Duane Hunt Law

The Duane-Hunt law (also Duane-Hunt's law of displacement , named after the American physicists William Duane and Franklin Hunt ) describes the relationship between the acceleration voltage of an X-ray tube and the maximum frequency or the minimum wavelength of its brake spectrum .

Since electrons emit photons when generating X- rays instead of absorbing them as in the photoelectric effect , the law is also known as the inverse photoelectric effect .

Mathematical derivation

Spectrum of X-rays from a copper anode. The horizontal axis shows the deflection angle after Bragg reflection on a LiF crystal

The maximum energy that an electron can give off in an X-ray tube is the kinetic energy it received during acceleration. The conservation of energy is now applied.

${\displaystyle E_{\text{Elektrisch}}=E_{\text{Strahlung}}}$, with inserted sizes ${\displaystyle eU=h\nu _{\text{max}}}$

Adjusted according to the frequency this results in: The maximum frequency includes the minimum wavelength with Planck's quantum , the speed of light , the acceleration voltage and the elementary charge . ${\displaystyle \nu _{\text{max}}={\frac {eU}{h}}\,.}$ ${\displaystyle \lambda _{\text{min}}={\frac {hc}{eU}}}$ ${\displaystyle h}$ ${\displaystyle c}$ ${\displaystyle U}$ ${\displaystyle e}$

If the natural constants are inserted into the equation, the following relationship results for the minimum wavelength:

${\displaystyle {\lambda _{\mathrm {min} }}={\frac {1{,}23984\,\mathrm {\mu Vm} }{U}}}$

With a given voltage of the X-ray tube, the minimum possible wavelength of the brake spectrum can be determined.

In the adjacent picture, the Bragg angle , which is directly dependent on the wavelength, is plotted against the intensity of the radiation. Where the intensity becomes 0 (at around 10 °) the wavelength of the X-ray radiation is minimal. If you increase the voltage, the zero crossing shifts further to the left, hence the name displacement law .

Web links

• X-ray spectrum ( Memento from April 28, 2010 in the Internet Archive )

literature

• W. Duane, FL Hunt: On X-Ray Wave-Lengths . In: Physical Review . tape 6 , no. 2 , 1915, p. 166-172 , doi : 10.1103 / PhysRev.6.166 .