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 4, Problem 4.3P
To determine

To calculate:

The counting rates of 131I and198Au over 16-day period at time t=0, t=3, t=8, t=16 . Also, write the equation of curve for total count rate versus time by plotting graph of daily observation on semi-10 g paper.

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Answer to Problem 4.3P

Counting rates of 131I and198Au are as below:

  DayTotal count rate%  198Au%  131I056.66535332.45248814.63268185.61189

The equation of curve for count rate versus time is:

  A(t)=36.8 e0.257t+219.8 e0.086t

Explanation of Solution

Given Information:

Volume of solution = 1ml

Activity of 198Au =370 Bq

Activity of 131I = 185 Bq

Duration =16 days

Formula used:

  A=(A0e λt)198 Au+(A0e λt)131 I

Graph of count rate versus time is as below:

Introduction To Health Physics, Chapter 4, Problem 4.3P

We know that 198Au emits 99.5% γ of total transformation having half-life = 2.7 days.

While 131I emits at 107% γ of total transformation having half-life = 8.05 days.

  At t=0, For 198Au,370×99.5/100×10/100=36.8 count/secFor 131I,185×107/100×10/100=19.8 count/sec

Thus, total number of counts= 36.8+19.8 =56.6

Hence, ratio of counts at t=0

   For 198Au = 36.8/56.6=0.65=65% For 131I =19.8/56.6=0.35=35%

   At t=3,For 198Au,λ=0.693/2.7=0.257d 1A=A0e λt=36.8×e 0.257×3=17count/sec

Where,

  A0=36.8λ=0.257t=3

For 131I

  λ=0.693/8.05=8.6×102d1A=A0eλt=19.8×e8.6× 10 2×3=15.3count/sec

Where,

  A0=19.8λ=8.6×102t=3

  Thus, total number of count Hence ratio of counts at t=3 Fo r 198 Au=17/32.4 =0.52 =52% Fo r 131 I=15.3/32.4 =0.48 =48%

  At t=8

  For 198Auλ=0.257 d 1A0=36.8t =8

  A=A0eλt=36.8×e0.257×8=4.7 count/sec

  For131I,λ=8.6×102A0=19.8t=8

  A=A0eλt=19.8×e8.6×102×8=9.9 count /sec

  Thus, total number of count =4.7+9.9=14.6Hence, ratio of counts at t=8For 198Au=4.7/14.6=0.32=32%For 131I =9.9/14.6=0.68=68%

  At t=16

   For 198Auλ=0.257A0=36.8t=16

  A=A0eλt= 36.8×e0.257×16=0.60 count/sec

  For 131I,λ=8.6×102A0=19.8t=16

  A=A0eλt=19.8×e8.6×102×16=5count/sec

  Thus, total number of count =0.60+5=5.60Hence, ratio of counts at t=16For 198Au=0.60/5.6=0.11=11% 131Au =5/5.6=0.89=89%

Decay activity of a solution is plotted on graph, by plotting count rate per second over a period of 16 days; we get a curve of total activity as a function of time.

The equation of the curve is a summation of activities of two components 198Au and131I . we have the following data regarding each component:

   A0λ 198Au36.80.257 131I19.80.086

Equation of curve of activity versus time is:

  A= ( A 0 e λt ) 198 Au+ ( A 0 e λt ) 131 IA= 36.8 e 0.257t+19.8 e 0.086t

Conclusion:

We calculate the relation count rates over a period of 16 days for 198Au and131I

    198Au 131IAt t=065%35%At t=352%48%At t=832%68%At t=1611%89%

And the corresponding equation of curve obtained by plotting counting rates per second over a period of 16 days is:

  A=36.8 e0.257t+19.8e0.086t

The equation is the addition of activities of 198Au and131I .

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