Final answer:
The number of photons per second produced by a 650-kHz radio station with a power output of 50.0 kW can be calculated using the Planck-Einstein relation to find the energy of a single photon and then dividing the station's power output by this energy.
Step-by-step explanation:
To calculate the number of photons per second emitted by a 650-kHz radio station with a power output of 50.0 kW, we must first determine the energy of a single photon and then divide the total energy per second (power of the radio station) by the energy of one photon.
The energy E of a photon can be calculated using the Planck-Einstein relation E = hf, where h is Planck's constant (6.626 x 10-34 J⋅s) and f is the frequency of the photon. In this case, the frequency f is 650 kHz, or 650,000 Hz. Therefore, the energy of one photon is E = (6.626 x 10-34 J⋅s) (650,000 Hz), which gives us the energy in joules.
Once we have the energy of a single photon, we can determine the number of photons emitted per second by dividing the total power output in joules per second (since 1 watt = 1 joule per second) by the energy of a single photon. This means dividing 50,000 J/s by the energy we calculated for a single photon.
After performing these calculations, we can then also calculate the level of photons at a distance of 100 km, assuming no losses due to reflection or absorption. The surface area of a sphere with a radius of 100 km must be considered to determine the photons per second per square meter.