X Rays and the Ordering of the Elements — Question 6

Question 6

An electron tube can show a continuum without exciting a selected characteristic line

A target has K binding energy $B_K=18.0\,\mathrm{keV}$ and $K_\alpha$ photon energy $15.5\,\mathrm{keV}$. Electrons are accelerated from rest through 16.0 kV. Assume K vacancies must be made by these incident electrons.

1. Determine whether $K_\alpha$ emission is accessible even though the incident energy exceeds the line energy.

2. Find the continuum cutoff at 16.0 kV and the minimum threshold voltage for direct K-vacancy production.

Question 6 - Solution

An electron tube can show a continuum without exciting a selected characteristic line

(a) Method and calculation

$$K_e=16.0\,\mathrm{keV}<B_K=18.0\,\mathrm{keV}.$$$$\boxed{\text{K-vacancy creation is energetically forbidden in this model}}.$$

(b) Interpretation and further calculation

$$\boxed{\lambda_{\min}=1.240/16.0=.0775\,\mathrm{nm}}.$$$$eV_{\mathrm{th}}=B_K\Rightarrow\boxed{V_{\mathrm{th}}=18.0\,\mathrm{kV}}.$$

Physical check

The incident electron must first create a core hole, whose threshold exceeds the eventual line energy. An energetic threshold does not imply a large production rate exactly at threshold.