Calculate the energy of a photon of electromagnetic radiation at each of the fol

Question

Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies.

Calculate the energy of a photon of electromagnetic radiation at each of the following frequencies. 103.2 MHz (typical frequency for FM radio broadcasting) Express your answer using four significant figures. 1005 kHz (typical frequency for AM radio broadcasting) (assume four signifie; Express your answer using four significant figures. 835.6 MHz (common frequency used for cell phone communication) Express your answer using four significant figures.

Explanation / Answer

1) The energy of a photon with frequency, f is given by this equation:
E = hf, where h is Planck's constant
The frequency in this problem is given in MHz. One Hz = 1/s, and 1000 Hz = 1 MHz. We can use this to convert the given frequency to 1/s:
103.2 MHz * (1000 Hz/1 MHz) = 102,400 Hz = 103,200,000 1/s

Now we have both values for the energy equation:
h = 6.626 x 10^-34 m^2*kg/s
f = 103,200,000 1/s

So...
E = (6.626 x 10^-34 m^2*kg/s) * (103,200,000 1/s)
E = 6.83 x 10^-26 J
Each photon emitted from the radio station has an energy of 6.83 x 10^-26 Joules.

2) 1005 kHz = 1.005x10^6 Hz

This is actually a unit of frequency and not wavelength
E = hv = (6.626x10^-34 Js)(1.005x10^6 s-1) = 6.65x10^-28 J/photon or 6.65x10^-31 kJ/photon

Now, use Avogadro's number to convert to kJ/mol:

(6.65x10^-31 kJ/photon) x [(6.022x10^23 photons)/(1 mole)] = 4.01x10^-7 kJ/mole

3) E = (6.626 x 10^-34 m^2*kg/s) * (835,600,000 1/s)
E = 5.53 x 10^-25 J
Each photon emitted from the radio station has an energy of 5.53 x 10^-25 Joules.

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