
What is the ratio of their travel times, tradiotgamma\displaystyle \frac{t_{\text{radio}}}{t_{\text{gamma}}}tgammatradio, and what is the ratio of the energy of a single gamma-ray photon to a single radio photon, EgammaEradio\displaystyle \frac{E_{\text{gamma}}}{E_{\text{radio}}}EradioEgamma?
tradiotgamma=1\frac{t_{\text{radio}}}{t_{\text{gamma}}} = 1tgammatradio=1 and EgammaEradio=5.0×1014\frac{E_{\text{gamma}}}{E_{\text{radio}}} = 5.0 \times 10^{14}EradioEgamma=5.0×1014
tradiotgamma=1\frac{t_{\text{radio}}}{t_{\text{gamma}}} = 1tgammatradio=1 and EgammaEradio=2.0×10−15\frac{E_{\text{gamma}}}{E_{\text{radio}}} = 2.0 \times 10^{-15}EradioEgamma=2.0×10−15
tradiotgamma=2.0×10−15\frac{t_{\text{radio}}}{t_{\text{gamma}}} = 2.0 \times 10^{-15}tgammatradio=2.0×10−15 and EgammaEradio=5.0×1014\frac{E_{\text{gamma}}}{E_{\text{radio}}} = 5.0 \times 10^{14}EradioEgamma=5.0×1014
tradiotgamma=5.0×1014\frac{t_{\text{radio}}}{t_{\text{gamma}}} = 5.0 \times 10^{14}tgammatradio=5.0×1014 and EgammaEradio=2.0×10−15\frac{E_{\text{gamma}}}{E_{\text{radio}}} = 2.0 \times 10^{-15}EradioEgamma=2.0×10−15