What is the wavelength of a radio photon from an "AM" radio station that broadcasts at 1160 kilohertz?What is its energy in joules
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To determine the wavelength of a radio photon, we can use the formula:
wavelength = speed of light / frequency
where the speed of light is approximately 3.00 x 10^8 meters per second.
First, let's convert the frequency of the "AM" radio station from kilohertz (kHz) to hertz (Hz). We know that 1 kilohertz is equal to 1000 hertz, so:
frequency = 1160 kilohertz = 1160 x 1000 hertz = 1,160,000 hertz
Now we can substitute the values into the formula:
wavelength = (3.00 x 10^8 meters per second) / (1,160,000 hertz)
Calculating this, we find the wavelength to be approximately 258.62 meters.
To determine the energy of the radio photon in joules, we can use the formula:
energy = Planck's constant x frequency
where Planck's constant is approximately 6.63 x 10^-34 joule-seconds.
Substituting the values:
energy = (6.63 x 10^-34 joule-seconds) x (1,160,000 hertz)
Calculating this, we find the energy to be approximately 7.67 x 10^-26 joules.