Chemistry 150 Practice Exam 1d PDF

Chemistry 150: Structure & Properties Practice Exam 1d: Imaging Technology Dr. Scharf’s Sections Full Name: __________________________________________________________ Ins...

Chemistry 150: Structure & Properties Practice Exam 1d: Imaging Technology Dr. Scharf’s Sections Full Name: __________________________________________________________ Instructions: Cell phones must be turned OFF. You may use a pencil, a ruler, and a calculator. You may use your class notes and any materials made available for download from Canvas. If you use an electronic device to access these resources, it must not be used to access Internet resources aside from Canvas. The periodic table that I would like you to use is at the back of the exam; feel free to detach that page. Each of the exam questions has multiple parts; please be sure to answer each part. Good answers will fit in the space provided. Consultation with peers, tutors, or internet resources is not allowed during the exam. All work should be shown, including units. Dimensional analysis must be employed when applicable. By signing below, I acknowledge that I have read the instructions above and will take this examination under all standards and principles set forth by the Oxford College Honor Code. Signature: ___________________________________________________________ Part 1. Positron-Emission Tomography Positron-emission tomography (or PET imaging) is a technique that utilizes compounds containing radioactive isotopes which are injected into the body; the radioactive decay of these isotopes emits positrons, which are easily detected, allowing images of the body’s interior to be generated. 1. a) The most common compound utilized in PET imaging is [18F]-fluorodeoxyglucose (FDG), which is “enriched” in 18F, a radioactive isotope of fluorine with isotopic mass of 18.001 amu. The most abundant isotope of fluorine is 19F, with an isotopic mass of 18.998 amu. Assuming that these are the only two isotopes that exist naturally, what are their % abundances? (Hint: you may use ≈, >, or < symbols in your answer, if necessary.) b) The molecular formula of FDG is C6H1118FO5. What is the molar mass of this compound? c) A typical PET imaging procedure involves the injection of 1.85 mL of a solution of FDG, which has an FDG concentration of 12.5 µg/mL. How many atoms of hydrogen are in a typical dose of FDG?  d) FDG is synthesized on-site in hospitals using specialized “synchrotrons” that generate 18F atoms. Some synchrotrons generate the highly-reactive fluorine molecule, [18F]2, which is used to make FDG, according to the following equation: C6H10O4 + [18F]2 + 2 H2O → C6H1118FO5 + H3O+ + F 18 - The amount of water in this reaction must be closely controlled; if too much is present, it is rapidly oxidized to explosive hydrogen peroxide (H2O2). If the synchrotron generates 0.0453 moles of [18F]2 per minute, at what rate must water be added to the reaction in mL/min? (The density of water is 0.998 g/mL at 20°C, the temperature of the reaction vessel.) 2. PET imaging relies on the emission of positrons – particles of identical mass to electrons (9.109 x 10-31 kg), but with positive charge – as the 18F decays. In this process, positrons are emitted with kinetic energy = 0.1040 MeV. What is the de Broglie wavelength of one of these positrons (in m)? Part II. Magnetic Resonance Imaging (MRI) MRI is a common, non-invasive imaging technique used to diagnose many types of maladies, ranging from musculoskeletal injuries to Alzheimer’s disease, among many others. 3. MRI utilizes radio frequency photons (ν = 125 MHz) to detect hydrogen atoms within the body. What are the wavelength (in m) and energy (in J) of one such photon? Wavelength = Energy = 4. a) Some specialized MRI techniques require the use of MRI contrast agents; these compounds typically contain gadolinium ions, Gd3+. The most common isotope of gadolinium is 158 Gd. How many protons, neutrons, and electrons are in a single ion of 158Gd3+? Protons = Neutrons = Electrons = b) A neutral atom of gadolinium has the unusual electron configuration [Xe]6s25d14f7. i) How many valence electrons does an atom of Gd have? ____________________ ii) Is an atom of gadolinium diamagnetic or paramagnetic ? (Circle one.) iii) What is the value of S for an atom of Gd? ________________ iv) What is the electron configuration of a Gd3+ ion? ___________________________________ BONUS) Suggest a reason why the 3+ cation of the rare element gadolinium may be so valuable in magnetic resonance imaging. 