1. The problem statement, all variables and given/known data Does an AM radio station broadcasting at 750 KHz emit enough energy to ionize a hydrogen atom? 2. Relevant equations Frequency = 7.5E+5 /s Ionization E of H atom = 2.18E-18 J Planck constant h = 6.625E-34 J-s AM Radio speed = c Energy AM radio wave = h*frequency 3. The attempt at a solution This is a topic on my study guide. I am a little confused about the concept of the radio station energy emissions. My calculation for energy of a 750KHz AM radio frequency results in 4.97E-28 J. Is this the amount of energy emitted by the station in 1 second? I am not sure about this, but I am guessing that the station emits 4.97E-28 J continuously, and that an H ion requires 2.18E-18 J continuously in order to remain ionized. So my initial calculations say that there is not enough energy coming from the radio station. Any tips here would be appreciated!
Your initial calculation is quite correct but the picture is somewhat wrong. Ionization happens when one sufficiently energetic photon hits an atom and knocks an electron free. There is no need for 'continuous power'. From the data given you have no idea how much power the station is putting out. You have just computed the energy per photon. You don't know how MANY photons. But that is enough to answer the question. The photons are too weak. It takes something more like ultraviolet to ionize hydrogen.