An FM radio station of frequency 107.7MHz puts out a signal of 50,000W. How many photons/s are emitted?
To calculate the number of photons emitted per second by an FM radio station, we need to know the energy of each photon.
The energy of a photon can be calculated using the equation:
E = h * f
where E is the energy of the photon, h is the Planck's constant (6.626 x 10^-34 J⋅s), and f is the frequency of the radio signal.
In this case, the frequency of the radio signal is given as 107.7 MHz, which needs to be converted to Hz.
1 MHz = 1,000,000 Hz
Converting the frequency to Hz:
f = 107.7 MHz * (1,000,000 Hz / 1 MHz)
f = 107,700,000 Hz
Now we can calculate the energy of each photon by substituting the values into the equation:
E = (6.626 x 10^-34 J⋅s) * (107,700,000 Hz)
E ≈ 7.120 x 10^-18 J
Since the power emitted by the radio station is given as 50,000 W, we divide the power by the energy of each photon to find the number of photons emitted per second:
Number of photons/s = Power / Energy
Number of photons/s = 50,000 W / (7.120 x 10^-18 J)
Number of photons/s ≈ 7.022 x 10^21 photons/s
Therefore, approximately 7.022 x 10^21 photons are emitted per second by the FM radio station.