High School

Your favorite radio station broadcasts at a frequency of 98.1 MHz with a power of 52.5 kW. How many photons does the antenna of the station emit each second?

A. \(7.15 \times 10^{29}\)
B. \(8.08 \times 10^{29}\)
C. \(9.13 \times 10^{29}\)
D. \(1.03 \times 10^{30}\)
E. \(1.17 \times 10^{30}\)
F. \(1.32 \times 10^{30}\)
G. \(1.49 \times 10^{30}\)
H. \(1.68 \times 10^{30}\)

Answer :

Final answer:

The antenna of the radio station emits approximately 8.08 x 10^29 photons in each second. So the correct option is B: 8.08 x 10²⁹ photons.

Explanation:

The number of photons emitted by an antenna can be calculated using the formula:

N = (P x t) / E

Where:

  • N is the number of photons emitted
  • P is the power of the radio station (in Watts)
  • t is the time (in seconds)
  • E is the energy of each photon (in Joules)

To calculate the number of photons emitted per second, we need to divide the power by the energy of each photon. The energy of a photon can be calculated using the formula:

E = hf

Where:

  • E is the energy of each photon
  • h is the Planck's constant (6.626 x 10-34 J·s)
  • f is the frequency of the radio station (in Hz)

Using the given values:

  • Power (P) = 52.5 kW = 52,500 W
  • Frequency (f) = 98.1 MHz = 98.1 x 106 Hz
  • Planck's constant (h) = 6.626 x 10-34 J·s

We can substitute these values into the formulas to find the number of photons emitted:

E = (6.626 x 10-34 J·s) x (98.1 x 106 Hz) = 6.493 x 10-18 J

N = (52,500 W) / (6.493 x 10-18 J) = 8.08 x 1029 photons

Therefore, the number of photons emitted by the antenna of the radio station in each second is approximately 8.08 x 1029.

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