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In the Feynman Lectures Vol. 1, it says that the Synchrotron at the California Institute of Technology is capable of producing electromagnetic Radiations with a frequency of $10^{24}$ cycles per second. Since I'm not familiar with cycles, I'd like to know where this lies in the UV Spectrum.

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You know the speed of light and can easily look up the wavelength of various parts of the spectrum EM... –  dmckee Jun 2 '12 at 18:19
    
Yes, but the frequencies are all in Hertz. –  Graviton Jun 2 '12 at 18:20
    
Yes. And you know the speed of light and the wavelength from which you can trivially compute the frequency. –  dmckee Jun 2 '12 at 18:21
    
But how does that have anything to do with "cycles"? Using the wave equation with SI units will only get me as far as Hertz. –  Graviton Jun 2 '12 at 18:22
    
And one Hertz is...? This is a place where you need to think about the meaning of the words in English. What is a cycle? –  dmckee Jun 2 '12 at 18:23

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I usually remember that red light is about 700nm and blue light about 400nm. Ultraviolet is shorter than blue so it's less than 400nm and I suppose extends down to the soft X-ray region.

Anyhow, wavelength, $\nu$, and frequency, $f$, are related by the simple equation:

$$ \nu f = c $$

where $c$ is the speed of light. So red light is about $4 \times 10^{14}$Hz and blue light is about $7.5 \times 10^{14}$Hz. A frequency of $10^{24}$Hz would be $3 \times 10^{-17}$m which is far far shorter than even X-rays. I think you're into the gamma ray range.

http://en.wikipedia.org/wiki/Electromagnetic_spectrum has a diagram of the wavelengths and frequencies of the various kinds of light.

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