1. (10 pts) At an average rate of 100 per second, what fraction of the intervals between randomly occurring events are shorter than 10 ms?
2. (10 pts) A measurement of possible Cs-137 contamination on an air filter is made on a daily basis. The measurement consists of placing the filter on a counting system with an absolute counting efficiency of 15% at 662 keV for a period of 30 min. A new uncontaminated filter is then substituted in the counting system and another 30 min background count recorded. The background count averages 100 counts per minute.
a. Where should the critical level LC be set (in units of counts per 30 min measurement) to declare the positive presence of contamination following the criteria outlined in the MDA discussion?
b. Under these conditions, find the minimum detectable amount (MDA) of Cs-137 on the filter as defined in the same discussion.
3. (10 pts) Counters A and B are nonparalyzable with dead time of 30 and 100 us, respectively. At what true event rate will dead time losses in counter B be twice as great as those from counter A?
4. (10 pts) A paralyzable detector system has a dead time of 1.5 us. If a counting rate of 105 per second is recorded, find the two possible values for the true interaction rate.
5. (10 pts) Sketch both the differential and integral pulse height spectra (using the same horizontal scale) for the following cases:
a. Pulses with single amplitude of 1 V
b. Pulses uniformly distributed in amplitude between 0 and 1 V
c. Pulses distributed around an average amplitude of 1.5 V with a pulse height resolution of 8%