Power and frequency of photons and its relationship with biological safety I understand that x-rays are more dangerous than radio waves because they are of higher energy, since they have higher frequency. However, it’s less dangerous to stand near a radio station with a higher power output than to be near an x-ray machine with a lower power output. (This is what I’ve been told, anyway.) Why is that the case? Is power not energy per unit time? Should a lower power indicate lower energy (and therefore greater safety) regardless of the frequency of the wave?
 A: There are two types of energy involved, and the blurring of this distinction is cause of a huge number of misunderstandings.
Light comes in discrete packets called photons. The energy of each photon is proportional to the frequency of the light. On top of that, a light beam can have any number of photons in it, and this gives it its overall power. The power of the beam is the energy it transmits per unit time:
$$
\text{power}=\frac{\text{energy}}{\text{time}}=(\text{photon energy})\times\frac{\text{no. of photons}}{\text{unit time}}.
$$
It is perfectly possible for an x-ray beam to transmit as much power as a radio beam, simply by having lots of radio photons and comparatively few x-ray ones.
Biological damage, on the other hand, is slightly different. The biomolecules inside cells that suffer radiation damage interact with individual photons, one at a time. 


*

*If the photon energy is small, the biomolecule can usually dispose of that extra energy in a safe manner, even if there are lots of small photons around - each photon gets handled in turn, unless there really are lots of photons around. 

*If the photon energy is big, on the other hand, the biomolecule needs to handle a large amount of energy in a single go, and this usually makes it change its chemical state into a bunch of pretty reactive fragments. 
This is why it’s less dangerous to stand near a radio station with a higher power output than to be near an x-ray machine with a lower power output.
