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[[Image:TubeSpectrum.jpg|thumb|300px|right|Spectrum of the X-rays emitted by an [[X-ray tube]] with a [[rhodium]] target, operated at 60 [[kilovolt|kV]]. The continuous curve is due to ''[[bremsstrahlung]]'', and the spikes are [[Energy-dispersive X-ray spectroscopy|characteristic K lines]] for rhodium. The Duane–Hunt law explains why the continuous curve goes to zero at 21 [[picometer|pm]].]]
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The '''Duane–Hunt law''', named after the American physicists [[William Duane (physicist)|William Duane]] and [[Franklin Hunt]],<ref>{{cite journal
| author = William Duane and Franklin L. Hunt
| year = 1915
| title = On X-Ray Wave-Lengths
| journal = [[Physical Review]]
| volume = 6
| issue = 2
| pages = 166–172
| doi =  10.1103/PhysRev.6.166
|bibcode = 1915PhRv....6..166. }}</ref> gives the maximum [[frequency]] of [[X-rays]] that can be emitted by [[Bremsstrahlung]] in an [[X-ray tube]] by accelerating electrons through an excitation [[voltage]] ''V'' into a metal target.
 
The maximum frequency ''&nu;''<sub>max</sub> is given by<ref>Handbook of X-ray spectrometry by René Grieken, Andrzej Markowicz, page 3, [http://books.google.com/books?id=i_iDRTp75AsC&pg=PA3 Google books link]</ref>
:<math>
\nu_{\rm max} = \frac{eV}{h}\,
</math>
which corresponds to a minimum wavelength
:<math>
\lambda_{\rm min} = \frac{hc}{eV}
</math>
where ''h'' is [[Planck's constant]], ''e'' is the [[charge of the electron]], and ''c'' is the [[speed of light]]. This can also be written as:
:<math>\lambda_{\rm min} \approx \frac{1239.8 \text{ pm}}{V\text{ in kV}} \,</math>.
The process of X-ray emission by incoming electrons is also known as the inverse [[photoelectric effect]].
 
==Explanation==
In an [[X-ray tube]], electrons are accelerated in a vacuum by an [[electric field]] and shot into a piece of metal called the "target". X-rays are emitted as the electrons slow down (decelerate) in the metal. The output spectrum consists of a continuous spectrum of X-rays, with additional sharp peaks at certain energies (see graph on right). The continuous spectrum is due to ''[[bremsstrahlung]]'', while the sharp peaks are [[characteristic x-ray|characteristic X-rays]] associated with the atoms in the target.
 
The spectrum has a sharp cutoff at low wavelength (high frequency), which is due to the limited energy of the incoming electrons. For example, if each electron in the tube is accelerated through 60 [[kilovolt|kV]], then it will acquire a kinetic energy of 60 [[electron-volt|keV]], and when it strikes the target it can create X-ray [[photon]]s with energy of at most 60 keV, by [[conservation of energy]]. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray [[photon]]. Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of 60 keV or less has a wavelength of 21 [[picometer|pm]] or more, so the X-ray spectrum has exactly that cutoff, as seen in the graph. This cutoff applies to both the continuous (''bremsstrahlung'') spectrum and the [[characteristic x-ray|characteristic sharp peaks]]: There is no X-ray of any kind beyond the cutoff. However, the cutoff is most obvious for the continuous spectrum.
 
The exact formula for the cutoff comes from setting equal the kinetic energy of the electron, {{nowrap|''E'' {{=}} ''eV''}}, and the [[photon|energy of the X-ray photon]], {{nowrap|''E'' {{=}} ''h&nu;'' {{=}} ''hc/λ''}}.
 
== References ==
{{reflist}}
 
{{DEFAULTSORT:Duane-Hunt law}}
[[Category:X-rays]]

Revision as of 11:12, 11 February 2014

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