Question

What is the short-wavelength limit of the continuum produced by an X-ray tube having a tungsten target and operated at $50kV$?

Short answer

The short wavelength limit is$0.25{\mathrm{A}}^{\circ }$

Step-by-step solution

Step 1. Given information

Operating voltage is given as$50kV$

step 2. Duane Hunt law

Electronic transitions of electrons in the inner orbitals of atoms create X-rays, which are high-energy electromagnetic radiation.

The minimum wavelength of ${\lambda }_{\circ }$X-rays generated is inversely linked to the maximum accelerating voltage , according to the Duane-Hunt law:

${\lambda }_0=\frac{12398}{V}.....\left(1\right)$

Units of ${\lambda }_{\circ }$is $A^{\circ }$and $v$is in volts.

Step 3. Short wavelength limit

Change kV into volts as,

$$\begin{gathered} 50\mathrm{kV}=50\mathrm{kV}\times 1000 \\ =50000V \end{gathered}$$

Substitute in equation $\left(1\right)$

$$\begin{gathered} {\lambda }_0=\left(\frac{12398}{50000}\right) \\ =0.25{\mathrm{A}}^{\circ } \end{gathered}$$