X-Rays Edited 2/19/18 by DGH & Stephen Albright

Size: px

Start display at page:

Download "X-Rays Edited 2/19/18 by DGH & Stephen Albright"

Alexandra Booker
5 years ago
Views:

$X-Rays Edited 2/19/18 by DGH & Stephen Albright PURPOSE OF EXPERIMENT: To investigate the production, diffraction and absorption of x-rays.$

1 X-Rays Edited 2/19/18 by DGH & Stephen Albright PURPOSE OF EXPERIMENT: To investigate the production, diffraction and absorption of x-rays. REFERENCES: Tipler, 3-6, 4-4; Enge, Wehr and Richards, Chapter 10; Eisberg and Resnick, 2-6 and 9-8; Preston and Dietz, Expt. 10 (p. 180). The X-Ray machine manual - which includes theory and exercises - can be found on the wiki under Reference and Resources : APPARATUS: You will be using a Tel-X-O meter student x-ray machine. This compact unit contains an x-ray tube with a copper anode, a central post for mounting a crystal NaCl or LiF Do not touch the crystals, a rotatable carriage arm, a Geiger tube, a stepper motor/computer interface and a computer running TEL-X-Driver software. Other auxiliary equipment including collimators and filters may be used. Figure 1

2 THEORY: The interlayer spacing of NaCl has been measured to be 2.82 Å. The lattice constant, which is 2d, is therefore 5.64 Å. NaCl and LiF are of cubic form. Figure 2 shows a crystal lattice of NaCl. Figure 2 The first condition for Bragg diffraction to be observed is that, when the x-rays strike the crystal, the angle of incidence equals the angle of reflection, both of which we can call ϴ. This produces a total angle of 2ϴ. The angles measured from the device are therefore twice the actual angle. A diagram of this reflection is shown in figure 3. Figure 3 The second condition for Bragg diffraction is that the reflections from all such layers must interfere constructively. This yields the Bragg condition: AB + BC = nλ = 2dsinϴ (1) where d is the interlayer distance, ϴ is the incident and reflection angle, and AB and BC are the path lengths depicted in the figure above, and n is the order of the diffraction, which is the number of wavelengths difference between photons scattered off of two adjacent layers. We will study two different peaks, each associated with a specific wavelength. These are known as K and K ẞ. In figure 4, each pair of peaks represents the K and K ẞ emissions. The first pair of peaks is the first order, at n = 1, the second pair is the second order, at n = 2, and so on.

3 Figure 4 K ẞ is the first peak in each pair, corresponding to a slightly shorter wavelength than K, which is the second peak in each pair, as shown in figure 4. Note that changing the x-ray source energy will affect the amplitude of these peaks, but will not change the angle at which they are observed. The energy level of an electron in a coulomb potential is traditionally referred to as n. Confusingly, this n is completely unrelated to the order of diffraction, referred to in the previous paragraph. As depicted in figure 5, when the electrons from the ground state, n = 1, become ionized from the x- rays, electrons in higher orbitals drop down to fill in the missing space. When electrons drop from the n = 2 to n = 1 level, this produces the K emission. When electrons drop from the n = 3 to n = 1 level, this produces the K ẞ emission. Figure 5 A table similar to the one in figure 6 will be useful in tabulating the data.

Figure 6 While most groups will cycle through the stations out of order, the experiment is best thought of in the following chronology: the known properties of NaCl are used to measure the wavelength

4 Figure 6 While most groups will cycle through the stations out of order, the experiment is best thought of in the following chronology: the known properties of NaCl are used to measure the wavelength of x- ray radiation (and its uncertainty). This is done with the crystal lattice is positioned at both 0 o and 45 o for redundancy. The information about the x-ray source is then used in measuring the lattice structure constant of LiF with the crystal lattice is positioned at 0 o. A measurement of LiF with the crystal lattice at 45 o is then used to confirm that the lattice is square in the 2D plane considered. Note that when the crystals are oriented at 45 o, the distance probed is no longer the interlayer spacing d, as shown in figure 7. Figure 7 The wavelengths of each K transition can then be used to find the photon energy, as shown in equation 2. E = hc/λ (2) This energy can then be compared to the theoretical Bohr model predictions using equation 3. E = (13.6 ev) Z 2 (1/n f 2 1/n i 2 ) (3) Here, Z is the number of protons in the atom (the atomic number), n f is the final energy level and n i is the initial energy level. In relation to K and K ẞ, the equation becomes slightly modified because the Bohr model is based on classical principles. If shielding is taken into account, this equation becomes slightly modified. For K, Z Z 1 because when the electron is in the n=2 level, this is essentially the same as an electron in the field of an atom with one less proton: Z 1. For K ẞ, Z Z 2 because when an electron is in the level n=3, this is essentially the same as an electron in the field generated by an atom with two fewer protons: Z 2. These modifications to the Bohr model

