Difference between revisions of "LB Feb 2017 Geometric Efficiency Calculations"

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:= <math>\left (1.788 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)=  259596.144 Hz </math> for the 511 keV line
 
:= <math>\left (1.788 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)=  259596.144 Hz </math> for the 511 keV line
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Below is a table where the actual efficiency will be calculated for position R (farthest position).
 

Revision as of 20:29, 4 March 2017

Below are the theoretical calculations for the theoretical decay frequencies


Na-22, 10.19 uCi on July 15, 2013, half life 2.602 +/- 0.002 years, 99.937% for 1274.52 keV line and 178.8 for 511 keV line , activity in Feb 4, 2017 = 3.947 uCi

= [math]\left (0.99937 \right )\left ( 3.947 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,946 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.947 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 261,117.732 Hz [/math] for the 511 keV line

Now compute the expected rate for February 5, 2017.

The activity on Feb 5, 2017 is 3.944 uCi, so the expected rates for the 2 lines are

= [math]\left (0.99937 \right )\left ( 3.944 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,836 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.944 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 260919.264 Hz [/math] for the 511 keV line

Now compute the expected rate for February 9, 2017

The activity on Feb 9, 2017 is 3.933 uCi, so the expected rate for the 2 lines are


= [math]\left (0.99937 \right )\left ( 3.933 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,429.32 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.933 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 260,191.55 Hz [/math] for the 511 keV line

Now compute the expected rate for Feb 12, 2017

The activity on Feb 12, 2017 is 3.924 uCi, so the expected rate for the 2 lines are

= [math]\left (0.99937 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145096.5316 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 259596.144 Hz [/math] for the 511 keV line
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