Visible light diapason is 400 - 700 nm which is 1.43 - 2.5 Mhz.

If using an antenna I would broadcast steady sinusoidal wave in this range, why the EM emitted by the antenna are not visible?

Suppose the power source for antenna in a range of Kilo or Mega watts

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    $\begingroup$ 400nm is 750THz not 2.5MHz. Likewise 700nm light is 429THz. $\endgroup$ – John Rennie Mar 1 '14 at 19:27

$400$ - $700\text{ nm}$ corresponds to about $430$ - $750\text{ THz}$ ($10^{12}\text{ Hz}$), not $\text{MHz}$ ($10^6\text{ Hz}$).

To convert from wavelength to frequency, use

$$ f = \dfrac{c}{\lambda}, $$

where $\lambda$ is the wavelength, $f$ is the frequency and $c$ is the speed of light.

So, for $400\text{ nm}$, this is:

$$ f = \dfrac{299'792'458\ \mathrm{m}/\mathrm{s}}{400 \cdot 10^{-9}\ \mathrm{m}} \approx 7.49 \cdot 10^{14}\ \mathrm{s}^{-1} = 7.49 \cdot 10^{14}\ \mathrm{Hz}. $$

If one would build a half wavelength dipole antenna for a $700\text{ nm}$ wave, this would be $350\text{ nm}$ wide, i.e. only visible with a microscope. With a typical distance between atoms in matter of about $0.1\text{ nm}$, such an antenna would only span around 3500 atoms in length.

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    $\begingroup$ To end your answer: EM radiation from this tiny antenna could indeed be seen if powerful enough $\endgroup$ – WetSavannaAnimal Mar 3 '14 at 0:16
  • $\begingroup$ When I was a little kid, my chemistry set had a small cylindrical device with a lens on one end. I don't remember what it was called. You would sit in a dark closet and stare into the lense and you would see occasional flashes of light. Would this light be within the range discussed on this post? It's atomic in nature. $\endgroup$ – Fred Kline Sep 3 '14 at 21:22

This is primarily a biological question. We (humans in particular, mammals specifically) can't see radio waves because our bodies do not have the sensors to detect them. We can detect light in the visible spectrum because the rods and cones of our retina that constitute our light sensors absorb photons in that spectrum, ultimately activating neurons in our visual system. Other animals, such as birds (some species of which can see in the ultraviolet range), have photoreceptors that detect a different range of frequencies. I won't rule out the existence of animals (insects?) that can "see" EM energy at radio frequencies, via an eye or other type of sensory epithelia, but it's hard to see what the evolutionary advantage would be.

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    $\begingroup$ It's not that hard to see what the advantage would be, especially if they also had a way to transmit the same range of wavelengths. The advantage is long distance communication that isn't line-of-sight. The exact reason that we humans use it now. $\endgroup$ – reirab Jun 4 '15 at 18:40
  • $\begingroup$ @reirab sadly, this would only happen by evolution if having the receptor alone first helped in anything (for example, we already use mechanical waves for communication -talking-, but from the evolution standpoint, hearing alone is a very powerful tool, developing a sound producing mechanism is an advantage only after that) $\endgroup$ – Alvaro Jan 12 at 13:09

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