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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

2 Answers 2

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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. has a diagram of the wavelengths and frequencies of the various kinds of light.

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From Wikipedia:

The hertz (symbol Hz) is the unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves.

In English, "hertz" is also used as the plural form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, $10^3$ Hz), MHz (megahertz, $10^6$ Hz), GHz (gigahertz, $10^9$ Hz) and THz (terahertz, $10^{12}$ Hz). One hertz simply means "one cycle per second" (typically that which is being counted is a complete cycle); 100 Hz means "one hundred cycles per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz. The rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second (1/s or s$^{−1}$) in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radionuclide event per second.

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This does not appear to really answer the question, which asks where in the EM spectrum a particular frequency lies. – Sean Sep 10 at 23:56

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