Question

5. a) Explain what is meant by the dead-time of a radiation detector and, with the aid of diagrams and equations, distinguish between the non-paralysable and paralysable models. b) Describe one method by which the dead-time of a detector can be measured using two radioactive sources. 12] c) Give one disadvantage of using a two source method for measuring dead-time and also give one practical refinement which may be incorporated into your method to obtain more accurate results. 12] d) Calculate the dead time of a detector in which the count rate from Source A alone is 7000 s1, the count rate from Source B alone is 6500 s and the count rate from both sources together is 13100 s1 You may assume that a non-paralysable model applies and that the background count rate is negligibly small. You may also utilise the fact that, in order to obtain a single value of the expected order of magnitude for the calculated dead time, convention is to use the negative option only in the solution to the quadratic equation. [10]

Answer 1

5 a)

When ionization radiation enters the GM tube through the window and loses its energy by creating electron-ion pairs, the electrons that are produced in the resulting avalanche are accelerated to the anode and collected in a short period of time. The positive ions, however, are more massive and make their way slowly to the cylindrical cathode. If their average transient time is T, the GM tube is busy, so to speak, during T. if another ionizing particle enters the GM tube during T, it will not be counted. This time (T) is called the dead time.

b) A commonly used method for dead time measurements is known as two source method. The method is based on observing the counting rate from two sources individually and in combination. Because the counting losses are nonlinear, the observed rate due to the combined sources will be less than the sum of the rates due to the two sources counted individually, and the dead time can be calculated from the discrepancy.

c) A disadvantage is that the geometry of the experiment should be maintained. The background radiation in all three readings should not fluctuate too much. we can reduce this by being careful about the apparatus set-up and using shields to block background radiation.

d) The two source method requires you to take a total of three readings S₁ (Source 1 alone) , S₂(Source 2 alone) and S₃ (combining the two sources)

$\tau = \frac{X \sqrt{1-Z}}{Y}$

where  

mim2 mbm12

mlm2(772 12+mb)-mb772 12(772 1 + m2) y

and

y(m1 + m2-772 12-772 b)

m1, m2 and m12 represent the corresponding observed rates. Also let nb and mb be the true and measured background rates