Sukhpreet Kaur 23026113 MSE 104 Problem Set 11.1 What is the frequency (per second) and energy per quantum(in joules) of x-ray beams of wavelength .71 Ǻ (Mo Kα) and 1.5 Ǻ (Cu Kα). The frequency of the wave is given by = , where f= frequency, c = velocity of light = 3.00 × 108 / , and = ℎ. So, = = .71 ×10−10 s = . × − 3.00×108 3.00×108 And = = 1.5 ×10−10s = . × − Energy = E = hf where h= 6.63 × 10−34 ∗ So, Energy of Mo= = ( 6.63 × 10−34 ∗ ) × 4.23 × 1018 −1 = . × − Energy of Cu= = ( 6.63 × 10−34 ∗ ) × 1.98 × 1018 −1 = . × − When the electrons strike the anode. Since this is true. [The force on a charge e (coulombs) by a field E (volts/m) in eE newtons. ] The kinetic energy of the electrons on impact with the target is. the high voltage draws the electrons to the target/anode. x rays are produced at the point of impact. m is the mass of the electro and v is the velocity. The tube is a vacuum tube. electron will stay in constant motion and will not accelerate over distance. so variance in distance doesn’t matter.1. = = 1 2 2 where e= charge on electron. In x-ray tube. . which they strike with very high velocity. thus the electrons do not feel inference of any other force accept that from the voltage. V is the voltage.3 Show that the velocity with which electrons strike the target of an x-ray tube depends only on the voltage between anode (target) and cathode and not on the distance between them. Thus it could be seen that the Eq 1-13 is right.3 0.6 0.24 ×103 30000 1. ℎ = = . From the curve.14 cm^2/g. is the density and Z is the atomic number of the absorber.8. The wavelengths. 84.1 0.8 Wavelength The curve produced is roughly similar to how the graph of the equation y^3 would look like. were found in from Appendix 7. ( The mass absorption coefficients of lead for these radiations are 122.7 0. By using the absorption edge and the data given. (1-13) for a lead absorber and Mo Kα. for 30. respectively). determine the mass absorption coefficient of lead for the shortest wavelength radiation from a tube operated at 30.98) of Pb.4 0. along with the absorption edges ( .4133 Ǻ .14 and . = 1.5 0.2 0. Equation 1-13 is: = λ3 3 Where is the mass absorption coefficient. Rh Kα and Ag Kα radiation.000 volts. the following graph was produced: Mass Absorption Coefficient and Wavelength plot 140 Mass absorption coefficient 120 100 80 60 40 20 0 0 0.13 and 66.24 × 103 .1.000 volts. The shortest wavelength limit can be found by using the following equation: = So.6 Graphically verify Eq. ~ 45 cm^2 / g .To get the mass absorption coefficient for this wavelength. interpolate from the above mass. the following graph was generated. = (. and by using various path lengths between 0 to 20 cm. 2)(37. .42) + (. According to 1-12. the mass absorption coefficient is the weighted average of the mass absorption coefficients of the two elements it’s composed of.29 × 10−3 ^3 .48 × 10−2 −1 (b) When x-rays come in contact with matter. In this case.29 × 10−3 3 ) = 3. the transmission factor decreased as the path length increased. The following graph plots the transmission factor of air in relation to the path lengths.97 2 ) ( 1. . As can be seen from the graph below. 0 . It’s given by the following equation: = − 0 The linear absorption coefficient was calculated earlier. 8)(24. (b) Plot the transmission factor of air for Cr Kα radiation and a path length of 0 to 20 cm. they are transmitted and partly absorbed.19) = 26. Assume that air contains 80% nitrogen and 20 % oxygen by weight and has a density of 1. The linear absorption coefficient is = (26.97 2 The mass absorption values of N and O for Cr Ka radiation were found from the Appendix 8 of the textbook. Intensity of the x-ray beam as it passes through an object tends to decrease proportionally to the distance traveled x. = 1 ( ) + 2 ( ) + ⋯ 1 2 Since air contains 80% nitrogen and 20 % oxygen.8 (a) Calculate the mass and linear absorption coefficients of air for Cr Kα radiation. 8) () + (.1. The transmission factor is the ratio of final intensity . after penetrating the length x over the initial. 2) () = (. incident intensity. (a) Air is composed of more than one element. 4 0.8 0.2 0 0 5 10 Path Length 15 20 25 .6 0.Transmission factor of air for Cr Kα radiation and vs Path length Plot.2 1 Transmission Factor 0. 1.