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This is an occasional series of problem solving exercises of interest to power reactor health physicists. Please send me your comments, as well as suggestions for new problems.

Given: An instantaneous, 1 liter grab sample of containment atmosphere is counted on a gamma spectroscopy system for Kr-89 (half life = 3.15 min). The elapsed time between sampling and the start of counting is 5 minutes. The count time is 10 minutes, with a net count of 5 in the 221 keV photopeak. The overall system efficiency (accounting for photon abundance) for this peak is 0.51%.

Given:

line source: length = 2 meters, total

activity = 1 Ci of Co-60, evenly distributed

Find the dose (exposure) rate at 0.5 m from the center of the source

Given: general kinetics problems, e.g. serial decay, activation, ventilation

Find the general system of differential equations describing these systems, and the solutions.

solution

The equations describing these systems are known as the Bateman equations. The equations and their solutions are described in a

I have described these in more detail at

This is an application of the Bateman equations to a classic problem.

Given: Tc-99m (half life = 6.01 hours) is one of the most commonly used medical radionuclides. Because of its short half life, it is not practical to ship it directly to the user. Rather, its parent, Mo-99 (half life = 65.94 hours) is shipped in a resin column, where the daughter Tc-99m builds up. The Tc-99m is periodically eluted ("milked") from the column for use.

Find: Determine the interval between elutions which will result in the maximum Tc-99m yield.

This is another application of the Bateman equations. Given: Water in the fuel pool at a reactor contains tritium with a concentration of 1 E-2 uCi/liter. This water evaporates into the room above the fuel pool. The water volume is 200 cubic meters. The volume of the room above the fuel pool is 5000 cubic meters. The room ventilation provides 5 air changes per hour. An air sample shows the airborne tritium concentration to be 1 E-10 Curies per cubic meter. Assume: (1) the tritium concentration in the fuel pool stays constant, (2) evaporated water is instantaneously and uniformly distributed in the room, and (3) fuel pool evaporation is the only source of airborne tritium in the room.

Find the fuel pool evaporation rate.

SI Units and Unit Conversions in General - April 3, 2012

Here's a link to a

You are a male RP Technician at an auxiliary control point during a refueling outage. No other RP personnel are present. It takes 15 minutes to reach the main control point.

A female, non-RP supervisor leaving the Radiological Restricted Area (RRA) alarms multiple zones on an exit portal monitor. A survey with a GM "frisker" shows off-scale readings. There are no clothing change facilities nearby. However, female RP Technicians and a decon facility are available at the main control point.

What should you initial actions be?

solution

This is an occasional series of problem solving exercises of interest to power reactor health physicists. Please send me your comments, as well as suggestions for new problems.

**Problem 1 - July 7, 2010**Given: An instantaneous, 1 liter grab sample of containment atmosphere is counted on a gamma spectroscopy system for Kr-89 (half life = 3.15 min). The elapsed time between sampling and the start of counting is 5 minutes. The count time is 10 minutes, with a net count of 5 in the 221 keV photopeak. The overall system efficiency (accounting for photon abundance) for this peak is 0.51%.

__Find__the Kr-89 concentration in containment atmosphere at the time of sampling.__Solution__**Problem 2 - October 13, 2010**Given:

line source: length = 2 meters, total

activity = 1 Ci of Co-60, evenly distributed

Find the dose (exposure) rate at 0.5 m from the center of the source

__Solution__**Problem 3 - April 1, 2011**Given: general kinetics problems, e.g. serial decay, activation, ventilation

Find the general system of differential equations describing these systems, and the solutions.

solution

The equations describing these systems are known as the Bateman equations. The equations and their solutions are described in a

__paper by Dr. Skrable__.I have described these in more detail at

__this link__.**Problem 4 - May 25, 2011**This is an application of the Bateman equations to a classic problem.

Given: Tc-99m (half life = 6.01 hours) is one of the most commonly used medical radionuclides. Because of its short half life, it is not practical to ship it directly to the user. Rather, its parent, Mo-99 (half life = 65.94 hours) is shipped in a resin column, where the daughter Tc-99m builds up. The Tc-99m is periodically eluted ("milked") from the column for use.

Find: Determine the interval between elutions which will result in the maximum Tc-99m yield.

__solution__.**Problem 5 - October 19, 2011**This is another application of the Bateman equations. Given: Water in the fuel pool at a reactor contains tritium with a concentration of 1 E-2 uCi/liter. This water evaporates into the room above the fuel pool. The water volume is 200 cubic meters. The volume of the room above the fuel pool is 5000 cubic meters. The room ventilation provides 5 air changes per hour. An air sample shows the airborne tritium concentration to be 1 E-10 Curies per cubic meter. Assume: (1) the tritium concentration in the fuel pool stays constant, (2) evaporated water is instantaneously and uniformly distributed in the room, and (3) fuel pool evaporation is the only source of airborne tritium in the room.

Find the fuel pool evaporation rate.

__solution__.**Problem 6 - April 3, 2012**SI Units and Unit Conversions in General - April 3, 2012

Here's a link to a

__short presentation__.**Problem 7 - February 16, 2013**You are a male RP Technician at an auxiliary control point during a refueling outage. No other RP personnel are present. It takes 15 minutes to reach the main control point.

A female, non-RP supervisor leaving the Radiological Restricted Area (RRA) alarms multiple zones on an exit portal monitor. A survey with a GM "frisker" shows off-scale readings. There are no clothing change facilities nearby. However, female RP Technicians and a decon facility are available at the main control point.

What should you initial actions be?

solution