5. In magnetic-resonance guided focused ultrasound, MRI is used to guide highly focused sound waves toward a precise area of tissue, heating it to ~75 °C, thereby killing the tissue; this technique is often used to destroy small tumors, fibroids, kidney stones, and cysts. a) Which property of these ultrasound waves provides the energy to heat tissue? b) Ultrasound devices must be pressed directly against the skin so that the sound waves do not pass through any air; bubbles of air against the skin can cause errors in the image generated. What property or behavior of sound waves would cause a problem if the sound passed through air? c) In medical ultrasound, images are generated by echoes that are generated by sound waves bouncing off a particular “target” in the body and heading back to the ultrasound device, which is typically pressed directly against the skin. If the sound waves have a frequency of 3.5 MHz, and a wavelength of 4.4 x 10-4 m, how long (in seconds) does it take for an ultrasound device to detect an object 4.0 cm beneath the skin? (Hint: What is the speed of sound through the body’s soft tissue?) Image courtesy of Science ABC, scienceabc.com, copyright 2022. Part III. X-Ray Imaging Most people are familiar with traditional X-ray imaging, which is used to obtain images of bones. 6. X-ray imaging utilizes photons in the x-ray region of the electromagnetic spectrum. Circle the correct descriptors of x-rays below: X-rays have higher or lower frequency than microwaves. X-rays have longer or shorter wavelengths than gamma (γ) rays. X-rays have higher or lower energy than visible light. 7. X-rays are particularly useful for imaging bones because X-rays generally are NOT absorbed by C, H, N, O, Na, P, S, and Cl (which are the most abundant elements in the human body), but are absorbed by the calcium ions (Ca2+) present in bones. This absorption causes a 1s (core) electron in calcium to be promoted to the lowest-energy empty orbital. a) What is the electron configuration of an atom of Ca? ___________________________________ b) What is the complete (non-abbreviated) electron configuration of an ion of Ca2+? c) What is the lowest-energy unoccupied subshell in a Ca2+ ion? ____________________________ d) What are the quantum numbers that apply to that subshell? ml = n= l= (give all possible values) e) The calcium ions in bone absorb X-rays with wavelength 306 pm. If the 1s orbital of Ca2+ has a potential energy of -6.506 x 10-16 J, what is the potential energy (in J) of the lowest energy unoccupied subshell you identified in #7c-d? 8. When X-ray images are obtained, the patient typically wears a heavy apron with a thin layer of lead (Pb) in it; this protects the patient from the potentially harmful effects of X-rays. a) X-rays are considered “ionizing radiation,” and can cause damage to tissue by ionizing it through the photoelectric effect. Given this information, concisely describe what x-rays do to tissue that might cause damage. Your description should include the term threshold and provide a definition of “ionizing.” b) Lead is an effective shield from X-rays largely due to its high atomic mass and related density. The mass spectrum of (atomic) lead is below. Fill in the table for the four isotopes of lead observed. (You do not need to show work for this problem.) Atomic Mass % Number Number Abundance Isotope 1 Isotope 2 Isotope 3 Isotope 4 Part IV. Transmission Electron Microscopy (TEM) While electron microscopy is not typically used for imaging in vivo (that is, in the body), it is often used to generate images of cellular structures, viruses, bacteria, and biological molecules. 9. Traditional microscopy (using lenses to magnify objects) has been utilized since the late 17th century. Although traditional microscopes cannot be used to see things at the molecular scale, chemists have discovered that the color of objects can tell you something about the chemical composition of a cell. For instance, tomato cells appear red due to the presence of a dye molecule called lycopene. a) Lycopene appears red to us because it primarily absorbs what color of visible light? b) It turns out that the wavelength of absorbed light gives a decent rough estimate of the length of a dye molecule. If lycopene absorbs photons with energy = 4.22 x 10-19 J, approximately how long is the lycopene molecule (in nm?) c) How many lycopene molecules would need to be strung together end-to-end to reach entirely across a tomato cell with diameter 0.316 mm? 10. In TEM, a beam of high-speed electrons are directed at the surface of an object, and the interaction of the electrons with the surface can give information about the “appearance” of that surface. The resolution of a TEM image depends on the wavelike nature of high-speed electrons, and can be estimated using the Heisenberg Uncertainty Principle, in which the resolution is Δx. What is the approximate resolution (in m) of the microscope if the electrons in the beam travel at (5.586 x 105) ± (0.013 x 105) m/s?