Difference between revisions of "Measurements and Calculations (Introduction to Radiochemistry)"

From mn/safe/nukwik
Jump to: navigation, search
(Background)
(Twenty Measurements with Constant Distance from the Source)
 
(10 intermediate revisions by 2 users not shown)
Line 1: Line 1:
<br>
+
<br>  
  
Return to [[Introduction to Radiochemistry - Counting statistics|Main]]
+
Return to [[Introduction to Radiochemistry - Counting statistics|Main]] <br> <br>  
<br>
+
 
<br>
+
Which detector did you use?
  
Which detector did you use?
 
 
==== Background  ====
 
==== Background  ====
  
Note down the values from the background counting you started the day before.<br> Counting number:<br>
+
Note down the values from the background counting you started the day before.<br> Counting number:<br> <math>N_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}</math><br> Counting time:<br><math>t_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{sec}</math><br>
 +
 
 +
Counting speed:<br> <math>\frac{N_{bck}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}</math> <br> Standard deviation:<br> <math>\frac{\sqrt{N_{bck}}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}</math>
 +
 
  
 
==== Counting Efficiency  ====
 
==== Counting Efficiency  ====
Line 16: Line 18:
 
{| cellspacing="1" cellpadding="1" border="1" style="width: 564px; height: 147px;"
 
{| cellspacing="1" cellpadding="1" border="1" style="width: 564px; height: 147px;"
 
|-
 
|-
|  
+
| <br>
| Counting number for each shelf (CPM)  
+
| align="center" | Counting number for each shelf (CPM)  
| Counting Efficency
+
| align="center" | Counting Efficency
 
|-
 
|-
 
| 1  
 
| 1  
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 2  
 
| 2  
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 3  
 
| 3  
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 4  
 
| 4  
|  
+
| <br>
|  
+
| <br>
 
|}
 
|}
 +
  
 
==== Twenty Measurements with Constant Distance from the Source  ====
 
==== Twenty Measurements with Constant Distance from the Source  ====
Line 49: Line 52:
 
|-
 
|-
 
| 1  
 
| 1  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 2  
 
| 2  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 3  
 
| 3  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 4  
 
| 4  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 5  
 
| 5  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 6  
 
| 6  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 7  
 
| 7  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 8  
 
| 8  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 9  
 
| 9  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 10  
 
| 10  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 11  
 
| 11  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 12  
 
| 12  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 13  
 
| 13  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 14  
 
| 14  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 15  
 
| 15  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 16  
 
| 16  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 17  
 
| 17  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 18  
 
| 18  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 19  
 
| 19  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| 20  
 
| 20  
|  
+
| <br>
|  
+
| <br>
|  
+
| <br>
 
|-
 
|-
 
| SUM:  
 
| SUM:  
|  
+
| <br>
 
| SUM:  
 
| SUM:  
|  
+
| <br>
 
|}
 
|}
  
 
<br>  
 
<br>  
  
<br> Mean value of the counting numbers <br> <math>\overline{N}=\frac{\sum N_{P}}{20}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}</math><br> The squere of the mean value <math>\sqrt{\overline{N}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}</math><br> Standard deviation <math>S_{N}=\sqrt{\frac{\left(N_{P}-\overline{N}\right)^{2}}{19}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}</math><br> Discuss the results from <math>S_{N}\,</math>and <math> \sqrt{\overline{N}}</math>?  
+
<br> Mean value of the counting numbers <br> <math>\overline{N}=\frac{\sum N_{P}}{20}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}</math><br> The squere of the mean value <math>\sqrt{\overline{N}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}</math><br> Standard deviation <math>S_{N}=\sqrt{\frac{\sum\left(N_{P}-\overline{N}\right)^{2}}{19}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}</math><br> Discuss the results from <math>S_{N}\,</math>and <math> \sqrt{\overline{N}}</math>?
  
 
==== Assessment of the Results  ====
 
==== Assessment of the Results  ====
<br>
 
<br>
 
<br>
 
Write down the given measurements and calculate how many&nbsp;% of the countings that are outside of the intervals &lt;N-S<sub>N</sub>,N+S<sub>N</sub> and &lt;N-2S<sub>N</sub>,N+2S<sub>N</sub>&gt;:
 
  
{| width="200" cellspacing="1" cellpadding="1" border="1"
+
<br> <br> <br> Write down the given measurements and calculate how many&nbsp;% of the countings that are outside of the intervals &lt;N-S<sub>N</sub>,N+S<sub>N</sub>&gt and &lt;N-2S<sub>N</sub>,N+2S<sub>N</sub>&gt;:
 +
 
 +
{| cellspacing="1" cellpadding="1" border="1" width="200"
 
|-
 
|-
 
| <math>\overline{N}</math>  
 
| <math>\overline{N}</math>  
Line 193: Line 194:
 
|}
 
|}
  
Is there, in your opinion, to many single measurements outside of the given areas? Give a answer based on statistical normal distribution.
+
Is there, in your opinion, to many single measurements outside of the given areas? Give a answer based on statistical normal distribution.  
 +
 
 +
[[Category:Half_life]] [[Category:Natural_activity]] [[Category:Human_Produced_Radioactivity]] [[Category:Laboratory_exercise]] [[Category:Detection]] [[Category:Gamma_Detector]] [[Category:Master]]

Latest revision as of 17:47, 11 November 2013


Return to Main

Which detector did you use?

Background

Note down the values from the background counting you started the day before.
Counting number:
[math]N_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
Counting time:
[math]t_{bck}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{sec}[/math]

Counting speed:
[math]\frac{N_{bck}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}[/math]
Standard deviation:
[math]\frac{\sqrt{N_{bck}}}{t_{bck}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{cps}[/math]


Counting Efficiency

Do a one minute count on every shelf. Use these measurements to calculate the counting-efficiency of the GM-detector in %, for 234mPa. The activity of the sample can be calculated from the amount of UO3 used.


Counting number for each shelf (CPM) Counting Efficency
1

2

3

4


Twenty Measurements with Constant Distance from the Source

Do twenty measurements lasting for one minute with the source in the same position. Calculate the standard deviation and complete the table:

Nr [math]N_{P}\,[/math] [math]N_{P}-\overline{N}[/math] [math]\left(N_{P}-\overline{N}\right)^{2}[/math]
1


2


3


4


5


6


7


8


9


10


11


12


13


14


15


16


17


18


19


20


SUM:
SUM:



Mean value of the counting numbers
[math]\overline{N}=\frac{\sum N_{P}}{20}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
The squere of the mean value [math]\sqrt{\overline{N}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\mbox{counts}[/math]
Standard deviation [math]S_{N}=\sqrt{\frac{\sum\left(N_{P}-\overline{N}\right)^{2}}{19}}=\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}[/math]
Discuss the results from [math]S_{N}\,[/math]and [math] \sqrt{\overline{N}}[/math]?

Assessment of the Results




Write down the given measurements and calculate how many % of the countings that are outside of the intervals <N-SN,N+SN&gt and <N-2SN,N+2SN>:

[math]\overline{N}[/math] [math]\sqrt{\overline{N}}[/math] [math]N\pm S_{N}[/math] [math]N\pm 2S_{N}[/math]









Is there, in your opinion, to many single measurements outside of the given areas? Give a answer based on statistical normal distribution.