Question

The minimum wavelength of X-ray emitted from X-ray machine operating at an accelerating potential of V volts is

• A. $\frac{hc}{eV}$
• B. $\frac{Vc}{eh}$
• C. $\frac{eh}{Vc}$
• D. $\frac{eV}{hc}$

Answer 1

Answer: (A)

Some of the collisions between the photoelectrons and the target result in the emission of a continuous spectrum of X-rays called white radiation or Bremsstrahlung. White radiation is beloved due to the collision of the accelerated electrons with the nuclei of the target atoms. If all of the kinetic energy carried by an electron is converted into radiation, the energy of the X-rays photon would be given by $E_{\max }=h{v}_{\max }=eV$ where h is Plancks constant, $v_{\max }$ the largest frequency, e charge of an electron and V the applied voltage. This maximum energy or minimum wavelength is called the Duane-Hunt limit. $\therefore$ $h{v}_{\max }=\frac{hc}{{\lambda }_{\min }}=eV$ $\Rightarrow$ ${\lambda }_{\min }=\frac{hc}{eV}$