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If the power output of a 650-kHz radio station is 50.0 kW, how many photons per second are produced?

a) (1.20 × 10²¹) photons/s
b) (2.68 × 10²¹) photons/s
c) (1.95 × 10²¹) photons/s
d) (1.38 × 10²¹) photons/s

User Suzanna
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1 Answer

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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.

User HAJJAJ
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