Mosley’s Law Introduction (From University of Florida Advanced Physics Laboratory Manual) When an electron beam of energy around 20 keV strikes a metal target, two different processes produce x-rays. In one process, the deceleration of beam electrons from collisions with the target produces a broad continuum of radiation called Bremsstrahlung having a short wavelength limit that arises because the energy of the photon E=hc/ λ ¸can be no larger than the kinetic energy of the electron. In the other process, beam electrons knock atomic electrons in the target out of inner shells. When electrons from higher shells fall into the vacant inner shells, a series of discrete xray lines characteristic of the target material are emitted. In our machine, which has a copper target, only two emission lines are of appreciable intensity. Copper Kα x-rays (λ = 0.1542 nm) are produced when an n = 2 electron makes a transition to a vacancy in the n = 1 shell. A weaker Kβ xray with a shorter wavelength (λ = 0.1392 nm) occurs when the vacancy is filled by an n = 3 electron. Thus, the spectrum of x-rays from an x-ray tube consists of the discrete lines superimposed on the Bremsstrahlung continuum. This spectrum can be analyzed in much the same way that a visible spectrum is analyzed using a grating. Because x-rays have much smaller wavelengths than visible light, the grating spacing must be much smaller. A single crystal with its regularly spaced, parallel planes of atoms is often used as a grating for x-ray spectroscopy. The incident x-ray wave is reflected specularly as it leaves the crystal planes, but most of the wave energy continues through to subsequent planes where additional reflected waves are produced. The path length difference for waves reflected from successive planes is 2d sin θ, where d is the distance between atomic planes. Note that the scattering angle (the angle between the original and outgoing rays) is 2θ. Constructive interference of the reflected waves occurs when 2d sin θ is equal to an integer number of wavelengths nλ. In addition to being diffracted, a portion of the x-rays are absorbed. This absorption depends on the absorbing material, the thickness of the material, and the energy (wavelength) of the x-rays. For a given x-ray energy, the absorption of x-rays depends exponentially on the thickness of the material I=Ioe-tµ where µ, is the linear absorption coefficient. Different energy x-rays, however, will be absorbed differently. Most materials have “absorption edges”, energies above which x-rays are absorbed, and below which x-rays are transmitted. The absorption decrease occurs at an x-ray energy near but greater than the energy needed to excite electrons via the photoelectric effect, and can be measured by determining the 2θ angle at which there is a jump in transmitted intensity through a material, and relating 2θ to wavelength using the diffraction equation. If the absorption changes near an absorption edge, this means that the absorption coefficient depends on wavelength, and has a minimum and maximum. Because the location of the absorption edge changes with material, due to the different energy levels between electrons in different atoms, the absorption of x-rays also depends on atomic mass of the absorbing material. Following the absorption of a photon, emission, or fluorescence, of the same or different photon can also occur as the electron relaxes to its unexcited state. For a given x-ray energy the fluorescence of atoms in different materials will of course vary, and depend on the arrangement of electrons within theatoms. Before 1913, elements were arranged in the periodic table according to atomic mass. However, in 1913, Henry Mosley demonstrated using the observation of x-ray fluorescence that atomic number is a better way to characterize the properties of atoms. As you know, it is the number of protons and electrons that determine the energy levels of the electrons, and that the mass does not increase linearly with proton number due to quantum effects. In addition to investigating absorption and emission of x-rays you will have the opportunity to recreate this experiment in this lab. For more detail about the theory of diffraction, the Tel-X-Ometer manual has a lengthy explanation, as does the Art of Experimental Physics (excerpt from the textbook is linked here), which is available in hardcopy in the classroom. The first two chapters of C. Kittel, Introduction to Solid State Physics, or an equivalent text such as Fundamentals of Modern Physics by Eisberg also have good background on diffraction. For some discussions about the x-ray emission and absorption you may want to look here http://xdb.lbl.gov/Section1/Periodic_Table/X-ray_Elements.html and http://www.chem.ucalgary.ca/research/groups/faridehj/xas.pdf here. Equipment: • X-ray diffraction system (Tel-X-Ometer) experiment manual and its setup manual • Geiger-Müller tube and stepping motor • Computer and interface software • Alkali halide large single crystals, absorption foils, and “rotary radiator” • Radiation safety guide (just in case you want to know more) Procedure: 1. Please read the Tel-X-Ometer setup manual (particularly sections 10.1-12.5), and any sections regarding safety features. Realize, you are working with a radioactive source, and thus should be aware of any possible hazards. 2. Also read the Tel-X-Driver manual which explains how to use the software. 3. To operate the Tel-X-Ometer: a. To open or close the scatter shield (the main cover), the whole shield must be displaced to the right or the left of center, depending on the position of the detector. b. To turn on the power to the unit, turn POWER ON key on the control panel; the unit will only function when the TIME SWITCH is rotated away from zero, and when the key is turned ON. This is to ensure that the x-rays only turn on when enclosed within the leaded glass. The filament of the x-ray tube should then be illuminated. Wait 5 minutes, then depress the X-RAYS ON switch (the red light will turn on). If it does not turn on, wiggle the lid to ensure the metal pin is in the exact center. c. Use the radiation test kit (Geiger-Mueller counter at the gamma ray experiment) to measure radiation levels outside the unit when x-rays are on.d. The Tel-atomic software (Tel-X-Driver v2.32 shortcut link on the Desktop) measures the counts from the Geiger-Mueller tube, the