5 comprise part of Moseley s Law. This is observed and discussed further in the second part of this lab. PROCEDURE: 1) The TA will teach you how to open, close and operate the x-ray machine. The TA will also go over the safety features of the instrument and point out precautions. Note: Keep the tube current between 65 & 80 µ A. The tube may be damaged if the current is greater than 80 µ A for an extended time. 2) There are four x-ray-machine setups in the lab. Each is configured for a different experiment. You are expected to perform the assigned experiments on all four of the setups: A) 0º B) 0º C) 45º D) 45º 3) A Geiger-Muller tube is mounted in slot 26 near the end of the carriage arm with an NaC1 (yellow tipped) or LiF (blue tipped) crystal mounted in the post that defines the precise center of the arms rotation. X-Rays are emitted from the large clear domed object at the back of the machine. The TA will rotate the carriage arm from ~20º deg through ~90º. Note: when the carriage arm 20º the crystal 10º (relative the x-ray beam) and when the carriage arm 90º the crystal 45º. This is called a Theta/2Theta (Ɵ/2Ɵ) configuration. 4) Select one of the setups and perform the associated experiment. When done, move to a different setup and perform the assigned experiment. Continue in this fashion until you have worked with all four of the X-Ray machines A) For Setups A&B Use the TEL-X-Driver software to measure the spectrum of the copper anode x-ray tube via the instructions below. The software will measure the counting rate as a function of the position (2Ɵ) of the carriage arm. Instructions for Setups A&B 1.) Confirm there is a 3mm Collimator in slot 13 and a 1mm Collimator in slot 18 of the carriage arm. 2.) Confirm with your TA that the X-ray voltage is set to 30kV. 3.) Use the TEL-X-Driver software to do a wide scan from the arm s minimum to maximum setting, around 20 o to 115 o using 1 second readings at.5º intervals to identify the peaks. Around each peak, scan a narrow angular range with a longer counting time and a smaller angular resolution, around 0.1 deg, in order to identify the peaks in detail.

6 Questions: I. How can you estimate the accuracy? II. What should the uncertainty be theoretically? B) For Setups C&D - Use the TEL-X-Driver software to explore the crystal lattice oriented at 45 o. Follow the instructions for Setups A&B but when scanning min to max increase the dwell time to 2 sec. Refer to the theory section addressing crystals oriented at 45 o for clarification. Instructions for Setups C&D 1.) The NaCl and LiF crystals are already mounted in the crystal posts so that they are oriented at 45 o. 2.) Remember, the crystals are angled at 45 o, so the interlayer distance experienced by the x-ray is not the lattice constant, d, as it was in the 0ºcase. Refer to the theory section above for clarification. NOTES: Keep the tube current between 65 & 80 µ A. Check it frequently. The peaks in the x-ray spectrum are due to the K nd K lines. The interlayer distance of NaCl is known to be 2.82 Å and therefore has a lattice constant of 5.64 Å. The wavelengths of K and K ẞ calculated using the NaCl crystals will be used to find the lattice constant of LiF. Data Analysis: Use your data to complete the tables described in the theory section. Use the NaCl data to find the wavelengths of K nd K emission. Use the wavelengths of K nd K to find the lattice constant of LiF and compare this to theory. Compute the aspect ratio of the LiF primitive cell. Discussion of Results: Be sure to include an interpretation of the data, in physical terms, and a critical evaluation of their accuracy. Explain the origin of the main features observed in the x-ray spectrum. Determine the photon energy of the K nd K lines, and estimate the error in this energy. Compare with the original and modified Bohr model predictions (Moseley s Law), as described in the theory section. Why are the K nd K lines not equally intense? Is the measured aspect ratio of the primitive cell within uncertainty of square?

Lab Manual: Determination of Planck s constant with x-rays

Lab Manual: Determination of Planck s constant with x-rays 1. Purpose: To obtain a better understanding on the production of X-rays, the bremsstrahlung radiation and the characteristic radiation of a Molybdenum