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The formula $E=hf$ shows the energy contained in one photon. Here, we use the simple half wave dipole antenna to evaluate the energy of photons at different frequencies. Surprisingly that gives a different relation between Photon energy and its frequency.

Half wave dipole antenna is a special antenna. At resonance frequency, there is no return loss, and all the applied energy will radiate. Its resistance at resonance frequency is 73 ohms, regardless of the resonance frequency.

For a current source of I applied to the antenna, we have

$P=R\times I\times I$, $R=73\;\Omega$ , So $P$ is constant

Energy of one cycle $=P/f$ $f=$frequency

$E=P/f$
$E$ is the energy of one cycle which is related to the quantum concept, and its energy is inversely proportional to the frequency!

In the case of light photons, bonding energy of the electron plays the major role in emission characteristic, where the formula $E=hf$ completely works. But in antennas, electrons move freely inside the antenna's conductor that produce electromagnetic waves.

jtn
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2 Answers2

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"E is the energy of one cycle which is related to the quantum concept". No, not true. The energy of a photon doesn't relate to "cycles" in this way in the theory. Indeed, for a monochromatic photon one calculates its propagation by assuming an endless train of waves.

John Doty
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In your scenario, you keep the power P constant;then it is no wonder that the energy is inversely proportional to the frequency, since it merely means that you calculate the energy in a shorter time interval, if you increase the frequency.

The energy of a single photon is not related to the power P of your device.
So you really are comparing two different energies.

Martin
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