## Download Complete Solutions Manual to Radiation Detection and by Glenn F. Knoll PDF

By Glenn F. Knoll

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This limit is achieved later (higher multiplication) with increased electric fields in the detector. Since increased applied voltage implies increased electric field, the pulse height will be larger with higher applied voltages. 4. Voltage for Geiger discharge in tube. To operate in the Geiger region, �n0 �'p � 1 (let's just assume that �n0 �'p = 1 for this problem, since we are interested in finding the minimum voltage for Geiger operation). Since �n0 �' is the number of excited atoms created in an avalanche, and there are 3 excited atoms per ion pair created in an avalanche, then �n0 �'= 3M, where M is the gas multiplication factor (an avalanche is initiated by a single electron, thus M is the number of ion pairs created in an avalanche).

Assume that electrons and ions move with saturated velocities ve and vi . The distance between the negatively charged cathode and positively charged anode is d. Show that the minimum rise time of the resulting pulse occurs when x d � ve and ve �vi is trisemin � d where vtotal vtotal � ve � vi . Solution: Plot trise�� distance to collection�velocity� as a function of interaction position x for both the electrons and ions. The plot will form an "X", with the upper "v" of the "X" shape representing the total charge collection time as a function of x.

E. �Etot 2 � �Eint2 � �Enoise 2 Using this relationship, we want to evaluate �Etot . This is done below, where we solve for �Etot and give the appropriate energy resolution values (in fractions, not percents). 02 to get the expected overal pulse height resolution (expressed as a fraction, not a percent). 10. Solid angle. We use the correct and approximate expressions for a right circular cylinder's solid angle to solve this problem (note that we should get a relatively accurate result using the approximate calculation because, using the same variable meanings as in the textbook, since d=4a then.