Calculate the approximate energy of a K x ray from a tungsten anode in an x-ray
Question:
Calculate the approximate energy of a Kα x ray from a tungsten anode in an x-ray tube.
Strategy
How do we calculate energies in a multiple-electron atom? In the case of characteristic x rays, the following approximate calculation is reasonable. Characteristic x rays are produced when an inner-shell vacancy is filled. Inner-shell electrons are nearer the nucleus than others in an atom and thus feel little net effect from the others. This is similar to what happens inside a charged conductor, where its excess charge is distributed over the surface so that it produces no electric field inside. It is reasonable to assume the inner-shell electrons have hydrogen-like energies, as given by 
. As noted, a Kα x ray is produced by an n = 2 to n = 1 transition. Since there are two electrons in a filled K shell, a vacancy would leave one electron, so that the effective charge would be Z - 1 rather than Z. For tungsten, Z = 74, so that the effective charge is 73.
Step by Step Answer:
gives the orbital energies for hydrogenlike atoms to be E n Z 2 n 2 E 0 where E 0 136 eV As noted ...View the full answer
