By what factor does the energy of a 1-nm x-ray photon exceed that of a 10-mhz radio photon

3x10^10, or 30 billion times as much energy. The energy of a photon is expressed as E = hf where E = energy h = Planck constant f = frequency of photon We've been given the frequency of 1 of the photons (radio), but have been only given the wavelength of the other (x-ray). So let's convert from wavelength to frequency. We can perform the conversion from wavelength to frequency by dividing the speed of light by the wavelength, so 299792458 m/s / 1e-9 m = 2.99792458x10^17 Hz 2.99792458x10^17 Hz / 1e6 = 2.99792458x10^11 mHz Looking at the equation for photon energy, we don't need to bother with Planck constant since we're just dealing with relative energy between the photons. So let's divide the frequency of the x-ray photon with the radio photon. 2.99792458x10^11 mHz / 10 mHz = 2.99792458x10^10 Rounding to 1 significant figure gives 3x10^10. So the x-ray photon has about 30 billion times the energy as the radio photon.