X Rays and the Numbering of the Elements
When a solid target, such as solid copper or tungsten, is bombarded with electrons whose kinetic energies are in the kilo electron-volt range, electromagnetic radiation called x rays is emitted. Our concern here is what these rays-whose medical, dental, and industrial usefulness is so well known and widespread-can teach us about the atoms that absorb or emit them. Figure 41-14 shows the wavelength spectrum of the x rays produced when a beam of 35 keV electrons falls on a molybdenum target, We see a broad. continuous spectrum of radiation on which are superimposed two peaks of sharply defined wavelengths. The continuous spectrum and the peaks arise in different ways, which we next discuss separately.
The Continuous X-Ray Spectrum
Here we examine the continuous x-ray spectrum of , ignoring for the time being the two prominent peaks that rise from it. Consider an electron of initial kinetic energy Ko that collides (interacts) with one of the target atoms, as in . The electron may lose an amount of energy l1K, which will appear as the energy of anx-ray photon that is radiated away from the site of the collision. (Very little energy is transferred to the recoiling atom because of the relatively large mass of the atom; here we neglect that transfer.)The scattered electron in whose energy is now less than Ko, may have a second collision with a target atom, generating a second photon, whose energy will in general be different from the energy of the photon produced in the first collision. This electron-scattering process can continue until the electron is approximately stationary. All the photons generated by these collisions found part of then on tenuous x-ray spectrum. A p prominent feature of that spectrum in is the sharply defined cutotTwavelength A.nin’ below which the continuous spectrum does not exist: This minimum wavelength corresponds to a collision in which an incident electron loses all its initial kinetic energy Ko in a single head-on collision with a target atom. Essentially all this energy appears as the energy of a single photon, whose associated wavelength-the minimum possible x-ray wavelength-is found from
The cut of wavelength is totally independent of the target material. If we were to switch from a molybdenum target to a copper target, for example, all features of the x-ray spectrum of would change except the cutoff wavelength.
CHECKPOINT : Does the cutoff wavelength Amin of the continuous x-ray spectrum increase, decrease, or remain the same if you (a) increase the kinetic energy of the electrons that strike the x-ray target, (b) allow the electrons to strike a thin foil rather than a thick block of the target material, (c) change the target to an element of higher atomic number?
A beam of 35.0 keY electrons strikes a molybdenum target, generating the x rays whose spectrum is shown in What is the cutoff wavelength.
SOLUTION: The Key Idea here is that the cutoff wavelength Amin responds to an electron transferring (approximately) all of its energy to an x-ray photon, thus producing a photon with the greatest.possible frequency and least possible wavelength. From Eq. 41-23, we have.