Laboratory for 2/16/98

The Tel-X-Ometer x-ray spectrometer creates x-rays by accelerating electrons through a 20 kV potential, which then collide with a copper target. (There is also a 30 kV setting) A continuous spectrum of x-rays (bremsstrahlung) is produced, with energy from 20 keV (30 keV) and below. The beam electrons occasionally liberate inner K-shell electrons from the Cu atom. Sharp peaks in the x-ray spectrum (see Fig 1 below) are created when free electrons fall into these vacated energy levels, emitting an x-ray photon. Copper produces two such peaks called the K-alpha and K-beta lines.

X-ray diffraction is achieved by collimating the x-rays and allowing them to strike a crystal. The rays reflect from adjacent atomic planes (called Bragg planes) created by the crystal lattice structure. Constructive and destructive interference occurs at different angles of incidence due to the wave nature of the x-rays. With the angle theta measured from the reflecting plane, a crystal with atomic spacing d between planes will create constructive interference at angles such that

where lambda is the wavelength of the x-rays. The constructive interference due to the two sharp lines, K-alpha and K-beta, can be detected above the continuous background using a G.M. tube that detects individual x-ray photons.

In this experiment, the wavelengths of the K-alpha and K-beta x-rays will be determined using a NaCl crystal. The spacing of Bragg planes for LiF will then be determined using the results of the experiment with the NaCl crystal.

The procedure for setting up the x-ray spectrometer is detailed in the Tel-X-Ometer Manual. The instructor will outline the relevant details. Follow the experimental procedure (Experiment D14, provided in the lab) generally as outlined with the following alterations and additions.

1. Restrict the range of angles to 20 - 40 degrees for the NaCl crystal. This will include only the first order peaks.

2. Connect the G.M. tube to the Nucleus counter and take data at one degree increments for 1 minute. You may use a longer period for a greater statistical sample, but be sure to normalize any variations in time among the intervals.

3. Plot number of counts vs angle for the entire range, and make a separate expanded plot in the regions of the K-alpha and K-beta peaks. Determine the exact angles for the first order peaks and calculate the wavelengths of the alpha and beta x-rays using 2.82 Å for the spacing of the Bragg planes in NaCl.

4. Repeat steps 1 through 3 for the LiF crystal for 20 - 50 degrees. However, use the values for the x-ray wavelengths calculated in step 3 to find the spacing between the Bragg planes in LiF.

Discuss the limitations of accuracy in the experiment and estimate the error in the value calculated for the spacing in LiF. Compare the spacing for LiF to that of NaCl. Offer an explanation for the difference based upon your knowledge of the atomic sizes of Na and Li.