MSE104_Sp08_Midterm01_Solution

MSE104_Sp08_Midterm01_Solution - UNIVERSITY OF CALIFORNIA...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science & Engineering MSE 104 Spring Semester 2008 Professor R. Gronsky Instructions This is an OPEN-book (textbook only) exam. Calculators and drawing tools ARE permitted. Please PRINT your name in the box above and INITIAL all pages. Solutions MUST be written neatly and concisely in the spaces provided. Guidelines There are 5 equally-weighted questions. Average pace = 10 minutes per problem. Show ALL of your work for partial credit, as appropriate. Please read each question FULLY before commencing your answer. Solutions Midterm 01 The continuous spectrum has no sharp limit on the long wavelength side. The slightest deceleration of electrons entering the target generates low energy radiation, which can be of very long wavelength, approaching infinite length. However, there is a sharp limit on the short wavelength side of the continuous spectrum. This short wavelength limit is given by Equation (1-4) of the text, Substituting V = 12,400 volts gives a short wavelength limit of 1 Å. Therefore the range of wavelengths comprising the continuous spectrum from an x-ray tube operated at 50 kV is 1 Å ≤ λ ≤ ∞ . This range of wavelengths will be the same for a Cu tube as a W tube. Continuous radiation is generated by the deceleration of the incident electron beam striking the target, and although the brightness of the radiation depends upon Z (part ( b ) below), the bandwidth does not. A “brighter” source emits more radiation per unit time. For brighter continuous emission from the same source, it is necessary to increase the flux of incident electrons into the target by either heating the filament more aggressively (increasing the filament current, i ), or increasing the potential (the tube voltage, V ) through which the electrons are accelerated towards the target. The latter also increases the range of velocities over which deceleration occurs, which increases brightness. But there is another way to increase the brightness of continuous or Bremstrahlung ("braking") radiation, the topic of this question, and that is to “brake” harder. When the target presents more “obstacles” to the incoming electrons, there is more serious deceleration, producing a higher radiative output in the continuous band. A tungsten tube has a W ( Z = 74) target, which, compared to a copper tube with a Cu ( Z = 29) target, provides much more severe deceleration to the incoming electrons through its greater electron concentration and nuclear charge. The empirical equation describing this effect is given in the text, Equation (1-5)....
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This test prep was uploaded on 04/07/2008 for the course MSE 104 taught by Professor Gronsky during the Spring '08 term at University of California, Berkeley.

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MSE104_Sp08_Midterm01_Solution - UNIVERSITY OF CALIFORNIA...

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