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Unformatted text preview: Lesson 04 Exponential Attenuation MP200 Radiation Physics  2010 Duke Medical Physics Graduate Program 1 Introduction This concept is relevant primarily to uncharged ( photons, neutrons) radiation. Charged particles undergo many small collisions and lose their kinetic energy gradually. Simple Exponential Attenuation Indirectly ionizing radiation incidents on a slab of thickness L . Then, Figure 1: Simple Exponential Attenuation N L = N e μL Scattered and secondary particles may be produced, but are not counted in N L μ = Linear attenuation coefficient Units of μ is cm Definition of μ μ = ( n N ) dx 2 Probability of uncharged particle interactions per unit distance N L N = e μL ( if μL < . 05 ) e μL = 1 μL + ( μL ) 2 2! · = 1 μL Mean free path or Relaxation Length Relaxation length = 1 μ cm It is the average distance a single particle travels through a given medium before interacting. It is also the depth to which a fraction of 1 e (37%) of a large homogeneous beam can penetrate. Exponential Attenuation for Plural Modes of Absorption Assume that each event by each process is totally absorbing producing no scatterings. μ = μ 1 + μ 2 + μ 3 + ··· N L = N e μL = N e ( μ 1 + μ 2 ) L + ··· or N L = N ( e μ 1 L )( e μ 2 L ) ··· Total number of interactions by all types of processes, Δ N = N N L = N N e μL No. of interactions by a single process, Δ N x = ( N N L ) μ x μ = N (1 N e μL ) μ x μ μ x μ = fraction of interactions for process x 3 Example μ 1 = 0 . 02 cm 1 and μ 2 = 0 . 04 cm 1 are partial linear attenuation coeffi cients. If L = 3 cm and N = 10 6 particles, what is N L and how many absorbed in each process in slab? Solution: N L = N e ( μ 1 + μ 2 ) L = 10 6 e (0 . 02+0 . 04)5 = 7 . 408 × 10 5 Total number of particles absorbed is, N N L = (10 6 7 . 408 × 10 5 ) = 2 . 592 × 10 5 The number absorbed by process 1, Δ N 1 = ( N N L ) μ 1 μ = 2 . 592 × 10 5 × . 02 . 06 = 8 . 64 × 10 4 Similarly, by process 2, Δ N 2 = ( N N L ) μ 2 μ = 2 . 592 × 10 5 × . 04 . 06 = 1 . 728 × 10 5 ”Narrow Beam” Attenuation of Uncharged Radiation Consider a beam on uncharged particles on a slab. The scattered and secondary uncharged particles can be counted in N L or not. Figure 2: Narrowbeam geometry. If they are counted, the attenuation equation is invalid and the case is said to be ” broad beam attenuation ”. 4 If scattered or secondary uncharged radiation reaches the detector, but only the pri maries are counted in N L , one has Broad beam geometry but narrow beam attenuation . Then, the attenuation remains valid under these conditions even for real beams of uncharged primary radiation....
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This note was uploaded on 10/30/2010 for the course MP 200 taught by Professor Guna during the Fall '10 term at Duke.
 Fall '10
 Guna

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