Final answer:
To find the required distance from a 650-kHz radio station to receive only one photon per second per square meter, the energy of a single photon is calculated using Planck's equation, the total number of photons emitted per second is found from the station's power, and the inverse square law is applied to determine the distance.
Step-by-step explanation:
To answer the question 'How far away must you be from a 650-kHz radio station with power 50.0 kW for there to be only one photon per second per square meter?', we need to apply the concepts of electromagnetic wave propagation and the quantization of energy represented by photons.
First, we determine the energy of a single photon at the given frequency using Planck's equation, which is E = hf, where h is Planck's constant and f is the frequency. The power output of the radio station is given, and from that, we would calculate the total number of photons emitted per second. This number is the power divided by the energy per photon.
Since the radio waves spread out uniformly in all directions, the intensity of the radio waves decreases with the square of the distance from the source. Thus, we can set up an equation that relates the desired number of photons hitting a square meter per second to the intensity of the radio waves at a certain distance from the radio station.
The calculation will involve finding the square root of the power output divided by the product of the desired number of photons per second per square meter, the energy per photon, and 4π (since radio waves form a spherical wavefront as they travel). The answer would match one of the provided options, and considering constants and units, we can solve for the required distance.