Lecture 20: X-ray Generation

Lecture 20: X-ray Generation Summary Atoms are too small to see with visible light, but x-rays have just the right range of wavelengths to image at the atomic scale. Wilhelm Rontgen first discovered x-rays by observing electrons striking a metal target in a cathode ray tube. Electrons were emitted from a heated filament and directed by an electric field inside the tube to very high velocities. When the high-speed electrons strike metal atoms, two kinds of xrays are generated. Continuous x-ray radiation is caused by the deflection of an incoming electron as it interacts with a metal target atom: as the name suggests, the alX-ray Continuum Radiation lowed wavelengths for the Bremsstrahlung (which translates (Brehmsstrahlung) figure removed to ”braking radiation”) are a continuous spectrum above a due to copyright restrictions. lower bound. The lower bound on wavelength (upper bound on energy) is set by the energy of the incoming electron, because the energy of the emitted x-ray cannot be greater. The second type of x-ray that can be generated is a product of the electronic structure of the metal target atoms. When a high-energy electron is incident on a metal atom, it can knock out an electron in the inner core of the target atom, allowing a higher energy core electron to cascade down. If the electron cascades down from the n=2 to the n=1 energy level, the photon that’s emitted is called an alpha photon. These x-rays are discrete: they occur at a single wavelength that corresponds to the difference in energy levels. Crystallographers use a slightly different notation for the energy levels within an atom: the ground state (n=1) is called the K shell, n=2 is the L shell, and n=3 is the M shell. Using this notation, a photon that is emitted via the process of an electron falling from n=2 to n=1 is called a K-alpha photon. The energy difference between inner-shell electrons is huge- that’s why the photons that are emitted are x-rays. Heavier elements have bigger differences between the energy levels, so the K-alpha wavelength is smaller. It is therefore possible to determine which kind of atom the x-ray was emitted from, just by knowing the wavelength: these x-rays are called characteristic xrays. In this plot, the Brehmsstrahlung and the characteristic x-rays are shown together, as they’d be measured. The first two peaks are the K-beta (M to K) and K-alpha (L to K) lines, since those correspond to the biggest energy transitions within the atom. Then come the L-beta (N to L) and L-alpha (M to L) lines, which 57 X-ray spectrum figure © source unknown. All rights reserved. Creative Commons license. For information, see https://ocw.mit.edu/fairuse. are much smaller energy gaps. The intensity can be changed by changing the number of electrons that are incident on the target. The lower-bound Brehmsstrahlung wavelength can be changed by adjusting the kinetic energy of the incident electrons, though this wouldn’t change the location of the characteristic x-ray peaks at all. The only way to shift the characteristic x-rays is to change the target metal used to generate the x-rays. If the energy of the incident x-rays is too low, though, no characteristic x-rays would appear: the incident electrons must have enough energy to knock out a core electron to kick off the cascade. Why this matters The discovery of x-rays, and the subsequent ability to fully control what wavelength of x-ray is generated, has had so much impact on modern life that it’s really tough to choose only one example for Why This Matters. But I guess since I have to pick, I may as well go back to the roots of Rontgen himself and one of the very first ways he used his new rays. That would be to take a picture of his wife! More precisely, her hand - it’s the first x-ray picture ever taken and it started a revolution (The black circle on the second finger from the left is her ring, by the way). The key thing about x-rays, which Rontgen noticed right away, is that they are able to pass through soft body tissue like skin and flesh, but they get absorbed by the denser material like bone. This means that if you shine x-rays on a body part, the bones inside cast shadows, which can be captured with a photographic plate. This was an incredible advance for medicine because for the first time a doctor could see inside a living patient without having to cut the patient open. Some of the earliest users of x-rays in medicine were military doctors, who could use them to optimize removal of bullets from a wounded soldier. As doctors saw how useful they could be, x-rays became central to diagnosis and by the 1930s they had led to the specialized field of radiology. Not only are x-rays currently utilized routinely in many aspects of medicine, but the technology of x-ray imaging continues to improve dramatically. Beyond improved contrast in the images, one very recent breakthrough applies techniques originally developed for the Large Hadron Collider in Geneva, which is still the world’s largest particle accelerator at 27 km long. With a combination of advanced shutters, cameras, and software, a completely new type of x-ray imaging is possible, with 3D and color images. Take a look at this very first x-ray picture of teeth, taken in 1896 with a 9-minute exposure time (!). Now look at a modern-day x-ray picture of teeth next to it. That’s an incredible improvement, and even more so when you realize that the picture on the right is fully 3D and a dentist can spin it around to see all angles. 58 First medical x-ray by Wilhelm Röntgen of his wife Anna Bertha Ludwig's hand is in the public domain. Other x-ray images © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. Why this employs There’s a whole lot of X-ray generation that goes on in the world, and the medical imaging example I gave above in Why This Matters is only one part of it. For example, X-rays are also used as scanners at airports, or as ways to do quality control for many industrial parts, or to analyze the degradation of valuable paintings, or in the field now called “X-ray astronomy,” to name only a few examples. X-rays are also used not only to see an illness like cancer, but also to treat it (“radiation therapy”). Just the medical market for X-rays alone is set to surpass $16.5B globally by 2025. And all these uses for X-rays spells jobs. There are many companies out there that make X-ray equipment. Siemens for example sells 6 different types of “digital X-ray equipment,” but that’s just one category – they’ve also got a robotic X-ray machine, as well as two types of CT scanners (yes those also use X-rays), and a fluoroscopy machine which uses X-rays to examine movement. And that’s just one company! Siemens is a very large company, with the subsidiary “Siemens Healthineers” making this type of equipment. 41% of their US workforce of 13K people is in RD, engineering, IT, or tech support. And there are many others: Philips, GE Healthcare, Hitachi Healthcare America, Medtronic, Samsung Medical Devices, Eizo, Xoran Technologies, and United Imaging, Canon Medical Systems, and I’m still just getting started. All of these companies are selling wide ranges of X-ray equipment and they’re all competing with one another for customers, which means they’re constantly trying to improve their technology and differentiate what they’re selling from their competitors. And beyond these large companies, there are many small-scale companies looking to innovate the field. For example the company MARS Bioimaging, based in New Zealand, is commercializing the 3D color X-ray technology that came out of the Hadron Collider. And that’s just the equipment side. There are also all the companies working on new software to analyze the images produced by all this X-ray equipment. For example, there are many start-ups applying AI to analyze the X-ray image data and in some cases AI has been shown to perform better than human doctors! 59 Example problems 1. Look at the x-ray spectrum below. You can see that λκβ is lower than λκα . What about λΛα ? Draw this peak on the spectrum. 2. What is the wavelength of κα x-rays produced by a copper source? Figure above © source unknown. All rights reserved. This content is excluded from our Creative Commons license. For information, see https://ocw.mit.edu/fairuse. 60 Solutions 1. Eκα = 13.3(6 − 1)2 ( 1 1 − 2 ) = 255eV 2 2 1 Lα : ni = 3; nf = 3 + 1 = 4 Lα : ni = 3; nf = 3 + 1 = 4 1 1 − 2 ) = 3.7eV 3 22 > ELα ELα = 13.6(6 − 7.4)2 ( Eκα λκα < λLα 2. E= hc 1 1 = −13.6(Z − 1)2 ( 2 − 2 ) λ nf ni Z = 29, nf = 1, ni = 2λ = 1.54A 61