Introduction To Health Physics
Introduction To Health Physics
5th Edition
ISBN: 9780071835275
Author: Johnson, Thomas E. (thomas Edward), Cember, Herman.
Publisher: Mcgraw-hill Education,
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Chapter 9, Problem 9.14P

A counting system has a background of 360 counts during a 20-minute counting period. What is the lower limit of detection with this system for counting times of
(a) 2 minutes?
(b) 20 minutes?
(c) 200 minutes?

(a)

Expert Solution
Check Mark
To determine

Lower limit of detection for counting times of 2 min

Answer to Problem 9.14P

Lower limit detection is 24 cpm.

Explanation of Solution

Given:

Time during which gross count was made, tg=2min

Background count, nb=360counts

Time during which background count was made, tb=20min

Formula used:

Background counting rate, rb=nbtb

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

Calculation:

Background counting rate, rb=nbtb=36020=18cpm

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

  LLD=3.29×( 18  counts  min )×2min×( 1+ 2min 20min )+32min=12cpm

Conclusion:

Lower limit detection is 12 cpm.

(b)

Expert Solution
Check Mark
To determine

Lower limit of detection for counting times of 20 min

Answer to Problem 9.14P

Lower limit detection is 4.6 cpm.

Explanation of Solution

Given:

Time during which gross count was made, tg=20min

Background count, nb=360counts

Time during which background count was made, tb=20min

Formula used:

Background counting rate, rb=nbtb

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

Calculation:

Background counting rate, rb=nbtg=36020=18cpm

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

  LLD=3.29×( 18  counts  min )×20min×( 1+ 20min 20min )+320min=4.6cpm

Conclusion: Lower limit detection is 4.6 cpm.

(c)

Expert Solution
Check Mark
To determine

Lower limit of detection for counting times of 200 min

Answer to Problem 9.14P

Lower limit detection is 658 cpm.

Explanation of Solution

Given:

Time during which gross count was made, tg=200min

Background count, nb=360counts

Time during which background count was made, tb=20min

Formula used:

Background counting rate, rb=nbtb

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

Calculation:

Background counting rate, rb=nbtb=36020=18cpm

Lower limit of detection, LLD=3.29rbtg( 1+ t g t b )+3tg

  LLD=3.29×( 18  counts  min )×200min×( 1+ 200min 20min )+3200min=3.3cpm

Conclusion:

Lower limit detection is 3.3 cpm.

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