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HW4_solutions - ECE 380 Biomedical Imaging Spring 2010...

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1 ECE 380 Biomedical Imaging Spring 2010 Solutions Homework 4 _____________________________________________________ 1. Photon Energy (10 points) a) What voltage should be applied to accelerate an electron from zero velocity in order that it acquire the same energy as a photon of wavelength λ=1 m? Planks constant=6.63 x 10 -34 J.s ; 1eV=1.602 x 10 -19 J 19 1.9902 x 10 hc E hf J = 1.24 eV 1.24 Volts would be required b) 5000 photons of wavelength 450nm are produced for incident X-ray with a conversion efficiency of 15%. What is the energy in Electron Volts of the incident X-rays? Energy of 5000 photons=5000 hc =2.21 x 10 -15 Joules As the efficiency is 15% Energy = (1/0.15) x 2.21 x 10 -15 Joules Hence, energy of electrons is 91.968 keV 2. Bevel Angle (10 points) The X-ray system has a coverage area of 0.5m and the patient will be 2.0m from the source. What anode bevel angle should you specify for this system? Using the relationship coverage 2. tan d . We will get θ = 7.12 o 3. Linear attenuation of x-rays (25 points) a) Calculate the relative intensities of the signal S 1 , S 2 and S 3 in the figure shown below. The attenuation coefficient μ crystal (x) for crystal is 2x cm -1 and the half-value layer (HVL) of tissue and bone are 1.8 cm and 0.4 cm respectively.
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2 Tissue
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